Daily Papers

Many recent works have explored using language models for planning problems. One line of research focuses on translating natural language descriptions of planning tasks into structured planning languages, such as the planning domain definition language (PDDL). While this approach is promising, accurately measuring the quality of generated PDDL code continues to pose significant challenges. First, generated PDDL code is typically evaluated using planning validators that check whether the problem can be solved with a planner. This method is insufficient because a language model might generate valid PDDL code that does not align with the natural language description of the task. Second, existing evaluation sets often have natural language descriptions of the planning task that closely resemble the ground truth PDDL, reducing the challenge of the task. To bridge this gap, we introduce \benchmarkName, a benchmark designed to evaluate language models' ability to generate PDDL code from natural language descriptions of planning tasks. We begin by creating a PDDL equivalence algorithm that rigorously evaluates the correctness of PDDL code generated by language models by flexibly comparing it against a ground truth PDDL. Then, we present a dataset of 132,037 text-to-PDDL pairs across 13 different tasks, with varying levels of difficulty. Finally, we evaluate several API-access and open-weight language models that reveal this task's complexity. For example, 87.6% of the PDDL problem descriptions generated by GPT-4o are syntactically parseable, 82.2% are valid, solve-able problems, but only 35.1% are semantically correct, highlighting the need for a more rigorous benchmark for this problem.

Solving complex planning problems requires Large Language Models (LLMs) to explicitly model the state transition to avoid rule violations, comply with constraints, and ensure optimality-a task hindered by the inherent ambiguity of natural language. To overcome such ambiguity, Planning Domain Definition Language (PDDL) is leveraged as a planning abstraction that enables precise and formal state descriptions. With PDDL, we can generate a symbolic world model where classic searching algorithms, such as A*, can be seamlessly applied to find optimal plans. However, directly generating PDDL domains with current LLMs remains an open challenge due to the lack of PDDL training data. To address this challenge, we propose to scale up the test-time computation of LLMs to enhance their PDDL reasoning capabilities, thereby enabling the generation of high-quality PDDL domains. Specifically, we introduce a simple yet effective algorithm, which first employs a Best-of-N sampling approach to improve the quality of the initial solution and then refines the solution in a fine-grained manner with verbalized machine learning. Our method outperforms o1-mini by a considerable margin in the generation of PDDL domain, achieving over 50% success rate on two tasks (i.e., generating PDDL domains from natural language description or PDDL problems). This is done without requiring additional training. By taking advantage of PDDL as state abstraction, our method is able to outperform current state-of-the-art methods on almost all competition-level planning tasks.

A fundamental problem in combinatorial optimization is identifying equivalent formulations, which can lead to more efficient solution strategies and deeper insights into a problem's computational complexity. The need to automatically identify equivalence between problem formulations has grown as optimization copilots--systems that generate problem formulations from natural language descriptions--have proliferated. However, existing approaches to checking formulation equivalence lack grounding, relying on simple heuristics which are insufficient for rigorous validation. Inspired by Karp reductions, in this work we introduce quasi-Karp equivalence, a formal criterion for determining when two optimization formulations are equivalent based on the existence of a mapping between their decision variables. We propose EquivaMap, a framework that leverages large language models to automatically discover such mappings, enabling scalable and reliable equivalence verification. To evaluate our approach, we construct the first open-source dataset of equivalent optimization formulations, generated by applying transformations such as adding slack variables or valid inequalities to existing formulations. Empirically, EquivaMap significantly outperforms existing methods, achieving substantial improvements in correctly identifying formulation equivalence.

Pre-trained large language model (LLM) is under exploration to perform NLP tasks that may require logical reasoning. Logic-driven data augmentation for representation learning has been shown to improve the performance of tasks requiring logical reasoning, but most of these data rely on designed templates and therefore lack generalization. In this regard, we propose an AMR-based logical equivalence-driven data augmentation method (AMR-LE) for generating logically equivalent data. Specifically, we first parse a text into the form of an AMR graph, next apply four logical equivalence laws (contraposition, double negation, commutative and implication laws) on the AMR graph to construct a logically equivalent/inequivalent AMR graph, and then convert it into a logically equivalent/inequivalent sentence. To help the model to better learn these logical equivalence laws, we propose a logical equivalence-driven contrastive learning training paradigm, which aims to distinguish the difference between logical equivalence and inequivalence. Our AMR-LE (Ensemble) achieves #2 on the ReClor leaderboard https://eval.ai/web/challenges/challenge-page/503/leaderboard/1347 . Our model shows better performance on seven downstream tasks, including ReClor, LogiQA, MNLI, MRPC, RTE, QNLI, and QQP. The source code and dataset are public at https://github.com/Strong-AI-Lab/Logical-Equivalence-driven-AMR-Data-Augmentation-for-Representation-Learning .

There is a growing interest in applying pre-trained large language models (LLMs) to planning problems. However, methods that use LLMs directly as planners are currently impractical due to several factors, including limited correctness of plans, strong reliance on feedback from interactions with simulators or even the actual environment, and the inefficiency in utilizing human feedback. In this work, we introduce a novel alternative paradigm that constructs an explicit world (domain) model in planning domain definition language (PDDL) and then uses it to plan with sound domain-independent planners. To address the fact that LLMs may not generate a fully functional PDDL model initially, we employ LLMs as an interface between PDDL and sources of corrective feedback, such as PDDL validators and humans. For users who lack a background in PDDL, we show that LLMs can translate PDDL into natural language and effectively encode corrective feedback back to the underlying domain model. Our framework not only enjoys the correctness guarantee offered by the external planners but also reduces human involvement by allowing users to correct domain models at the beginning, rather than inspecting and correcting (through interactive prompting) every generated plan as in previous work. On two IPC domains and a Household domain that is more complicated than commonly used benchmarks such as ALFWorld, we demonstrate that GPT-4 can be leveraged to produce high-quality PDDL models for over 40 actions, and the corrected PDDL models are then used to successfully solve 48 challenging planning tasks. Resources including the source code will be released at: https://guansuns.github.io/pages/llm-dm.

Large Language Models (LLMs) are capable of transforming natural language domain descriptions into plausibly looking PDDL markup. However, ensuring that actions are consistent within domains still remains a challenging task. In this paper we present a novel concept to significantly improve the quality of LLM-generated PDDL models by performing automated consistency checking during the generation process. Although the proposed consistency checking strategies still can't guarantee absolute correctness of generated models, they can serve as valuable source of feedback reducing the amount of correction efforts expected from a human in the loop. We demonstrate the capabilities of our error detection approach on a number of classical and custom planning domains (logistics, gripper, tyreworld, household, pizza).

Ensuring alignment of language models' outputs with human preferences is critical to guarantee a useful, safe, and pleasant user experience. Thus, human alignment has been extensively studied recently and several methods such as Reinforcement Learning from Human Feedback (RLHF), Direct Policy Optimisation (DPO) and Sequence Likelihood Calibration (SLiC) have emerged. In this paper, our contribution is two-fold. First, we show the equivalence between two recent alignment methods, namely Identity Policy Optimisation (IPO) and Nash Mirror Descent (Nash-MD). Second, we introduce a generalisation of IPO, named IPO-MD, that leverages the regularised sampling approach proposed by Nash-MD. This equivalence may seem surprising at first sight, since IPO is an offline method whereas Nash-MD is an online method using a preference model. However, this equivalence can be proven when we consider the online version of IPO, that is when both generations are sampled by the online policy and annotated by a trained preference model. Optimising the IPO loss with such a stream of data becomes then equivalent to finding the Nash equilibrium of the preference model through self-play. Building on this equivalence, we introduce the IPO-MD algorithm that generates data with a mixture policy (between the online and reference policy) similarly as the general Nash-MD algorithm. We compare online-IPO and IPO-MD to different online versions of existing losses on preference data such as DPO and SLiC on a summarisation task.

Despite significant advancements in large language models (LLMs) that enhance robot agents' understanding and execution of natural language (NL) commands, ensuring the agents adhere to user-specified constraints remains challenging, particularly for complex commands and long-horizon tasks. To address this challenge, we present three key insights, equivalence voting, constrained decoding, and domain-specific fine-tuning, which significantly enhance LLM planners' capability in handling complex tasks. Equivalence voting ensures consistency by generating and sampling multiple Linear Temporal Logic (LTL) formulas from NL commands, grouping equivalent LTL formulas, and selecting the majority group of formulas as the final LTL formula. Constrained decoding then uses the generated LTL formula to enforce the autoregressive inference of plans, ensuring the generated plans conform to the LTL. Domain-specific fine-tuning customizes LLMs to produce safe and efficient plans within specific task domains. Our approach, Safe Efficient LLM Planner (SELP), combines these insights to create LLM planners to generate plans adhering to user commands with high confidence. We demonstrate the effectiveness and generalizability of SELP across different robot agents and tasks, including drone navigation and robot manipulation. For drone navigation tasks, SELP outperforms state-of-the-art planners by 10.8% in safety rate (i.e., finishing tasks conforming to NL commands) and by 19.8% in plan efficiency. For robot manipulation tasks, SELP achieves 20.4% improvement in safety rate. Our datasets for evaluating NL-to-LTL and robot task planning will be released in github.com/lt-asset/selp.

Today's classical planners are powerful, but modeling input tasks in formats such as PDDL is tedious and error-prone. In contrast, planning with Large Language Models (LLMs) allows for almost any input text, but offers no guarantees on plan quality or even soundness. In an attempt to merge the best of these two approaches, some work has begun to use LLMs to automate parts of the PDDL creation process. However, these methods still require various degrees of expert input. We present NL2Plan, the first domain-agnostic offline LLM-driven planning system. NL2Plan uses an LLM to incrementally extract the necessary information from a short text prompt before creating a complete PDDL description of both the domain and the problem, which is finally solved by a classical planner. We evaluate NL2Plan on four planning domains and find that it solves 10 out of 15 tasks - a clear improvement over a plain chain-of-thought reasoning LLM approach, which only solves 2 tasks. Moreover, in two out of the five failure cases, instead of returning an invalid plan, NL2Plan reports that it failed to solve the task. In addition to using NL2Plan in end-to-end mode, users can inspect and correct all of its intermediate results, such as the PDDL representation, increasing explainability and making it an assistive tool for PDDL creation.

Quantizing the weights of large language models (LLMs) from 16-bit to lower bitwidth is the de facto approach to deploy massive transformers onto more affordable accelerators. GPTQ emerged as one of the standard methods for one-shot post-training quantization at LLM scale. Yet, its inner workings are described as a sequence of ad-hoc algebraic updates that obscure any geometric meaning or worst-case guarantees. In this work, we show that, when executed back-to-front (from the last to first dimension) for a linear layer, GPTQ is mathematically identical to Babai's nearest plane algorithm for the classical closest vector problem (CVP) on a lattice defined by the Hessian matrix of the layer's inputs. This equivalence is based on a sophisticated mathematical argument, and has two analytical consequences: (i) the GPTQ error propagation step gains an intuitive geometric interpretation; (ii) GPTQ inherits the error upper bound of Babai's algorithm under the no-clipping condition. Taken together, these results place GPTQ on firm theoretical footing and open the door to importing decades of progress in lattice algorithms towards the design of future quantization algorithms for billion-parameter models.

Despite the rapid development of large language models (LLMs), a fundamental challenge persists: the lack of high-quality optimization modeling datasets hampers LLMs' robust modeling of practical optimization problems from natural language descriptions (NL). This data scarcity also contributes to the generalization difficulties experienced by learning-based methods. To address these challenges, we propose a scalable framework for synthesizing a high-quality dataset, named OptMATH. Starting from curated seed data with mathematical formulations (MF), this framework automatically generates problem data (PD) with controllable complexity. Then, a back-translation step is employed to obtain NL. To verify the correspondence between the NL and the PD, a forward modeling step followed by rejection sampling is used. The accepted pairs constitute the training part of OptMATH. Then a collection of rejected pairs is identified and further filtered. This collection serves as a new benchmark for optimization modeling, containing difficult instances whose lengths are much longer than these of NL4OPT and MAMO. Through extensive experiments, we demonstrate that models of various sizes (0.5B-32B parameters) trained on OptMATH achieve superior results on multiple modeling benchmarks, thereby validating the effectiveness and scalability of our approach. Our dataset is publicly available at https://github.com/AuroraLHL/OptMATH.

Extensive LLM applications demand efficient structured generations, particularly for LR(1) grammars, to produce outputs in specified formats (e.g., JSON). Existing methods primarily parse LR(1) grammars into a pushdown automaton (PDA), leading to runtime execution overhead for context-dependent token processing, especially inefficient under large inference batches. To address these issues, we propose Pre^3 that exploits deterministic pushdown automata (DPDA) to optimize the constrained LLM decoding efficiency. First, by precomputing prefix-conditioned edges during the preprocessing, Pre^3 enables ahead-of-time edge analysis and thus makes parallel transition processing possible. Second, by leveraging the prefix-conditioned edges, Pre^3 introduces a novel approach that transforms LR(1) transition graphs into DPDA, eliminating the need for runtime path exploration and achieving edge transitions with minimal overhead. Pre^3 can be seamlessly integrated into standard LLM inference frameworks, reducing time per output token (TPOT) by up to 40% and increasing throughput by up to 36% in our experiments. Our code is available at https://github.com/ModelTC/lightllm.

Large language models (LLMs) have demonstrated remarkable zero-shot generalization abilities: state-of-the-art chatbots can provide plausible answers to many common questions that arise in daily life. However, so far, LLMs cannot reliably solve long-horizon planning problems. By contrast, classical planners, once a problem is given in a formatted way, can use efficient search algorithms to quickly identify correct, or even optimal, plans. In an effort to get the best of both worlds, this paper introduces LLM+P, the first framework that incorporates the strengths of classical planners into LLMs. LLM+P takes in a natural language description of a planning problem, then returns a correct (or optimal) plan for solving that problem in natural language. LLM+P does so by first converting the language description into a file written in the planning domain definition language (PDDL), then leveraging classical planners to quickly find a solution, and then translating the found solution back into natural language. Along with LLM+P, we define a diverse set of different benchmark problems taken from common planning scenarios. Via a comprehensive set of experiments on these benchmark problems, we find that LLM+P is able to provide optimal solutions for most problems, while LLMs fail to provide even feasible plans for most problems.\footnote{The code and results are publicly available at https://github.com/Cranial-XIX/llm-pddl.git.

Large Language Models have been shown to fail to create executable and verifiable plans in grounded environments. An emerging line of work shows success in using LLM as a formalizer to generate a formal representation (e.g., PDDL) of the planning domain, which can be deterministically solved to find a plan. We systematically evaluate this methodology while bridging some major gaps. While previous work only generates a partial PDDL representation given templated and thus unrealistic environment descriptions, we generate the complete representation given descriptions of various naturalness levels. Among an array of observations critical to improve LLMs' formal planning ability, we note that large enough models can effectively formalize descriptions as PDDL, outperforming those directly generating plans, while being robust to lexical perturbation. As the descriptions become more natural-sounding, we observe a decrease in performance and provide detailed error analysis.

Large language models (LLMs) have demonstrated impressive capabilities across diverse tasks, yet their ability to perform structured symbolic planning remains limited, particularly in domains requiring formal representations like the Planning Domain Definition Language (PDDL). In this paper, we present a novel instruction tuning framework, PDDL-Instruct, designed to enhance LLMs' symbolic planning capabilities through logical chain-of-thought reasoning. Our approach focuses on teaching models to rigorously reason about action applicability, state transitions, and plan validity using explicit logical inference steps. By developing instruction prompts that guide models through the precise logical reasoning required to determine when actions can be applied in a given state, we enable LLMs to self-correct their planning processes through structured reflection. The framework systematically builds verification skills by decomposing the planning process into explicit reasoning chains about precondition satisfaction, effect application, and invariant preservation. Experimental results on multiple planning domains show that our chain-of-thought reasoning based instruction-tuned models are significantly better at planning, achieving planning accuracy of up to 94% on standard benchmarks, representing a 66% absolute improvement over baseline models. This work bridges the gap between the general reasoning capabilities of LLMs and the logical precision required for automated planning, offering a promising direction for developing better AI planning systems.

Optimizing Register Transfer Level (RTL) code is crucial for improving the power, performance, and area (PPA) of digital circuits in the early stages of synthesis. Manual rewriting, guided by synthesis feedback, can yield high-quality results but is time-consuming and error-prone. Most existing compiler-based approaches have difficulty handling complex design constraints. Large Language Model (LLM)-based methods have emerged as a promising alternative to address these challenges. However, LLM-based approaches often face difficulties in ensuring alignment between the generated code and the provided prompts. This paper presents SymRTLO, a novel neuron-symbolic RTL optimization framework that seamlessly integrates LLM-based code rewriting with symbolic reasoning techniques. Our method incorporates a retrieval-augmented generation (RAG) system of optimization rules and Abstract Syntax Tree (AST)-based templates, enabling LLM-based rewriting that maintains syntactic correctness while minimizing undesired circuit behaviors. A symbolic module is proposed for analyzing and optimizing finite state machine (FSM) logic, allowing fine-grained state merging and partial specification handling beyond the scope of pattern-based compilers. Furthermore, a fast verification pipeline, combining formal equivalence checks with test-driven validation, further reduces the complexity of verification. Experiments on the RTL-Rewriter benchmark with Synopsys Design Compiler and Yosys show that SymRTLO improves power, performance, and area (PPA) by up to 43.9%, 62.5%, and 51.1%, respectively, compared to the state-of-the-art methods.

We present Generative Logic (GL), a deterministic architecture that begins from user-supplied axiomatic definitions -- written in a minimalist Mathematical Programming Language (MPL) -- and systematically explores their deductive neighborhood. Definitions are compiled into a distributed grid of simple Logic Blocks (LBs) that exchange messages; any time several expressions unify under an inference rule, a new fact is emitted with full provenance to its sources, yielding replayable, auditable proof graphs. A prototype software implementation instantiates the workflow on first-order Peano arithmetic. Starting only from the Peano axioms, GL enumerates candidate implications, applies normalization and type filters, and automatically reconstructs machine-checkable proofs of foundational arithmetic laws including associativity and commutativity of addition, associativity and commutativity of multiplication, and distributivity. Generated proofs export to navigable HTML so that every inference step can be inspected independently. We outline a hardware-software co-design path toward massively parallel realizations and describe prospective integration with probabilistic models (e.g., Large Language Models (LLMs)) for autoformalization and conjecture seeding. The Python and MPL code to reproduce the Peano experiments, along with the full HTML proof graphs, are available in the project's GitHub repository at https://github.com/Generative-Logic/GL/tree/35a111ea9ba53afe051703d6050be0c3923e9724 and are permanently archived at https://doi.org/10.5281/zenodo.16408441. We invite community feedback and collaboration.

We propose a general two-stage algorithm that enjoys a provable scaling law for the test-time compute of large language models (LLMs). Given an input problem, the proposed algorithm first generates N candidate solutions, and then chooses the best one via a multiple-round knockout tournament where each pair of candidates are compared for K times and only the winners move on to the next round. In a minimalistic implementation, both stages can be executed with a black-box LLM alone and nothing else (e.g., no external verifier or reward model), and a total of N times (K + 1) highly parallelizable LLM calls are needed for solving an input problem. Assuming that a generated candidate solution is correct with probability p_{gen} > 0 and a comparison between a pair of correct and incorrect solutions identifies the right winner with probability p_{comp} > 0.5 (i.e., better than a random guess), we prove theoretically that the failure probability of the proposed algorithm decays to zero exponentially with respect to N and K: $P(final output is incorrect) le (1 - p_{gen})^N + lceil log_2 N rceil e^{-2 K (p_{comp} - 0.5)^2}.$ Our empirical results with the challenging MMLU-Pro benchmark validate the technical assumptions, as well as the efficacy of the proposed algorithm and the gains from scaling up its test-time compute.

Recent availability of Large Language Models (LLMs) has led to the development of numerous LLM-based approaches aimed at providing natural language interfaces for various end-user tasks. These end-user tasks in turn can typically be accomplished by orchestrating a given set of APIs. In practice, natural language task requests (user queries) are often incomplete, i.e., they may not contain all the information required by the APIs. While LLMs excel at natural language processing (NLP) tasks, they frequently hallucinate on missing information or struggle with orchestrating the APIs. The key idea behind our proposed approach is to leverage logical reasoning and classical AI planning along with an LLM for accurately answering user queries including identification and gathering of any missing information in these queries. Our approach uses an LLM and ASP (Answer Set Programming) solver to translate a user query to a representation in Planning Domain Definition Language (PDDL) via an intermediate representation in ASP. We introduce a special API "get_info_api" for gathering missing information. We model all the APIs as PDDL actions in a way that supports dataflow between the APIs. Our approach then uses a classical AI planner to generate an orchestration of API calls (including calls to get_info_api) to answer the user query. Our evaluation results show that our approach significantly outperforms a pure LLM based approach by achieving over 95\% success rate in most cases on a dataset containing complete and incomplete single goal and multi-goal queries where the multi-goal queries may or may not require dataflow among the APIs.

We present a complete formalization in Isabelle/HOL of the object part of an equivalence between L-mosaics and bounded join-semilattices, employing an AI-assisted methodology that integrates large language models as reasoning assistants throughout the proof development process. The equivalence was originally established by Cangiotti, Linzi, and Talotti in their study of hypercompositional structures related to orthomodular lattices and quantum logic. Our formalization rigorously verifies the main theoretical result and demonstrates the mutual inverse property of the transformations establishing this equivalence. The development showcases both the mathematical depth of multivalued algebraic operations and the potential for AI-enhanced interactive theorem proving in tackling complex formalization projects.

Large Language Models (LLMs) excel at complex reasoning through search algorithms, yet current strategies often suffer from massive token consumption due to redundant exploration of semantically equivalent steps. Existing semantic similarity methods struggle to accurately identify such equivalence in domain-specific contexts like mathematical reasoning. To address this, we propose EquivPruner, a simple yet effective approach that identifies and prunes semantically equivalent actions during LLM reasoning search. We also introduce MathEquiv, the first dataset we created for mathematical statement equivalence, which enables the training of a lightweight equivalence detector. Extensive experiments across various models and tasks demonstrate that EquivPruner significantly reduces token consumption, improving searching efficiency and often bolstering reasoning accuracy. For instance, when applied to Qwen2.5-Math-7B-Instruct on GSM8K, EquivPruner reduced token consumption by 48.1\% while also improving accuracy. Our code is available at https://github.com/Lolo1222/EquivPruner.

We propose FlowRL: matching the full reward distribution via flow balancing instead of maximizing rewards in large language model (LLM) reinforcement learning (RL). Recent advanced reasoning models adopt reward-maximizing methods (\eg, PPO and GRPO), which tend to over-optimize dominant reward signals while neglecting less frequent but valid reasoning paths, thus reducing diversity. In contrast, we transform scalar rewards into a normalized target distribution using a learnable partition function, and then minimize the reverse KL divergence between the policy and the target distribution. We implement this idea as a flow-balanced optimization method that promotes diverse exploration and generalizable reasoning trajectories. We conduct experiments on math and code reasoning tasks: FlowRL achieves a significant average improvement of 10.0% over GRPO and 5.1% over PPO on math benchmarks, and performs consistently better on code reasoning tasks. These results highlight reward distribution-matching as a key step toward efficient exploration and diverse reasoning in LLM reinforcement learning.

The last year has witnessed the rapid progress of large language models (LLMs) across diverse domains. Among them, CodeLLMs have garnered particular attention because they can not only assist in completing various programming tasks but also represent the decision-making and logical reasoning capabilities of LLMs. However, current CodeLLMs mainly focus on pre-training and supervised fine-tuning scenarios, leaving the alignment stage, which is important for post-training LLMs, under-explored. This work first identifies that the commonly used PPO algorithm may be suboptimal for the alignment of CodeLLM because the involved reward rules are routinely coarse-grained and potentially flawed. We then advocate addressing this using the DPO algorithm. Based on only preference data pairs, DPO can render the model rank data automatically, giving rise to a fine-grained rewarding pattern more robust than human intervention. We also contribute a pipeline for collecting preference pairs for DPO on CodeLLMs. Studies show that our method significantly improves the performance of existing CodeLLMs on benchmarks such as MBPP and HumanEval.

We present a novel approach to formalise and solve search-based problems using large language models, which significantly improves upon previous state-of-the-art results. We demonstrate the efficacy of this approach on the logic puzzles benchmark ZebraLogicBench. Instead of letting the LLM attempt to directly solve the puzzles, our method prompts the model to formalise the problem in a logic-focused domain-specific language (DSL) called Logic.py. This formalised representation is then solved using a constraint solver, leveraging the strengths of both the language model and the solver. Our approach achieves a remarkable 65% absolute improvement over the baseline performance of Llama 3.1 70B on ZebraLogicBench, setting a new state-of-the-art with an accuracy of over 90%. This significant advancement demonstrates the potential of combining language models with domain-specific languages and auxiliary tools on traditionally challenging tasks for LLMs.

Large language models (LLMs) trained via reinforcement learning with verifiable reward (RLVR) have achieved breakthroughs on tasks with explicit, automatable verification, such as software programming and mathematical problems. Extending RLVR to electronic design automation (EDA), especially automatically generating hardware description languages (HDLs) like Verilog from natural-language (NL) specifications, however, poses three key challenges: the lack of automated and accurate verification environments, the scarcity of high-quality NL-code pairs, and the prohibitive computation cost of RLVR. To this end, we introduce CodeV-R1, an RLVR framework for training Verilog generation LLMs. First, we develop a rule-based testbench generator that performs robust equivalence checking against golden references. Second, we propose a round-trip data synthesis method that pairs open-source Verilog snippets with LLM-generated NL descriptions, verifies code-NL-code consistency via the generated testbench, and filters out inequivalent examples to yield a high-quality dataset. Third, we employ a two-stage "distill-then-RL" training pipeline: distillation for the cold start of reasoning abilities, followed by adaptive DAPO, our novel RLVR algorithm that can reduce training cost by adaptively adjusting sampling rate. The resulting model, CodeV-R1-7B, achieves 68.6% and 72.9% pass@1 on VerilogEval v2 and RTLLM v1.1, respectively, surpassing prior state-of-the-art by 12~20%, while matching or even exceeding the performance of 671B DeepSeek-R1. We will release our model, training pipeline, and dataset to facilitate research in EDA and LLM communities.

Let p denote a generative language model. Let r denote a reward model that returns a scalar that captures the degree at which a draw from p is preferred. The goal of language model alignment is to alter p to a new distribution phi that results in a higher expected reward while keeping phi close to p. A popular alignment method is the KL-constrained reinforcement learning (RL), which chooses a distribution phi_Delta that maximizes E_{phi_{Delta}} r(y) subject to a relative entropy constraint KL(phi_Delta || p) leq Delta. Another simple alignment method is best-of-N, where N samples are drawn from p and one with highest reward is selected. In this paper, we offer a closed-form characterization of the optimal KL-constrained RL solution. We demonstrate that any alignment method that achieves a comparable trade-off between KL divergence and reward must approximate the optimal KL-constrained RL solution in terms of relative entropy. To further analyze the properties of alignment methods, we introduce two simplifying assumptions: we let the language model be memoryless, and the reward model be linear. Although these assumptions may not reflect complex real-world scenarios, they enable a precise characterization of the asymptotic behavior of both the best-of-N alignment, and the KL-constrained RL method, in terms of information-theoretic quantities. We prove that the reward of the optimal KL-constrained RL solution satisfies a large deviation principle, and we fully characterize its rate function. We also show that the rate of growth of the scaled cumulants of the reward is characterized by a proper Renyi cross entropy. Finally, we show that best-of-N is asymptotically equivalent to KL-constrained RL solution by proving that their expected rewards are asymptotically equal, and concluding that the two distributions must be close in KL divergence.

Large language models (LLMs) achieve remarkable performance in code generation tasks. However, a significant performance disparity persists between popular programming languages (e.g., Python, C++) and others. To address this capability gap, we leverage the code translation task to train LLMs, thereby facilitating the transfer of coding proficiency across diverse programming languages. Moreover, we introduce OORL for training, a novel reinforcement learning (RL) framework that integrates on-policy and off-policy strategies. Within OORL, on-policy RL is applied during code translation, guided by a rule-based reward signal derived from unit tests. Complementing this coarse-grained rule-based reward, we propose Group Equivalent Preference Optimization (GEPO), a novel preference optimization method. Specifically, GEPO trains the LLM using intermediate representations (IRs) groups. LLMs can be guided to discern IRs equivalent to the source code from inequivalent ones, while also utilizing signals about the mutual equivalence between IRs within the group. This process allows LLMs to capture nuanced aspects of code functionality. By employing OORL for training with code translation tasks, LLMs improve their recognition of code functionality and their understanding of the relationships between code implemented in different languages. Extensive experiments demonstrate that our OORL for LLMs training with code translation tasks achieves significant performance improvements on code benchmarks across multiple programming languages.

Implementing Boolean functions with circuits consisting of logic gates is fundamental in digital computer design. However, the implemented circuit must be exactly equivalent, which hinders generative neural approaches on this task due to their occasionally wrong predictions. In this study, we introduce a generative neural model, the "Circuit Transformer", which eliminates such wrong predictions and produces logic circuits strictly equivalent to given Boolean functions. The main idea is a carefully designed decoding mechanism that builds a circuit step-by-step by generating tokens, which has beneficial "cutoff properties" that block a candidate token once it invalidate equivalence. In such a way, the proposed model works similar to typical LLMs while logical equivalence is strictly preserved. A Markov decision process formulation is also proposed for optimizing certain objectives of circuits. Experimentally, we trained an 88-million-parameter Circuit Transformer to generate equivalent yet more compact forms of input circuits, outperforming existing neural approaches on both synthetic and real world benchmarks, without any violation of equivalence constraints.

Parallel scaling has emerged as a powerful paradigm to enhance reasoning capabilities in large language models (LLMs) by generating multiple Chain-of-Thought (CoT) traces simultaneously. However, this approach introduces significant computational inefficiency due to inter-trace redundancy -- our analysis reveals that over 80% of parallel reasoning traces yield identical final answers, representing substantial wasted computation. To address this critical efficiency bottleneck, we propose DeepPrune, a novel framework that enables efficient parallel scaling through dynamic pruning. Our method features a specialized judge model trained with focal loss and oversampling techniques to accurately predict answer equivalence from partial reasoning traces which realizes 0.87 AUROC on equivalence prediction, combined with an online greedy clustering algorithm that dynamically prunes redundant paths while preserving answer diversity. Comprehensive evaluations across three challenging benchmarks (AIME 2024, AIME 2025, and GPQA) and multiple reasoning models demonstrate that DeepPrune achieves remarkable token reduction by over 80% compared to conventional consensus sampling on most cases, while maintaining competitive accuracy within 3 percentage points. Our work establishes a new standard for efficient parallel reasoning, making high-performance reasoning more efficient. Our code and data are here: https://deepprune.github.io/

In recent years, a variety of gradient-based first-order methods have been developed to solve bi-level optimization problems for learning applications. However, theoretical guarantees of these existing approaches heavily rely on the simplification that for each fixed upper-level variable, the lower-level solution must be a singleton (a.k.a., Lower-Level Singleton, LLS). In this work, we first design a counter-example to illustrate the invalidation of such LLS condition. Then by formulating BLPs from the view point of optimistic bi-level and aggregating hierarchical objective information, we establish Bi-level Descent Aggregation (BDA), a flexible and modularized algorithmic framework for generic bi-level optimization. Theoretically, we derive a new methodology to prove the convergence of BDA without the LLS condition. Our investigations also demonstrate that BDA is indeed compatible to a verify of particular first-order computation modules. Additionally, as an interesting byproduct, we also improve these conventional first-order bi-level schemes (under the LLS simplification). Particularly, we establish their convergences with weaker assumptions. Extensive experiments justify our theoretical results and demonstrate the superiority of the proposed BDA for different tasks, including hyper-parameter optimization and meta learning.

Large Language Models (LLMs) can acquire extensive world knowledge through pre-training on large corpora. However, due to exposure to low-quality data, LLMs may exhibit harmful behavior without aligning with human values. The dominant approach for steering LLMs towards beneficial behavior involves Reinforcement Learning with Human Feedback (RLHF), with Proximal Policy Optimization (PPO) serving as the default RL optimizer. Despite its effectiveness, PPO has limitations when optimizing rewards trained from comparison-based loss. Primarily, PPO is not invariant to equivalent reward functions containing identical preference information due to the need to calibrate the reward scale. Additionally, PPO's necessity for token-wise updates introduces complexity in both function approximation and algorithm design compared to trajectory-wise optimization. This paper proposes a new framework, reinforcement learning with relative feedback, and a novel trajectory-wise policy gradient algorithm, Pairwise Proximal Policy Optimization (P3O) that operates directly on comparative rewards. We show theoretically that P3O is invariant to equivalent rewards and avoids the complexity of PPO. Empirical evaluations demonstrate that P3O outperforms PPO in the KL-Reward trade-off and can align with human preferences as well as or better than prior methods. In summary, this work introduces a simpler yet effective approach for aligning LLMs to human preferences through relative feedback.

Recent work has considered whether large language models (LLMs) can function as planners: given a task, generate a plan. We investigate whether LLMs can serve as generalized planners: given a domain and training tasks, generate a program that efficiently produces plans for other tasks in the domain. In particular, we consider PDDL domains and use GPT-4 to synthesize Python programs. We also consider (1) Chain-of-Thought (CoT) summarization, where the LLM is prompted to summarize the domain and propose a strategy in words before synthesizing the program; and (2) automated debugging, where the program is validated with respect to the training tasks, and in case of errors, the LLM is re-prompted with four types of feedback. We evaluate this approach in seven PDDL domains and compare it to four ablations and four baselines. Overall, we find that GPT-4 is a surprisingly powerful generalized planner. We also conclude that automated debugging is very important, that CoT summarization has non-uniform impact, that GPT-4 is far superior to GPT-3.5, and that just two training tasks are often sufficient for strong generalization.

Instruct LLM provide a paradigm used in large scale language model to align LLM to human preference. The paradigm contains supervised fine tuning and reinforce learning from human feedback. This paradigm is also used in downstream scenarios to adapt LLM to specific corpora and applications. Comparing to SFT, there are many efforts focused on RLHF and several algorithms being proposed, such as PPO, DPO, IPO, KTO, MinorDPO and etc. Meanwhile most efforts for SFT are focused on how to collect, filter and mix high quality data. In this article with insight from DPO and MinorDPO, we propose a training metric for SFT to measure the discrepancy between the optimized model and the original model, and a loss function MinorSFT that can increase the training effectiveness, and reduce the discrepancy between the optimized LLM and original LLM.

We introduce the Diffusion Chain of Lateral Thought (DCoLT), a reasoning framework for diffusion language models. DCoLT treats each intermediate step in the reverse diffusion process as a latent "thinking" action and optimizes the entire reasoning trajectory to maximize the reward on the correctness of the final answer with outcome-based Reinforcement Learning (RL). Unlike traditional Chain-of-Thought (CoT) methods that follow a causal, linear thinking process, DCoLT allows bidirectional, non-linear reasoning with no strict rule on grammatical correctness amid its intermediate steps of thought. We implement DCoLT on two representative Diffusion Language Models (DLMs). First, we choose SEDD as a representative continuous-time discrete diffusion model, where its concrete score derives a probabilistic policy to maximize the RL reward over the entire sequence of intermediate diffusion steps. We further consider the discrete-time masked diffusion language model -- LLaDA, and find that the order to predict and unmask tokens plays an essential role to optimize its RL action resulting from the ranking-based Unmasking Policy Module (UPM) defined by the Plackett-Luce model. Experiments on both math and code generation tasks show that using only public data and 16 H800 GPUs, DCoLT-reinforced DLMs outperform other DLMs trained by SFT or RL or even both. Notably, DCoLT-reinforced LLaDA boosts its reasoning accuracy by +9.8%, +5.7%, +11.4%, +19.5% on GSM8K, MATH, MBPP, and HumanEval.

In this paper we present a Java-to-Python (J2P) and Python-to-Java (P2J) back-to-back code translation method, and associated tool called CoTran, based on large language models (LLMs). Our method leverages the attention mechanism of LLMs, compilation, and symbolic execution-based test generation for equivalence testing between the input and output programs. More precisely, we modify the typical LLM training loop to incorporate compiler and symbolic execution loss. Via extensive experiments comparing CoTran with 10 other transpilers and LLM-based translation tools over a benchmark of more than 57,000 Java-Python equivalent pairs, we show that CoTran outperforms them on relevant metrics such as compilation and runtime equivalence accuracy. For example, our tool gets 97.43% compilation accuracy and 49.66% runtime equivalence accuracy for J2P translation, whereas the nearest competing tool only gets 96.44% and 6.8% respectively.

A key challenge in applying reinforcement learning (RL) to diffusion large language models (dLLMs) lies in the intractability of their likelihood functions, which are essential for the RL objective, necessitating corresponding approximation in each training step. While existing methods approximate the log-likelihoods by their evidence lower bounds (ELBOs) via customized Monte Carlo (MC) sampling, the forward computational graphs of all MC samples need to be retained for the gradient computation of non-linear terms in the RL objective, resulting in significant memory overhead. This constraint restricts feasible sample sizes, leading to imprecise likelihood approximations and ultimately distorting the RL objective. To overcome this limitation, we propose Boundary-Guided Policy Optimization (BGPO), a memory-efficient RL algorithm that maximizes a specially constructed lower bound of the ELBO-based objective. This lower bound is carefully designed to satisfy two key properties: (1) Linearity: it is formulated in a linear sum where each term depends only on a single MC sample, thereby enabling gradient accumulation across samples and ensuring constant memory usage; (2) Equivalence: Both the value and gradient of this lower bound are equal to those of the ELBO-based objective in on-policy training, making it also an effective approximation for the original RL objective. These properties allow BGPO to adopt a large MC sample size, resulting in more accurate likelihood approximations and improved RL objective estimation, which in turn leads to enhanced performance. Experiments show that BGPO significantly outperforms previous RL algorithms for dLLMs in math problem solving, code generation, and planning tasks.

The rise of GPU-based high-performance computing (HPC) has driven the widespread adoption of parallel programming models such as CUDA. Yet, the inherent complexity of parallel programming creates a demand for the automated sequential-to-parallel approaches. However, data scarcity poses a significant challenge for machine learning-based sequential-to-parallel code translation. Although recent back-translation methods show promise, they still fail to ensure functional equivalence in the translated code. In this paper, we propose a novel Mutual-Supervised Learning (MSL) framework for sequential-to-parallel code translation to address the functional equivalence issue. MSL consists of two models, a Translator and a Tester. Through an iterative loop consisting of Co-verify and Co-evolve steps, the Translator and the Tester mutually generate data for each other and improve collectively. The Tester generates unit tests to verify and filter functionally equivalent translated code, thereby evolving the Translator, while the Translator generates translated code as augmented input to evolve the Tester. Experimental results demonstrate that MuSL significantly enhances the performance of the base model: when applied to Qwen2.5-Coder, it not only improves Pass@1 by up to 28.91% and boosts Tester performance by 68.90%, but also outperforms the previous state-of-the-art method CodeRosetta by 1.56 and 6.92 in BLEU and CodeBLEU scores, while achieving performance comparable to DeepSeek-R1 and GPT-4.1. Our code is available at https://github.com/kcxain/musl.

We propose a novel approach for learning interchangeable tokens in language models to obtain an extendable vocabulary that can generalize to new tokens. Our method is designed to address alpha-equivalence, the principle that renaming bound variables in a syntactic expression preserves semantics. This property arises in many formal languages such as temporal logics, in which all proposition symbols represent the same concept but are distinguishable from each other. To handle such tokens, we develop a dual-part embedding approach. The first part is shared across all interchangeable tokens, thereby enforcing that they represent the same core concept. The second part is randomly generated for each token, which enables distinguishability. We evaluate our method in a Transformer encoder-decoder model on two tasks: solving linear temporal logic formulae and copying with extendable vocabulary. Our method demonstrates promising generalization capabilities in addition to introducing a favorable inductive bias for alpha-equivalence.

Instructing large language models (LLMs) to solve elementary school math problems has shown great success using Chain of Thought (CoT). However, the CoT approach relies on an LLM to generate a sequence of arithmetic calculations which can be prone to cascaded calculation errors. We hypothesize that an LLM should focus on extracting predicates and generating symbolic formulas from the math problem description so that the underlying calculation can be done via an external code interpreter. We investigate using LLM to generate Prolog programs to solve mathematical questions. Experimental results show that our Prolog-based arithmetic problem-solving outperforms CoT generation in the GSM8K benchmark across three distinct LLMs. In addition, given the insensitive ordering of predicates and symbolic formulas in Prolog, we propose to permute the ground truth predicates for more robust LLM training via data augmentation.

In modern large language models (LLMs), LLM alignment is of crucial importance and is typically achieved through methods such as reinforcement learning from human feedback (RLHF) and direct preference optimization (DPO). However, in most existing methods for LLM alignment, all tokens in the response are optimized using a sparse, response-level reward or preference annotation. The ignorance of token-level rewards may erroneously punish high-quality tokens or encourage low-quality tokens, resulting in suboptimal performance and slow convergence speed. To address this issue, we propose AlignDistil, an RLHF-equivalent distillation method for token-level reward optimization. Specifically, we introduce the reward learned by DPO into the RLHF objective and theoretically prove the equivalence between this objective and a token-level distillation process, where the teacher distribution linearly combines the logits from the DPO model and a reference model. On this basis, we further bridge the accuracy gap between the reward from the DPO model and the pure reward model, by building a contrastive DPO reward with a normal and a reverse DPO model. Moreover, to avoid under- and over-optimization on different tokens, we design a token adaptive logit extrapolation mechanism to construct an appropriate teacher distribution for each token. Experimental results demonstrate the superiority of our AlignDistil over existing methods and showcase fast convergence due to its token-level distributional reward optimization.

The alignment of large language models (LLMs) often assumes that using more clean data yields better outcomes, overlooking the match between model capacity and example difficulty. Challenging this, we propose a new principle: Preference data vary in difficulty, and overly difficult examples hinder alignment, by exceeding the model's capacity. Through systematic experimentation, we validate this principle with three key findings: (1) preference examples vary in difficulty, as evidenced by consistent learning orders across alignment runs; (2) overly difficult examples significantly degrade performance across four LLMs and two datasets; and (3) the capacity of a model dictates its threshold for handling difficult examples, underscoring a critical relationship between data selection and model capacity. Building on this principle, we introduce Selective DPO, which filters out overly difficult examples. This simple adjustment improves alignment performance by 9-16% in win rates on the AlpacaEval 2 benchmark compared to the DPO baseline, suppressing a series of DPO variants with different algorithmic adjustments. Together, these results illuminate the importance of aligning data difficulty with model capacity, offering a transformative perspective for improving alignment strategies in LLMs. Code is available at https://github.com/glorgao/SelectiveDPO.

We enhance the calculus of string diagrams for monoidal categories with hierarchical features in order to capture closed monoidal (and cartesian closed) structure. Using this new syntax we formulate an automatic differentiation algorithm for (applied) simply typed lambda calculus in the style of [Pearlmutter and Siskind 2008] and we prove for the first time its soundness. To give an efficient yet principled implementation of the AD algorithm we define a sound and complete representation of hierarchical string diagrams as a class of hierarchical hypergraphs we call hypernets.

Mathematical reasoning presents a significant challenge for Large Language Models (LLMs) due to the extensive and precise chain of reasoning required for accuracy. Ensuring the correctness of each reasoning step is critical. To address this, we aim to enhance the robustness and factuality of LLMs by learning from human feedback. However, Direct Preference Optimization (DPO) has shown limited benefits for long-chain mathematical reasoning, as models employing DPO struggle to identify detailed errors in incorrect answers. This limitation stems from a lack of fine-grained process supervision. We propose a simple, effective, and data-efficient method called Step-DPO, which treats individual reasoning steps as units for preference optimization rather than evaluating answers holistically. Additionally, we have developed a data construction pipeline for Step-DPO, enabling the creation of a high-quality dataset containing 10K step-wise preference pairs. We also observe that in DPO, self-generated data is more effective than data generated by humans or GPT-4, due to the latter's out-of-distribution nature. Our findings demonstrate that as few as 10K preference data pairs and fewer than 500 Step-DPO training steps can yield a nearly 3% gain in accuracy on MATH for models with over 70B parameters. Notably, Step-DPO, when applied to Qwen2-72B-Instruct, achieves scores of 70.8% and 94.0% on the test sets of MATH and GSM8K, respectively, surpassing a series of closed-source models, including GPT-4-1106, Claude-3-Opus, and Gemini-1.5-Pro. Our code, data, and models are available at https://github.com/dvlab-research/Step-DPO.

This work investigates the selection of high-quality pre-training data from massive corpora to enhance LMs' capabilities for downstream usage. We formulate data selection as a generalized Optimal Control problem, which can be solved theoretically by Pontryagin's Maximum Principle (PMP), yielding a set of necessary conditions that characterize the relationship between optimal data selection and LM training dynamics. Based on these theoretical results, we introduce PMP-based Data Selection (PDS), a framework that approximates optimal data selection by solving the PMP conditions. In our experiments, we adopt PDS to select data from CommmonCrawl and show that the PDS-selected corpus accelerates the learning of LMs and constantly boosts their performance on a wide range of downstream tasks across various model sizes. Moreover, the benefits of PDS extend to ~400B models trained on ~10T tokens, as evidenced by the extrapolation of the test loss curves according to the Scaling Laws. PDS also improves data utilization when the pre-training data is limited, by reducing the data demand by 1.8 times, which mitigates the quick exhaustion of available web-crawled corpora. Our code, data, and model checkpoints can be found in https://github.com/microsoft/LMOps/tree/main/data_selection.

Large Language Models (LLMs) prompted to generate chain-of-thought (CoT) exhibit impressive reasoning capabilities. Recent attempts at prompt decomposition toward solving complex, multi-step reasoning problems depend on the ability of the LLM to simultaneously decompose and solve the problem. A significant disadvantage is that foundational LLMs are typically not available for fine-tuning, making adaptation computationally prohibitive. We believe (and demonstrate) that problem decomposition and solution generation are distinct capabilites, better addressed in separate modules, than by one monolithic LLM. We introduce DaSLaM, which uses a decomposition generator to decompose complex problems into subproblems that require fewer reasoning steps. These subproblems are answered by a solver. We use a relatively small (13B parameters) LM as the decomposition generator, which we train using policy gradient optimization to interact with a solver LM (regarded as black-box) and guide it through subproblems, thereby rendering our method solver-agnostic. Evaluation on multiple different reasoning datasets reveal that with our method, a 175 billion parameter LM (text-davinci-003) can produce competitive or even better performance, compared to its orders-of-magnitude larger successor, GPT-4. Additionally, we show that DaSLaM is not limited by the solver's capabilities as a function of scale; e.g., solver LMs with diverse sizes give significant performance improvement with our solver-agnostic decomposition technique. Exhaustive ablation studies evince the superiority of our modular finetuning technique over exorbitantly large decomposer LLMs, based on prompting alone.

Reinforcement learning for LLM reasoning has rapidly emerged as a prominent research area, marked by a significant surge in related studies on both algorithmic innovations and practical applications. Despite this progress, several critical challenges remain, including the absence of standardized guidelines for employing RL techniques and a fragmented understanding of their underlying mechanisms. Additionally, inconsistent experimental settings, variations in training data, and differences in model initialization have led to conflicting conclusions, obscuring the key characteristics of these techniques and creating confusion among practitioners when selecting appropriate techniques. This paper systematically reviews widely adopted RL techniques through rigorous reproductions and isolated evaluations within a unified open-source framework. We analyze the internal mechanisms, applicable scenarios, and core principles of each technique through fine-grained experiments, including datasets of varying difficulty, model sizes, and architectures. Based on these insights, we present clear guidelines for selecting RL techniques tailored to specific setups, and provide a reliable roadmap for practitioners navigating the RL for the LLM domain. Finally, we reveal that a minimalist combination of two techniques can unlock the learning capability of critic-free policies using vanilla PPO loss. The results demonstrate that our simple combination consistently improves performance, surpassing strategies like GRPO and DAPO.

Constraint Programming (CP) is a declarative programming paradigm that allows for modeling and solving combinatorial optimization problems, such as the Job-Shop Scheduling Problem (JSSP). While CP solvers manage to find optimal or near-optimal solutions for small instances, they do not scale well to large ones, i.e., they require long computation times or yield low-quality solutions. Therefore, real-world scheduling applications often resort to fast, handcrafted, priority-based dispatching heuristics to find a good initial solution and then refine it using optimization methods. This paper proposes a novel end-to-end approach to solving scheduling problems by means of CP and Reinforcement Learning (RL). In contrast to previous RL methods, tailored for a given problem by including procedural simulation algorithms, complex feature engineering, or handcrafted reward functions, our neural-network architecture and training algorithm merely require a generic CP encoding of some scheduling problem along with a set of small instances. Our approach leverages existing CP solvers to train an agent learning a Priority Dispatching Rule (PDR) that generalizes well to large instances, even from separate datasets. We evaluate our method on seven JSSP datasets from the literature, showing its ability to find higher-quality solutions for very large instances than obtained by static PDRs and by a CP solver within the same time limit.

As large language models (LLMs) are increasingly applied to scientific reasoning, the complexity of answer formats and the diversity of equivalent expressions make answer verification a critical yet challenging task. Existing verification studies in scientific domains suffer from two major limitations: (a) the absence of systematic evaluation standards and insufficient disciplinary coverage, which hinders their comprehensive assessment; and (b) heavy reliance on cumbersome rule design or prompt engineering, which reduces their effectiveness in complex reasoning scenarios or limits their cross-disciplinary generalization. To address these challenges, we propose solutions at both the data and model levels. On the data side, we construct SCI-VerifyBench, a cross-disciplinary benchmark covering mathematics, physics, biology, chemistry, and general scientific QA. The benchmark is built from real LLM responses and enhanced with domain-specific equivalence transformations that generate challenging and realistic data. Model-based and expert annotations ensure both quality and diversity, enabling rigorous evaluation of verification ability. On the model side, we emphasize the importance of reasoning for verification and introduce SCI-Verifier, a unified reasoning-augmented verifier for scientific domains. Through post-training, SCI-Verifier demonstrates strong logical reasoning and equivalence judgment capabilities while maintaining concise and stable outputs. Together, SCI-VerifyBench and SCI-Verifier provide a principled framework for scientific verification, offering both systematic evaluation and practical pathways to enhance the reliability and applicability of LLMs in scientific domains.

Reinforcement Learning (RL) has emerged as a central paradigm for advancing Large Language Models (LLMs), where pre-training and RL post-training share the same log-likelihood formulation. In contrast, recent RL approaches for diffusion models, most notably Denoising Diffusion Policy Optimization (DDPO), optimize an objective different from the pretraining objectives--score/flow matching loss. In this work, we establish a novel theoretical analysis: DDPO is an implicit form of score/flow matching with noisy targets, which increases variance and slows convergence. Building on this analysis, we introduce Advantage Weighted Matching (AWM), a policy-gradient method for diffusion. It uses the same score/flow-matching loss as pretraining to obtain a lower-variance objective and reweights each sample by its advantage. In effect, AWM raises the influence of high-reward samples and suppresses low-reward ones while keeping the modeling objective identical to pretraining. This unifies pretraining and RL conceptually and practically, is consistent with policy-gradient theory, reduces variance, and yields faster convergence. This simple yet effective design yields substantial benefits: on GenEval, OCR, and PickScore benchmarks, AWM delivers up to a 24times speedup over Flow-GRPO (which builds on DDPO), when applied to Stable Diffusion 3.5 Medium and FLUX, without compromising generation quality. Code is available at https://github.com/scxue/advantage_weighted_matching.

We introduce Prompt Curriculum Learning (PCL), a lightweight reinforcement learning (RL) algorithm that selects intermediate-difficulty prompts using a learned value model to post-train language models. Since post-training LLMs via RL remains sensitive to batching and prompt selection strategies, we first conduct a series of systematic experiments where we (1) determine the optimal training batch size that balances generation efficiency and gradient quality and (2) establish the importance of focusing on prompts of intermediate difficulty for the policy. We build upon these results to design PCL, which identifies prompts of intermediate difficulty for the current policy in an on-policy manner by using a value model that is concurrently updated based on the current policy. By focusing on informative prompts that yield high effective ratios, PCL achieves either the highest performance or requires significantly less time to reach comparable performance to its counterparts. Compared to rollout-based filtering methods, PCL avoids costly rollouts and achieves 12.1times and 16.9times faster speed on identifying intermediate-difficulty prompts when training on MATH and DeepScaleR, respectively. We further demonstrate that our value model accurately predicts prompt difficulty and allows PCL to focus on progressively more challenging prompts during RL. Our results present a new methodology that delivers improved tradeoff between upper-bound performance and efficiency for reasoning-focused RL.

With ever increasing parameters and computation, vision-language pre-trained (VLP) models exhibit prohibitive expenditure in downstream task adaption. Recent endeavors mainly focus on parameter efficient transfer learning (PETL) for VLP models by only updating a small number of parameters. However, excessive computational overhead still plagues the application of VLPs. In this paper, we aim at parameter and computation efficient transfer learning (PCETL) for VLP models. In particular, PCETL not only needs to limit the number of trainable parameters in VLP models, but also to reduce the computational redundancy during inference, thus enabling a more efficient transfer. To approach this target, we propose a novel dynamic architecture skipping (DAS) approach towards effective PCETL. Instead of directly optimizing the intrinsic architectures of VLP models, DAS first observes the significances of their modules to downstream tasks via a reinforcement learning (RL) based process, and then skips the redundant ones with lightweight networks, i.e., adapters, according to the obtained rewards. In this case, the VLP model can well maintain the scale of trainable parameters while speeding up its inference on downstream tasks. To validate DAS, we apply it to two representative VLP models, namely ViLT and METER, and conduct extensive experiments on a bunch of VL tasks. The experimental results not only show the great advantages of DAS in reducing computational complexity, e.g. -11.97% FLOPs of METER on VQA2.0, but also confirm its competitiveness against existing PETL methods in terms of parameter scale and performance. Our source code is given in our appendix.

Class incremental learning (CIL) trains a network on sequential tasks with separated categories but suffers from catastrophic forgetting, where models quickly lose previously learned knowledge when acquiring new tasks. The generalized CIL (GCIL) aims to address the CIL problem in a more real-world scenario, where incoming data have mixed data categories and unknown sample size distribution, leading to intensified forgetting. Existing attempts for the GCIL either have poor performance, or invade data privacy by saving historical exemplars. To address this, in this paper, we propose an exemplar-free generalized analytic class incremental learning (G-ACIL). The G-ACIL adopts analytic learning (a gradient-free training technique), and delivers an analytical solution (i.e., closed-form) to the GCIL scenario. This solution is derived via decomposing the incoming data into exposed and unexposed classes, allowing an equivalence between the incremental learning and its joint training, i.e., the weight-invariant property. Such an equivalence is theoretically validated through matrix analysis tools, and hence contributes interpretability in GCIL. It is also empirically evidenced by experiments on various datasets and settings of GCIL. The results show that the G-ACIL exhibits leading performance with high robustness compared with existing competitive GCIL methods. Codes will be ready at https://github.com/ZHUANGHP/Analytic-continual-learning.

Domain-independent heuristics have long been a cornerstone of AI planning, offering general solutions applicable across a wide range of tasks without requiring domain-specific engineering. However, the advent of large language models (LLMs) presents an opportunity to generate heuristics tailored to specific planning problems, potentially challenging the necessity of domain independence as a strict design principle. In this paper, we explore the use of LLMs to automatically derive planning heuristics from task descriptions represented as successor generators and goal tests written in general purpose programming language. We investigate the trade-offs between domain-specific LLM-generated heuristics and traditional domain-independent methods in terms of computational efficiency and explainability. Our experiments demonstrate that LLMs can create heuristics that achieve state-of-the-art performance on some standard IPC domains, as well as their ability to solve problems that lack an adequate Planning Domain Definition Language ({\sc pddl}) representation. We discuss whether these results signify a paradigm shift and how they can complement existing approaches.

Synthesizing inductive loop invariants is fundamental to automating program verification. In this work, we observe that Large Language Models (such as gpt-3.5 or gpt-4) are capable of synthesizing loop invariants for a class of programs in a 0-shot setting, yet require several samples to generate the correct invariants. This can lead to a large number of calls to a program verifier to establish an invariant. To address this issue, we propose a {\it re-ranking} approach for the generated results of LLMs. We have designed a ranker that can distinguish between correct inductive invariants and incorrect attempts based on the problem definition. The ranker is optimized as a contrastive ranker. Experimental results demonstrate that this re-ranking mechanism significantly improves the ranking of correct invariants among the generated candidates, leading to a notable reduction in the number of calls to a verifier.

The class of tree-adjoining languages can be characterized by various two-level formalisms, consisting of a context-free grammar (CFG) or pushdown automaton (PDA) controlling another CFG or PDA. These four formalisms are equivalent to tree-adjoining grammars (TAG), linear indexed grammars (LIG), pushdown-adjoining automata (PAA), and embedded pushdown automata (EPDA). We define semiring-weighted versions of the above two-level formalisms, and we design new algorithms for computing their stringsums (the weight of all derivations of a string) and allsums (the weight of all derivations). From these, we also immediately obtain stringsum and allsum algorithms for TAG, LIG, PAA, and EPDA. For LIG, our algorithm is more time-efficient by a factor of O(n|N|) (where n is the string length and |N| is the size of the nonterminal set) and more space-efficient by a factor of O(|Gamma|) (where |Gamma| is the size of the stack alphabet) than the algorithm of Vijay-Shanker and Weir (1989). For EPDA, our algorithm is both more space-efficient and time-efficient than the algorithm of Alonso et al. (2001) by factors of O(|Gamma|^2) and O(|Gamma|^3), respectively. Finally, we give the first PAA stringsum and allsum algorithms.

As a seemingly self-explanatory task, problem-solving has been a significant component of science and engineering. However, a general yet concrete formulation of problem-solving itself is missing. With the recent development of AI-based problem-solving agents, the demand for process-level verifiability is rapidly increasing yet underexplored. To fill these gaps, we present a principled formulation of problem-solving as a deterministic Markov decision process; a novel framework, FPS (Formal Problem-Solving), which utilizes existing FTP (formal theorem proving) environments to perform process-verified problem-solving; and D-FPS (Deductive FPS), decoupling solving and answer verification for better human-alignment. The expressiveness, soundness and completeness of the frameworks are proven. We construct three benchmarks on problem-solving: FormalMath500, a formalization of a subset of the MATH500 benchmark; MiniF2F-Solving and PutnamBench-Solving, adaptations of FTP benchmarks MiniF2F and PutnamBench. For faithful, interpretable, and human-aligned evaluation, we propose RPE (Restricted Propositional Equivalence), a symbolic approach to determine the correctness of answers by formal verification. We evaluate four prevalent FTP models and two prompting methods as baselines, solving at most 23.77% of FormalMath500, 27.47% of MiniF2F-Solving, and 0.31% of PutnamBench-Solving.

Minimizing the difference of two submodular (DS) functions is a problem that naturally occurs in various machine learning problems. Although it is well known that a DS problem can be equivalently formulated as the minimization of the difference of two convex (DC) functions, existing algorithms do not fully exploit this connection. A classical algorithm for DC problems is called the DC algorithm (DCA). We introduce variants of DCA and its complete form (CDCA) that we apply to the DC program corresponding to DS minimization. We extend existing convergence properties of DCA, and connect them to convergence properties on the DS problem. Our results on DCA match the theoretical guarantees satisfied by existing DS algorithms, while providing a more complete characterization of convergence properties. In the case of CDCA, we obtain a stronger local minimality guarantee. Our numerical results show that our proposed algorithms outperform existing baselines on two applications: speech corpus selection and feature selection.

This study focuses on improving the performance of lightweight Large Language Models (LLMs) in mathematical reasoning tasks. We introduce a novel method for measuring mathematical logic similarity and design an automatic screening mechanism to construct a set of reference problems that integrate both semantic and logical similarity. By employing carefully crafted positive and negative example prompts, we guide the model towards adopting sound reasoning logic. To the best of our knowledge, this is the first attempt to utilize retrieval-enhanced generation for mathematical problem-solving. Experimental results demonstrate that our method achieves a 15.8% improvement over the Chain of Thought approach on the SVAMP dataset and a 21.5 % improvement on the GSM8K dataset. Further application of this method to a large-scale model with 175 billion parameters yields performance comparable to the best results on both aforementioned datasets. Finally, we conduct an analysis of errors during the reasoning process, providing valuable insights and directions for future research on reasoning tasks using large language models.

Inequality proving, crucial across diverse scientific and mathematical fields, tests advanced reasoning skills such as discovering tight bounds and strategic theorem application. This makes it a distinct, demanding frontier for large language models (LLMs), offering insights beyond general mathematical problem-solving. Progress in this area is hampered by existing datasets that are often scarce, synthetic, or rigidly formal. We address this by proposing an informal yet verifiable task formulation, recasting inequality proving into two automatically checkable subtasks: bound estimation and relation prediction. Building on this, we release IneqMath, an expert-curated dataset of Olympiad-level inequalities, including a test set and training corpus enriched with step-wise solutions and theorem annotations. We also develop a novel LLM-as-judge evaluation framework, combining a final-answer judge with four step-wise judges designed to detect common reasoning flaws. A systematic evaluation of 29 leading LLMs on IneqMath reveals a surprising reality: even top models like o1 achieve less than 10% overall accuracy under step-wise scrutiny; this is a drop of up to 65.5% from their accuracy considering only final answer equivalence. This discrepancy exposes fragile deductive chains and a critical gap for current LLMs between merely finding an answer and constructing a rigorous proof. Scaling model size and increasing test-time computation yield limited gains in overall proof correctness. Instead, our findings highlight promising research directions such as theorem-guided reasoning and self-refinement. Code and data are available at https://ineqmath.github.io/.

Reasoning training incentivizes LLMs to produce long chains of thought (long CoT), which among other things, allows them to explore solution strategies with self-checking. This results in higher accuracy, but inflates context length, token/compute cost, and answer latency. We ask: Can current models leverage their metacognition to provide other combinations on this Pareto frontier, e.g., better accuracy with lower context length and/or latency? Abstractly, we view the model as an improvement operator on its own "thoughts" with a continuum of possible strategies. We identify an interesting inference family Parallel-Distill-Refine (PDR), which performs the following: (i) generate diverse drafts in parallel; (ii) distill them into a bounded, textual workspace; and (iii) refine conditioned on this workspace, producing an output that seeds the next round. Importantly, context length (hence compute cost) is controllable via degree of parallelism, and is no longer conflated with the total number of generated tokens. We report PDR instantiations of current models that give better accuracy than long CoT while incurring lower latency. Setting degree of parallelism to 1 yields an interesting subcase, Sequential Refinement (SR) (iteratively improve a single candidate answer) which provides performance superior to long CoT. Success of such model orchestrations raises the question whether further training could shift the Pareto frontier. To this end, we train an 8B thinking model with Reinforcement Learning (RL) to make it consistent with PDR as the inference method. On math tasks with verifiable answers, iterative pipelines surpass single-pass baselines at matched sequential budgets, with PDR delivering the largest gains (e.g., +11% on AIME 2024 and +9% on AIME 2025).

Direct Preference Optimization (DPO) has proven effective at improving the performance of large language models (LLMs) on downstream tasks such as reasoning and alignment. In this work, we propose Step-Controlled DPO (SCDPO), a method for automatically providing stepwise error supervision by creating negative samples of mathematical reasoning rationales that start making errors at a specified step. By applying these samples in DPO training, SCDPO can better align the model to understand reasoning errors and output accurate reasoning steps. We apply SCDPO to both code-integrated and chain-of-thought solutions, empirically showing that it consistently improves the performance compared to naive DPO on three different SFT models, including one existing SFT model and two models we finetuned. Qualitative analysis of the credit assignment of SCDPO and DPO demonstrates the effectiveness of SCDPO at identifying errors in mathematical solutions. We then apply SCDPO to an InternLM2-20B model, resulting in a 20B model that achieves high scores of 88.5% on GSM8K and 58.1% on MATH, rivaling all other open-source LLMs, showing the great potential of our method.

Large language models (LLMs) have shown impressive in-context learning (ICL) ability in code generation. LLMs take a prompt consisting of requirement-code examples and a new requirement as input, and output new programs. Existing studies have found that ICL is highly dominated by the examples and thus arises research on example selection. However, existing approaches randomly select examples or only consider the textual similarity of requirements to retrieve, leading to sub-optimal performance. In this paper, we propose a novel learning-based selection approach named LAIL (LLM-Aware In-context Learning) for code generation. Given a candidate example, we exploit LLMs themselves to estimate it by considering the generation probabilities of ground-truth programs given a requirement and the example. We then label candidate examples as positive or negative through the probability feedback. Based on the labeled data, we import a contrastive learning objective to train an effective retriever that acquires the preference of LLMs in code generation. We apply LAIL to three LLMs and evaluate it on three representative datasets (e.g., MBJP, MBPP, and MBCPP). LATA outperforms the state-of-the-art baselines by 11.58%, 6.89%, and 5.07% on CodeGen, and 4.38%, 2.85%, and 2.74% on GPT-3.5 in terms of Pass@1, respectively.

This thesis introduces quantum natural language processing (QNLP) models based on a simple yet powerful analogy between computational linguistics and quantum mechanics: grammar as entanglement. The grammatical structure of text and sentences connects the meaning of words in the same way that entanglement structure connects the states of quantum systems. Category theory allows to make this language-to-qubit analogy formal: it is a monoidal functor from grammar to vector spaces. We turn this abstract analogy into a concrete algorithm that translates the grammatical structure onto the architecture of parameterised quantum circuits. We then use a hybrid classical-quantum algorithm to train the model so that evaluating the circuits computes the meaning of sentences in data-driven tasks. The implementation of QNLP models motivated the development of DisCoPy (Distributional Compositional Python), the toolkit for applied category theory of which the first chapter gives a comprehensive overview. String diagrams are the core data structure of DisCoPy, they allow to reason about computation at a high level of abstraction. We show how they can encode both grammatical structures and quantum circuits, but also logical formulae, neural networks or arbitrary Python code. Monoidal functors allow to translate these abstract diagrams into concrete computation, interfacing with optimised task-specific libraries. The second chapter uses DisCopy to implement QNLP models as parameterised functors from grammar to quantum circuits. It gives a first proof-of-concept for the more general concept of functorial learning: generalising machine learning from functions to functors by learning from diagram-like data. In order to learn optimal functor parameters via gradient descent, we introduce the notion of diagrammatic differentiation: a graphical calculus for computing the gradients of parameterised diagrams.

Large language model (LLM) inference workload dominates a wide variety of modern AI applications, ranging from multi-turn conversation to document analysis. Balancing fairness and efficiency is critical for managing diverse client workloads with varying prefix patterns. Unfortunately, existing fair scheduling algorithms for LLM serving, such as Virtual Token Counter (VTC), fail to take prefix locality into consideration and thus suffer from poor performance. On the other hand, locality-aware scheduling algorithms in existing LLM serving frameworks tend to maximize the prefix cache hit rate without considering fair sharing among clients. This paper introduces the first locality-aware fair scheduling algorithm, Deficit Longest Prefix Match (DLPM), which can maintain a high degree of prefix locality with a fairness guarantee. We also introduce a novel algorithm, Double Deficit LPM (D^2LPM), extending DLPM for the distributed setup that can find a balance point among fairness, locality, and load-balancing. Our extensive evaluation demonstrates the superior performance of DLPM and D^2LPM in ensuring fairness while maintaining high throughput (up to 2.87times higher than VTC) and low per-client (up to 7.18times lower than state-of-the-art distributed LLM serving system) latency.

A proper code evaluation metric (CEM) profoundly impacts the evolution of code generation, which is an important research field in NLP and software engineering. Prevailing match-based CEMs (e.g., BLEU, Accuracy, and CodeBLEU) suffer from two significant drawbacks. 1. They primarily measure the surface differences between codes without considering their functional equivalence. However, functional equivalence is pivotal in evaluating the effectiveness of code generation, as different codes can perform identical operations. 2. They are predominantly designed for the Ref-only input format. However, code evaluation necessitates versatility in input formats. Aside from Ref-only, there are NL-only and Ref\&NL formats, which existing match-based CEMs cannot effectively accommodate. In this paper, we propose CodeScore, a large language model (LLM)-based CEM, which estimates the functional correctness of generated code on three input types. To acquire CodeScore, we present UniCE, a unified code generation learning framework, for LLMs to learn code execution (i.e., learning PassRatio and Executability of generated code) with unified input. Extensive experimental results on multiple code evaluation datasets demonstrate that CodeScore absolutely improves up to 58.87% correlation with functional correctness compared to other CEMs, achieves state-of-the-art performance, and effectively handles three input formats.

Planning in a text-based environment continues to be a major challenge for AI systems. Recent approaches have used language models to predict a planning domain definition (e.g., PDDL) but have only been evaluated in closed-domain simulated environments. To address this, we present Proc2PDDL , the first dataset containing open-domain procedural texts paired with expert-annotated PDDL representations. Using this dataset, we evaluate state-of-the-art models on defining the preconditions and effects of actions. We show that Proc2PDDL is highly challenging, with GPT-3.5's success rate close to 0% and GPT-4's around 35%. Our analysis shows both syntactic and semantic errors, indicating LMs' deficiency in both generating domain-specific prgorams and reasoning about events. We hope this analysis and dataset helps future progress towards integrating the best of LMs and formal planning.

Reinforcement learning from human feedback (RLHF) is one of the key techniques that helps large language models (LLMs) to follow instructions and provide helpful and harmless responses. While direct policy optimization methods exist, state-of-the-art LLMs adopt RL-based methods (usually PPO) in RLHF to train the policy to generate good responses guided by a reward model learned from preference data. The main challenge of these methods is the inaccuracy of the intermediate reward model, especially in code generation tasks that require long and complex reasoning to score a response. We find that the reliability of the reward model varies across responses assigned with different rewards. This motivates us to filter the samples whose rewards may be unreliable to improve signal-to-noise ratio during policy learning, resulting in Policy Filtration for Proximal Policy Optimization (PF-PPO). To choose a proper policy filtration strategy for a given reward model, the coefficient of determination (R^2) between rewards and actual scores on filtered samples serves as a good metrics and helps us find several promising strategies. We provide extensive experiments to validate the effectiveness of PF-PPO in code generation tasks, and find that some variants of PF-PPO are highly effective and achieve new state-of-the-art performance across 7-billion-parameter models on HumanEval, MBPP, and a new and more challenging LeetCode Contest benchmark.

The Abstraction and Reasoning Corpus (ARC) is a general artificial intelligence benchmark that poses difficulties for pure machine learning methods due to its requirement for fluid intelligence with a focus on reasoning and abstraction. In this work, we introduce an ARC solver, Generalized Planning for Abstract Reasoning (GPAR). It casts an ARC problem as a generalized planning (GP) problem, where a solution is formalized as a planning program with pointers. We express each ARC problem using the standard Planning Domain Definition Language (PDDL) coupled with external functions representing object-centric abstractions. We show how to scale up GP solvers via domain knowledge specific to ARC in the form of restrictions over the actions model, predicates, arguments and valid structure of planning programs. Our experiments demonstrate that GPAR outperforms the state-of-the-art solvers on the object-centric tasks of the ARC, showing the effectiveness of GP and the expressiveness of PDDL to model ARC problems. The challenges provided by the ARC benchmark motivate research to advance existing GP solvers and understand new relations with other planning computational models. Code is available at github.com/you68681/GPAR.

This note describes the development of an exact solver for Minimal Directed Feedback Vertex Set as part of the PACE 2022 competition. The solver is powered largely by aggressively trying to reduce the DFVS problem to a Minimal Cover problem, and applying reduction rules adapted from Vertex Cover literature. The resulting problem is solved as an Integer Linear Program (ILP) using SCIP. The resulting solver performed the second-best in the competition, although a bug at submission time disqualified it. As an additional note, we describe a new vertex cover reduction generalizing the Desk reduction rule.

Large language models (LLMs) have recently demonstrated an impressive ability to perform arithmetic and symbolic reasoning tasks, when provided with a few examples at test time ("few-shot prompting"). Much of this success can be attributed to prompting methods such as "chain-of-thought'', which employ LLMs for both understanding the problem description by decomposing it into steps, as well as solving each step of the problem. While LLMs seem to be adept at this sort of step-by-step decomposition, LLMs often make logical and arithmetic mistakes in the solution part, even when the problem is decomposed correctly. In this paper, we present Program-Aided Language models (PAL): a novel approach that uses the LLM to read natural language problems and generate programs as the intermediate reasoning steps, but offloads the solution step to a runtime such as a Python interpreter. With PAL, decomposing the natural language problem into runnable steps remains the only learning task for the LLM, while solving is delegated to the interpreter. We demonstrate this synergy between a neural LLM and a symbolic interpreter across 13 mathematical, symbolic, and algorithmic reasoning tasks from BIG-Bench Hard and other benchmarks. In all these natural language reasoning tasks, generating code using an LLM and reasoning using a Python interpreter leads to more accurate results than much larger models. For example, PAL using Codex achieves state-of-the-art few-shot accuracy on the GSM8K benchmark of math word problems, surpassing PaLM-540B which uses chain-of-thought by absolute 15% top-1. Our code and data are publicly available at http://reasonwithpal.com/ .

Aligning language models (LMs) with curated human feedback is critical to control their behaviors in real-world applications. Several recent policy optimization methods, such as DPO and SLiC, serve as promising alternatives to the traditional Reinforcement Learning from Human Feedback (RLHF) approach. In practice, human feedback often comes in a format of a ranked list over multiple responses to amortize the cost of reading prompt. Multiple responses can also be ranked by reward models or AI feedback. There lacks such a study on directly fitting upon a list of responses. In this work, we formulate the LM alignment as a listwise ranking problem and describe the Listwise Preference Optimization (LiPO) framework, where the policy can potentially learn more effectively from a ranked list of plausible responses given the prompt. This view draws an explicit connection to Learning-to-Rank (LTR), where most existing preference optimization work can be mapped to existing ranking objectives, especially pairwise ones. Following this connection, we provide an examination of ranking objectives that are not well studied for LM alignment withDPO and SLiC as special cases when list size is two. In particular, we highlight a specific method, LiPO-{\lambda}, which leverages a state-of-the-art listwise ranking objective and weights each preference pair in a more advanced manner. We show that LiPO-{\lambda} can outperform DPO and SLiC by a clear margin on two preference alignment tasks.

Decision-focused learning (DFL) is an emerging paradigm that integrates machine learning (ML) and constrained optimization to enhance decision quality by training ML models in an end-to-end system. This approach shows significant potential to revolutionize combinatorial decision-making in real-world applications that operate under uncertainty, where estimating unknown parameters within decision models is a major challenge. This paper presents a comprehensive review of DFL, providing an in-depth analysis of both gradient-based and gradient-free techniques used to combine ML and constrained optimization. It evaluates the strengths and limitations of these techniques and includes an extensive empirical evaluation of eleven methods across seven problems. The survey also offers insights into recent advancements and future research directions in DFL. Code and benchmark: https://github.com/PredOpt/predopt-benchmarks

Policy gradient algorithms have been successfully applied to enhance the reasoning capabilities of large language models (LLMs). Despite the widespread use of Kullback-Leibler (KL) regularization in policy gradient algorithms to stabilize training, the systematic exploration of how different KL divergence formulations can be estimated and integrated into surrogate loss functions for online reinforcement learning (RL) presents a nuanced and systematically explorable design space. In this paper, we propose regularized policy gradient (RPG), a systematic framework for deriving and analyzing KL-regularized policy gradient methods in the online RL setting. We derive policy gradients and corresponding surrogate loss functions for objectives regularized by both forward and reverse KL divergences, considering both normalized and unnormalized policy distributions. Furthermore, we present derivations for fully differentiable loss functions as well as REINFORCE-style gradient estimators, accommodating diverse algorithmic needs. We conduct extensive experiments on RL for LLM reasoning using these methods, showing improved or competitive results in terms of training stability and performance compared to strong baselines such as GRPO, REINFORCE++, and DAPO. The code is available at https://github.com/complex-reasoning/RPG.

Partial differential equations (PDEs) are fundamental to modeling physical systems, yet solving them remains a complex challenge. Traditional numerical solvers rely on expert knowledge to implement and are computationally expensive, while neural-network-based solvers require large training datasets and often lack interpretability. In this work, we frame PDE solving as a code generation task and introduce CodePDE, the first inference framework for generating PDE solvers using large language models (LLMs). Leveraging advanced inference-time algorithms and scaling strategies, CodePDE unlocks critical capacities of LLM for PDE solving: reasoning, debugging, selfrefinement, and test-time scaling -- all without task-specific tuning. CodePDE achieves superhuman performance across a range of representative PDE problems. We also present a systematic empirical analysis of LLM generated solvers, analyzing their accuracy, efficiency, and numerical scheme choices. Our findings highlight the promise and the current limitations of LLMs in PDE solving, offering a new perspective on solver design and opportunities for future model development. Our code is available at https://github.com/LithiumDA/CodePDE.

We present DuPO, a dual learning-based preference optimization framework that generates annotation-free feedback via a generalized duality. DuPO addresses two key limitations: Reinforcement Learning with Verifiable Rewards (RLVR)'s reliance on costly labels and applicability restricted to verifiable tasks, and traditional dual learning's restriction to strictly dual task pairs (e.g., translation and back-translation). Specifically, DuPO decomposes a primal task's input into known and unknown components, then constructs its dual task to reconstruct the unknown part using the primal output and known information (e.g., reversing math solutions to recover hidden variables), broadening applicability to non-invertible tasks. The quality of this reconstruction serves as a self-supervised reward to optimize the primal task, synergizing with LLMs' ability to instantiate both tasks via a single model. Empirically, DuPO achieves substantial gains across diverse tasks: it enhances the average translation quality by 2.13 COMET over 756 directions, boosts the mathematical reasoning accuracy by an average of 6.4 points on three challenge benchmarks, and enhances performance by 9.3 points as an inference-time reranker (trading computation for accuracy). These results position DuPO as a scalable, general, and annotation-free paradigm for LLM optimization.

We initiate a formal investigation into the design and analysis of LLM-based algorithms, i.e. algorithms that contain one or multiple calls of large language models (LLMs) as sub-routines and critically rely on the capabilities of LLMs. While LLM-based algorithms, ranging from basic LLM calls with prompt engineering to complicated LLM-powered agent systems and compound AI systems, have achieved remarkable empirical success, the design and optimization of them have mostly relied on heuristics and trial-and-errors, which is largely due to a lack of formal and analytical study for these algorithms. To fill this gap, we start by identifying the computational-graph representation of LLM-based algorithms, the design principle of task decomposition, and some key abstractions, which then facilitate our formal analysis for the accuracy and efficiency of LLM-based algorithms, despite the black-box nature of LLMs. Through extensive analytical and empirical investigation in a series of case studies, we demonstrate that the proposed framework is broadly applicable to a wide range of scenarios and diverse patterns of LLM-based algorithms, such as parallel, hierarchical and recursive task decomposition. Our proposed framework holds promise for advancing LLM-based algorithms, by revealing the reasons behind curious empirical phenomena, guiding the choices of hyperparameters, predicting the empirical performance of algorithms, and inspiring new algorithm design. To promote further study of LLM-based algorithms, we release our source code at https://github.com/modelscope/agentscope/tree/main/examples/paper_llm_based_algorithm.

Instruction tuning large language models (LLMs) remains a challenging task, owing to the complexity of hyperparameter selection and the difficulty involved in evaluating the tuned models. To determine the optimal hyperparameters, an automatic, robust, and reliable evaluation benchmark is essential. However, establishing such a benchmark is not a trivial task due to the challenges associated with evaluation accuracy and privacy protection. In response to these challenges, we introduce a judge large language model, named PandaLM, which is trained to distinguish the superior model given several LLMs. PandaLM's focus extends beyond just the objective correctness of responses, which is the main focus of traditional evaluation datasets. It addresses vital subjective factors such as relative conciseness, clarity, adherence to instructions, comprehensiveness, and formality. To ensure the reliability of PandaLM, we collect a diverse human-annotated test dataset, where all contexts are generated by humans and labels are aligned with human preferences. Our results indicate that PandaLM-7B achieves 93.75% of GPT-3.5's evaluation ability and 88.28% of GPT-4's in terms of F1-score on our test dataset. PandaLM enables the evaluation of LLM to be fairer but with less cost, evidenced by significant improvements achieved by models tuned through PandaLM compared to their counterparts trained with default Alpaca's hyperparameters. In addition, PandaLM does not depend on API-based evaluations, thus avoiding potential data leakage. All resources of PandaLM are released at https://github.com/WeOpenML/PandaLM.

The strong performance of large language models (LLMs) on natural language processing tasks raises extensive discussion on their application to code generation. Recent work suggests multiple sampling approaches to improve initial code generation accuracy or program repair approaches to refine the code. However, these methods suffer from LLMs' inefficiencies and limited reasoning capacity. In this work, we propose an LLM programming workflow (LPW) designed to improve both initial code generation and subsequent refinements within a structured two-phase workflow. Specifically, in the solution generation phase, the LLM first outlines a solution plan that decomposes the problem into manageable sub-problems and then verifies the generated solution plan through visible test cases. Subsequently, in the code implementation phase, the LLM initially drafts a code according to the solution plan and its verification. If the generated code fails the visible tests, the plan verification serves as the intended natural language solution to inform the refinement process for correcting bugs. We further introduce SLPW, a sampling variant of LPW, which initially generates multiple solution plans and plan verifications, produces a program for each plan and its verification, and refines each program as necessary until one successfully passes the visible tests. Compared to the state-of-the-art methods across various existing LLMs, our experimental results show that LPW significantly improves the Pass@1 accuracy by up to 16.4% on well-established text-to-code generation benchmarks, especially with a notable improvement of around 10% on challenging benchmarks. Additionally, SLPW demonstrates up to a 5.6% improvement over LPW and sets new state-of-the-art Pass@1 accuracy on various benchmarks, e.g., 98.2% on HumanEval, 84.8% on MBPP, 64.0% on APPS, and 35.3% on CodeContest, using GPT-4o as the backbone.

Combinatorial problems are present in a wide range of industries. Constraint Programming (CP) is a well-suited problem-solving paradigm, but its core process, namely constraint modelling, is a bottleneck for wider adoption. Aiming to alleviate this bottleneck, recent studies have explored using Large Language Models (LLMs) as modelling assistants, transforming combinatorial problem descriptions to executable constraint models, similar to coding assistants. However, the existing evaluation datasets for constraint modelling are often limited to small, homogeneous, or domain-specific instances, which do not capture the diversity of real-world scenarios. This work addresses this gap by introducing CP-Bench, a novel benchmark dataset that includes a diverse set of well-known combinatorial problem classes sourced from the CP community, structured explicitly for evaluating LLM-driven CP modelling. With this dataset, and given the variety of constraint modelling frameworks, we compare and evaluate the modelling capabilities of LLMs for three distinct constraint modelling systems, which vary in abstraction level and underlying syntax: the high-level MiniZinc language and Python-based CPMpy library, and the lower-level Python interface of the OR-Tools CP-SAT solver. In order to enhance the ability of LLMs to produce valid constraint models, we systematically evaluate the use of prompt-based and inference-time compute methods adapted from existing LLM-based code generation research. Our results underscore the modelling convenience provided by Python-based frameworks, as well as the effectiveness of documentation-rich system prompts, which, augmented with repeated sampling and self-verification, achieve further improvements, reaching up to 70\% accuracy on this new, highly challenging benchmark.

Aligning language models with preferences can be posed as approximating a target distribution representing some desired behavior. Existing approaches differ both in the functional form of the target distribution and the algorithm used to approximate it. For instance, Reinforcement Learning from Human Feedback (RLHF) corresponds to minimizing a reverse KL from an implicit target distribution arising from a KL penalty in the objective. On the other hand, Generative Distributional Control (GDC) has an explicit target distribution and minimizes a forward KL from it using the Distributional Policy Gradient (DPG) algorithm. In this paper, we propose a new approach, f-DPG, which allows the use of any f-divergence to approximate any target distribution that can be evaluated. f-DPG unifies both frameworks (RLHF, GDC) and the approximation methods (DPG, RL with KL penalties). We show the practical benefits of various choices of divergence objectives and demonstrate that there is no universally optimal objective but that different divergences present different alignment and diversity trade-offs. We show that Jensen-Shannon divergence strikes a good balance between these objectives, and frequently outperforms forward KL divergence by a wide margin, leading to significant improvements over prior work. These distinguishing characteristics between divergences persist as the model size increases, highlighting the importance of selecting appropriate divergence objectives.

Reward models have been increasingly critical for improving the reasoning capability of LLMs. Existing research has shown that a well-trained reward model can substantially improve model performances at inference time via search. However, the potential of reward models during RL training time still remains largely under-explored. It is currently unclear whether these reward models can provide additional training signals to enhance the reasoning capabilities of LLMs in RL training that uses sparse success rewards, which verify the correctness of solutions. In this work, we evaluate popular reward models for RL training, including the Outcome-supervised Reward Model (ORM) and the Process-supervised Reward Model (PRM), and train a collection of LLMs for math problems using RL by combining these learned rewards with success rewards. Surprisingly, even though these learned reward models have strong inference-time performances, they may NOT help or even hurt RL training, producing worse performances than LLMs trained with the success reward only. Our analysis reveals that an LLM can receive high rewards from some of these reward models by repeating correct but unnecessary reasoning steps, leading to a severe reward hacking issue. Therefore, we introduce two novel reward refinement techniques, including Clipping and Delta. The key idea is to ensure the accumulative reward of any reasoning trajectory is upper-bounded to keep a learned reward model effective without being exploited. We evaluate our techniques with multiple reward models over a set of 1.5B and 7B LLMs on MATH and GSM8K benchmarks and demonstrate that with a carefully designed reward function, RL training without any additional supervised tuning can improve all the evaluated LLMs, including the state-of-the-art 7B LLM Qwen2.5-Math-7B-Instruct on MATH and GSM8K benchmarks.

The process of revising (or constructing) a policy at execution time -- known as decision-time planning -- has been key to achieving superhuman performance in perfect-information games like chess and Go. A recent line of work has extended decision-time planning to imperfect-information games, leading to superhuman performance in poker. However, these methods involve solving subgames whose sizes grow quickly in the amount of non-public information, making them unhelpful when the amount of non-public information is large. Motivated by this issue, we introduce an alternative framework for decision-time planning that is not based on solving subgames, but rather on update equivalence. In this update-equivalence framework, decision-time planning algorithms replicate the updates of last-iterate algorithms, which need not rely on public information. This facilitates scalability to games with large amounts of non-public information. Using this framework, we derive a provably sound search algorithm for fully cooperative games based on mirror descent and a search algorithm for adversarial games based on magnetic mirror descent. We validate the performance of these algorithms in cooperative and adversarial domains, notably in Hanabi, the standard benchmark for search in fully cooperative imperfect-information games. Here, our mirror descent approach exceeds or matches the performance of public information-based search while using two orders of magnitude less search time. This is the first instance of a non-public-information-based algorithm outperforming public-information-based approaches in a domain they have historically dominated.

Recently, an intriguing class of non-convex optimization problems has emerged in the context of learning directed acyclic graphs (DAGs). These problems involve minimizing a given loss or score function, subject to a non-convex continuous constraint that penalizes the presence of cycles in a graph. In this work, we delve into the optimization challenges associated with this class of non-convex programs. To address these challenges, we propose a bi-level algorithm that leverages the non-convex constraint in a novel way. The outer level of the algorithm optimizes over topological orders by iteratively swapping pairs of nodes within the topological order of a DAG. A key innovation of our approach is the development of an effective method for generating a set of candidate swapping pairs for each iteration. At the inner level, given a topological order, we utilize off-the-shelf solvers that can handle linear constraints. The key advantage of our proposed algorithm is that it is guaranteed to find a local minimum or a KKT point under weaker conditions compared to previous work and finds solutions with lower scores. Extensive experiments demonstrate that our method outperforms state-of-the-art approaches in terms of achieving a better score. Additionally, our method can also be used as a post-processing algorithm to significantly improve the score of other algorithms. Code implementing the proposed method is available at https://github.com/duntrain/topo.

Recent direct preference alignment algorithms (DPA), such as DPO, have shown great promise in aligning large language models to human preferences. While this has motivated the development of many new variants of the original DPO loss, understanding the differences between these recent proposals, as well as developing new DPA loss functions, remains difficult given the lack of a technical and conceptual framework for reasoning about the underlying semantics of these algorithms. In this paper, we attempt to remedy this by formalizing DPA losses in terms of discrete reasoning problems. Specifically, we ask: Given an existing DPA loss, can we systematically derive a symbolic expression that characterizes its semantics? How do the semantics of two losses relate to each other? We propose a novel formalism for characterizing preference losses for single model and reference model based approaches, and identify symbolic forms for a number of commonly used DPA variants. Further, we show how this formal view of preference learning sheds new light on both the size and structure of the DPA loss landscape, making it possible to not only rigorously characterize the relationships between recent loss proposals but also to systematically explore the landscape and derive new loss functions from first principles. We hope our framework and findings will help provide useful guidance to those working on human AI alignment.

Large language models (LLMs) have recently demonstrated remarkable progress in formal theorem proving. Yet their ability to serve as practical assistants for mathematicians, filling in missing steps within complex proofs, remains underexplored. We identify this challenge as the task of subgoal completion, where an LLM must discharge short but nontrivial proof obligations left unresolved in a human-provided sketch. To study this problem, we introduce FormalML, a Lean 4 benchmark built from foundational theories of machine learning. Using a translation tactic that converts procedural proofs into declarative form, we extract 4937 problems spanning optimization and probability inequalities, with varying levels of difficulty. FormalML is the first subgoal completion benchmark to combine premise retrieval and complex research-level contexts. Evaluation of state-of-the-art provers highlights persistent limitations in accuracy and efficiency, underscoring the need for more capable LLM-based theorem provers for effective subgoal completion,

General-purpose Large Language Models (LLMs) have achieved remarkable success in intelligence, performing comparably to human experts on complex reasoning tasks such as coding and mathematical reasoning. However, generating formal proofs in specialized languages like Lean 4 remains a significant challenge for these models, limiting their application in complex theorem proving and automated verification. Current approaches typically require specializing models through fine-tuning on dedicated formal corpora, incurring high costs for data collection and training. In this work, we introduce Delta Prover, an agent-based framework that orchestrates the interaction between a general-purpose LLM and the Lean 4 proof environment. Delta Prover leverages the reflection and reasoning capabilities of general-purpose LLMs to interactively construct formal proofs in Lean 4, circumventing the need for model specialization. At its core, the agent integrates two novel, interdependent components: an algorithmic framework for reflective decomposition and iterative proof repair, and a custom Domain-Specific Language (DSL) built upon Lean 4 for streamlined subproblem management. Delta Prover achieves a state-of-the-art 95.9\% success rate on the miniF2F-test benchmark, surpassing all existing approaches, including those requiring model specialization. Furthermore, Delta Prover exhibits a significantly stronger test-time scaling law compared to standard Best-of-N proof strategies. Crucially, our findings demonstrate that general-purpose LLMs, when guided by an effective agentic structure, possess substantial untapped theorem-proving capabilities. This presents a computationally efficient alternative to specialized models for robust automated reasoning in formal environments.

While test-time reasoning enables language models to tackle complex tasks, searching or planning in natural language can be slow, costly, and error-prone. But even when LMs struggle to emulate the precise reasoning steps needed to solve a problem, they often excel at describing its abstract structure--both how to verify solutions and how to search for them. This paper introduces DisCIPL, a method for "self-steering" LMs where a Planner model generates a task-specific inference program that is executed by a population of Follower models. Our approach equips LMs with the ability to write recursive search procedures that guide LM inference, enabling new forms of verifiable and efficient reasoning. When instantiated with a small Follower (e.g., Llama-3.2-1B), DisCIPL matches (and sometimes outperforms) much larger models, including GPT-4o and o1, on challenging constrained generation tasks. In decoupling planning from execution, our work opens up a design space of highly-parallelized Monte Carlo inference strategies that outperform standard best-of-N sampling, require no finetuning, and can be implemented automatically by existing LMs.

We study the problem of (learning) algorithm comparison, where the goal is to find differences between models trained with two different learning algorithms. We begin by formalizing this goal as one of finding distinguishing feature transformations, i.e., input transformations that change the predictions of models trained with one learning algorithm but not the other. We then present ModelDiff, a method that leverages the datamodels framework (Ilyas et al., 2022) to compare learning algorithms based on how they use their training data. We demonstrate ModelDiff through three case studies, comparing models trained with/without data augmentation, with/without pre-training, and with different SGD hyperparameters. Our code is available at https://github.com/MadryLab/modeldiff .

Mathematical reasoning is a crucial capability for Large Language Models (LLMs), yet generating detailed and accurate reasoning traces remains a significant challenge. This paper introduces a novel approach to produce high-quality reasoning traces for LLM fine-tuning using online learning Flows. Our method employs an incremental output production Flow, where component LLMs collaboratively construct solutions through iterative communication. We train the Flow using online Direct Preference Optimization (DPO) learning with rollouts, generating DPO pairs for each training example and updating models in real-time. We directly compare the quality of reasoning traces generated by our method with those produced through direct model inference, demonstrating the effectiveness of our approach in improving LLM performance in mathematical reasoning tasks.

JSON Schema is an important, evolving standard schema language for families of JSON documents. It is based on a complex combination of structural and Boolean assertions, and features negation and recursion. The static analysis of JSON Schema documents comprises practically relevant problems, including schema satisfiability, inclusion, and equivalence. These three problems can be reduced to witness generation: given a schema, generate an element of the schema, if it exists, and report failure otherwise. Schema satisfiability, inclusion, and equivalence have been shown to be decidable, by reduction to reachability in alternating tree automata. However, no witness generation algorithm has yet been formally described. We contribute a first, direct algorithm for JSON Schema witness generation. We study its effectiveness and efficiency, in experiments over several schema collections, including thousands of real-world schemas. Our focus is on the completeness of the language, where we only exclude the uniqueItems operator, and on the ability of the algorithm to run in a reasonable time on a large set of real-world examples, despite the exponential complexity of the underlying problem.

Training autonomous agents able to generalize to multiple tasks is a key target of Deep Reinforcement Learning (DRL) research. In parallel to improving DRL algorithms themselves, Automatic Curriculum Learning (ACL) study how teacher algorithms can train DRL agents more efficiently by adapting task selection to their evolving abilities. While multiple standard benchmarks exist to compare DRL agents, there is currently no such thing for ACL algorithms. Thus, comparing existing approaches is difficult, as too many experimental parameters differ from paper to paper. In this work, we identify several key challenges faced by ACL algorithms. Based on these, we present TeachMyAgent (TA), a benchmark of current ACL algorithms leveraging procedural task generation. It includes 1) challenge-specific unit-tests using variants of a procedural Box2D bipedal walker environment, and 2) a new procedural Parkour environment combining most ACL challenges, making it ideal for global performance assessment. We then use TeachMyAgent to conduct a comparative study of representative existing approaches, showcasing the competitiveness of some ACL algorithms that do not use expert knowledge. We also show that the Parkour environment remains an open problem. We open-source our environments, all studied ACL algorithms (collected from open-source code or re-implemented), and DRL students in a Python package available at https://github.com/flowersteam/TeachMyAgent.

As large language models (LLMs) reach high scores on established mathematical benchmarks, such as GSM8K and MATH, the research community has turned to International Mathematical Olympiad (IMO) problems to push the evaluation frontier. However, existing Olympiad-level benchmarks suffer from practical constraints that introduce grading noise and potential bias, such as heterogeneous answer formats requiring model-based judges and a reliance on potentially flawed solutions. We introduce RIMO, a two-track benchmark designed to preserve peak Olympiad difficulty while eliminating this evaluation noise. The first track, RIMO-N, rewrites 335 IMO problems to admit a single, unique integer answer, allowing for deterministic correctness checking. The second track, RIMO-P, features 456 proof problems with expert-checked solutions, which are decomposed into a sequence of sub-problems to evaluate the step-by-step reasoning process via an automated grading system. Our benchmarking of ten frontier LLMs, including GPT-4o and Gemini 2.5 Flash, reveals that while these systems excel on older benchmarks, their performance drops sharply on RIMO. These results highlight a substantial gap between current LLM capabilities and actual Olympiad-level reasoning. By providing a challenging yet easy-to-evaluate suite, RIMO offers a high-resolution yardstick for future research, presenting a clear target for closing the profound reasoning gap our findings expose.

Visual programming languages (VPLs) allow users to create programs through graphical interfaces, which results in easier accessibility and their widespread usage in various domains. To further enhance this accessibility, recent research has focused on generating VPL code from user instructions using large language models (LLMs). Specifically, by employing prompting-based methods, these studies have shown promising results. Nevertheless, such approaches can be less effective for industrial VPLs such as Ladder Diagram (LD). LD is a pivotal language used in industrial automation processes and involves extensive domain-specific configurations, which are difficult to capture in a single prompt. In this work, we demonstrate that training-based methods outperform prompting-based methods for LD generation accuracy, even with smaller backbone models. Building on these findings, we propose a two-stage training strategy to further enhance VPL generation. First, we employ retrieval-augmented fine-tuning to leverage the repetitive use of subroutines commonly seen in industrial VPLs. Second, we apply direct preference optimization (DPO) to further guide the model toward accurate outputs, using systematically generated preference pairs through graph editing operations. Extensive experiments on real-world LD data demonstrate that our approach improves program-level accuracy by over 10% compared to supervised fine-tuning, which highlights its potential to advance industrial automation.

Reinforcement Learning from Human Feedback (RLHF) is currently the most widely used method to align large language models (LLMs) with human preferences. Existing RLHF methods can be roughly categorized as either reward-based or reward-free. Novel applications such as ChatGPT and Claude leverage reward-based methods that first learn a reward model and apply actor-critic algorithms, such as Proximal Policy Optimization (PPO). However, in academic benchmarks, state-of-the-art results are often achieved via reward-free methods, such as Direct Preference Optimization (DPO). Is DPO truly superior to PPO? Why does PPO perform poorly on these benchmarks? In this paper, we first conduct both theoretical and empirical studies on the algorithmic properties of DPO and show that DPO may have fundamental limitations. Moreover, we also comprehensively examine PPO and reveal the key factors for the best performances of PPO in fine-tuning LLMs. Finally, we benchmark DPO and PPO across various a collection of RLHF testbeds, ranging from dialogue to code generation. Experiment results demonstrate that PPO is able to surpass other alignment methods in all cases and achieve state-of-the-art results in challenging code competitions.

The controllable generation of diffusion models aims to steer the model to generate samples that optimize some given objective functions. It is desirable for a variety of applications including image generation, molecule generation, and DNA/sequence generation. Reinforcement Learning (RL) based fine-tuning of the base model is a popular approach but it can overfit the reward function while requiring significant resources. We frame controllable generation as a problem of finding a distribution that optimizes a KL-regularized objective function. We present SLCD -- Supervised Learning based Controllable Diffusion, which iteratively generates online data and trains a small classifier to guide the generation of the diffusion model. Similar to the standard classifier-guided diffusion, SLCD's key computation primitive is classification and does not involve any complex concepts from RL or control. Via a reduction to no-regret online learning analysis, we show that under KL divergence, the output from SLCD provably converges to the optimal solution of the KL-regularized objective. Further, we empirically demonstrate that SLCD can generate high quality samples with nearly the same inference time as the base model in both image generation with continuous diffusion and biological sequence generation with discrete diffusion. Our code is available at https://github.com/Owen-Oertell/slcd

This work studies the challenge of aligning large language models (LLMs) with offline preference data. We focus on alignment by Reinforcement Learning from Human Feedback (RLHF) in particular. While popular preference optimization methods exhibit good empirical performance in practice, they are not theoretically guaranteed to converge to the optimal policy and can provably fail when the data coverage is sparse by classical offline reinforcement learning (RL) results. On the other hand, a recent line of work has focused on theoretically motivated preference optimization methods with provable guarantees, but these are not computationally efficient for large-scale applications like LLM alignment. To bridge this gap, we propose SPAC, a new offline preference optimization method with self-play, inspired by the on-average pessimism technique from the offline RL literature, to be the first provable and scalable approach to LLM alignment. We both provide theoretical analysis for its convergence under single-policy concentrability for the general function approximation setting and demonstrate its competitive empirical performance for LLM alignment on a 7B Mistral model with Open LLM Leaderboard evaluations.

Large language models (LLMs) have shown increasing competence in solving mathematical reasoning problems. However, many open-source LLMs still struggle with errors in calculation and semantic understanding during intermediate reasoning steps. In this work, we introduce Prove, a simple yet effective framework that leverages translated programs derived from natural language solutions as a verification mechanism to filter out potentially incorrect reasoning paths before aggregating final answers. Unlike vanilla majority voting, our approach filters out solutions whose corresponding program output is inconsistent with the generated solution, aggregating only those that pass verification. We conducted extensive experiments using 13 open-source LLMs from various model families and sizes, ranging from 0.5B to 13B parameters, across eight mathematical benchmarks. Our results show that Prove consistently outperforms vanilla majority voting as a heuristic for solving mathematical reasoning tasks across all model sizes and datasets, achieving improvements of up to 18% on GSM8K and 8% on MATH-500. Our codes are available at https://github.com/declare-lab/prove.

Tensor network (TN) is a powerful framework in machine learning, but selecting a good TN model, known as TN structure search (TN-SS), is a challenging and computationally intensive task. The recent approach TNLS~li2022permutation showed promising results for this task, however, its computational efficiency is still unaffordable, requiring too many evaluations of the objective function. We propose TnALE, a new algorithm that updates each structure-related variable alternately by local enumeration, greatly reducing the number of evaluations compared to TNLS. We theoretically investigate the descent steps for TNLS and TnALE, proving that both algorithms can achieve linear convergence up to a constant if a sufficient reduction of the objective is reached in each neighborhood. We also compare the evaluation efficiency of TNLS and TnALE, revealing that Omega(2^N) evaluations are typically required in TNLS for reaching the objective reduction in the neighborhood, while ideally O(N^2R) evaluations are sufficient in TnALE, where N denotes the tensor order and R reflects the ``low-rankness'' of the neighborhood. Experimental results verify that TnALE can find practically good TN-ranks and permutations with vastly fewer evaluations than the state-of-the-art algorithms.

Reward models are central to aligning LLMs with human preferences, but they are costly to train, requiring large-scale human-labeled preference data and powerful pretrained LLM backbones. Meanwhile, the increasing availability of high-quality synthetic instruction-following datasets raises the question: can simpler, reference-based metrics serve as viable alternatives to reward models during RL-based alignment? In this paper, we show first that BLEU, a basic string-matching metric, surprisingly matches strong reward models in agreement with human preferences on general instruction-following datasets. Based on this insight, we develop BLEUBERI, a method that first identifies challenging instructions and then applies Group Relative Policy Optimization (GRPO) using BLEU directly as the reward function. We demonstrate that BLEUBERI-trained models are competitive with models trained via reward model-guided RL across four challenging instruction-following benchmarks and three different base language models. A human evaluation further supports that the quality of BLEUBERI model outputs is on par with those from reward model-aligned models. Moreover, BLEUBERI models generate outputs that are more factually grounded than competing methods. Overall, we show that given access to high-quality reference outputs (easily obtained via existing instruction-following datasets or synthetic data generation), string matching-based metrics are cheap yet effective proxies for reward models during alignment. We release our code and data at https://github.com/lilakk/BLEUBERI.

There has been considerable divergence of opinion on the reasoning abilities of Large Language Models (LLMs). While the initial optimism that reasoning might emerge automatically with scale has been tempered thanks to a slew of counterexamples, a wide spread belief in their iterative self-critique capabilities persists. In this paper, we set out to systematically investigate the effectiveness of iterative prompting of LLMs in the context of Graph Coloring, a canonical NP-complete reasoning problem that is related to propositional satisfiability as well as practical problems like scheduling and allocation. We present a principled empirical study of the performance of GPT4 in solving graph coloring instances or verifying the correctness of candidate colorings. In iterative modes, we experiment with the model critiquing its own answers and an external correct reasoner verifying proposed solutions. In both cases, we analyze whether the content of the criticisms actually affects bottom line performance. The study seems to indicate that (i) LLMs are bad at solving graph coloring instances (ii) they are no better at verifying a solution--and thus are not effective in iterative modes with LLMs critiquing LLM-generated solutions (iii) the correctness and content of the criticisms--whether by LLMs or external solvers--seems largely irrelevant to the performance of iterative prompting. We show that the observed increase in effectiveness is largely due to the correct solution being fortuitously present in the top-k completions of the prompt (and being recognized as such by an external verifier). Our results thus call into question claims about the self-critiquing capabilities of state of the art LLMs.

Process Reward Models (PRMs), which provide step-by-step feedback on the reasoning generated by Large Language Models (LLMs), are receiving increasing attention. However, two key research gaps remain: collecting accurate step-level error labels for training typically requires costly human annotation, and existing PRMs are limited to math reasoning problems. In response to these gaps, this paper aims to address the challenges of automatic dataset creation and the generalization of PRMs to diverse reasoning tasks. To achieve this goal, we propose FoVer, an approach for training PRMs on step-level error labels automatically annotated by formal verification tools, such as Z3 for formal logic and Isabelle for theorem proof, which provide automatic and accurate verification for symbolic tasks. Using this approach, we synthesize a training dataset with error labels on LLM responses for formal logic and theorem proof tasks without human annotation. Although this data synthesis is feasible only for tasks compatible with formal verification, we observe that LLM-based PRMs trained on our dataset exhibit cross-task generalization, improving verification across diverse reasoning tasks. Specifically, PRMs trained with FoVer significantly outperform baseline PRMs based on the original LLMs and achieve competitive or superior results compared to state-of-the-art PRMs trained on labels annotated by humans or stronger models, as measured by step-level verification on ProcessBench and Best-of-K performance across 12 reasoning benchmarks, including MATH, AIME, ANLI, MMLU, and BBH. The datasets, models, and code are provided at https://github.com/psunlpgroup/FoVer.

Recent advancements in post-training methodologies for large language models (LLMs) have highlighted reinforcement learning (RL) as a critical component for enhancing reasoning. However, the substantial computational costs associated with RL-based approaches have led to growing interest in alternative paradigms, such as Direct Preference Optimization (DPO). In this study, we investigate the effectiveness of DPO in facilitating self-improvement for LLMs through iterative preference-based learning. We demonstrate that a single round of DPO with coarse filtering significantly enhances mathematical reasoning performance, particularly for strong base model. Furthermore, we design an iterative enhancement framework for both the generator and the reward model (RM), enabling their mutual improvement through online interaction across multiple rounds of DPO. Finally, with simple verifiable rewards, our model DPO-VP achieves RL-level performance with significantly lower computational overhead. These findings highlight DPO as a scalable and cost-effective alternative to RL, offering a practical solution for enhancing LLM reasoning in resource-constrained situations.

Reinforcement Learning From Human Feedback (RLHF) has been a critical to the success of the latest generation of generative AI models. In response to the complex nature of the classical RLHF pipeline, direct alignment algorithms such as Direct Preference Optimization (DPO) have emerged as an alternative approach. Although DPO solves the same objective as the standard RLHF setup, there is a mismatch between the two approaches. Standard RLHF deploys reinforcement learning in a specific token-level MDP, while DPO is derived as a bandit problem in which the whole response of the model is treated as a single arm. In this work we rectify this difference, first we theoretically show that we can derive DPO in the token-level MDP as a general inverse Q-learning algorithm, which satisfies the Bellman equation. Using our theoretical results, we provide three concrete empirical insights. First, we show that because of its token level interpretation, DPO is able to perform some type of credit assignment. Next, we prove that under the token level formulation, classical search-based algorithms, such as MCTS, which have recently been applied to the language generation space, are equivalent to likelihood-based search on a DPO policy. Empirically we show that a simple beam search yields meaningful improvement over the base DPO policy. Finally, we show how the choice of reference policy causes implicit rewards to decline during training. We conclude by discussing applications of our work, including information elicitation in multi-tun dialogue, reasoning, agentic applications and end-to-end training of multi-model systems.

Leveraging mathematical Large Language Models (LLMs) for proof generation is a fundamental topic in LLMs research. We argue that the ability of current LLMs to prove statements largely depends on whether they have encountered the relevant proof process during training. This reliance limits their deeper understanding of mathematical theorems and related concepts. Inspired by the pedagogical method of "proof by counterexamples" commonly used in human mathematics education, our work aims to enhance LLMs' ability to conduct mathematical reasoning and proof through counterexamples. Specifically, we manually create a high-quality, university-level mathematical benchmark, CounterMATH, which requires LLMs to prove mathematical statements by providing counterexamples, thereby assessing their grasp of mathematical concepts. Additionally, we develop a data engineering framework to automatically obtain training data for further model improvement. Extensive experiments and detailed analyses demonstrate that CounterMATH is challenging, indicating that LLMs, such as OpenAI o1, have insufficient counterexample-driven proof capabilities. Moreover, our exploration into model training reveals that strengthening LLMs' counterexample-driven conceptual reasoning abilities is crucial for improving their overall mathematical capabilities. We believe that our work offers new perspectives on the community of mathematical LLMs.

Large language model (LLM) evaluations typically rely on aggregated metrics like accuracy or human preference, averaging across users and prompts. This averaging obscures user- and prompt-specific variations in model performance. To address this, we propose Prompt-to-Leaderboard (P2L), a method that produces leaderboards specific to a prompt. The core idea is to train an LLM taking natural language prompts as input to output a vector of Bradley-Terry coefficients which are then used to predict the human preference vote. The resulting prompt-dependent leaderboards allow for unsupervised task-specific evaluation, optimal routing of queries to models, personalization, and automated evaluation of model strengths and weaknesses. Data from Chatbot Arena suggest that P2L better captures the nuanced landscape of language model performance than the averaged leaderboard. Furthermore, our findings suggest that P2L's ability to produce prompt-specific evaluations follows a power law scaling similar to that observed in LLMs themselves. In January 2025, the router we trained based on this methodology achieved the \#1 spot in the Chatbot Arena leaderboard. Our code is available at this GitHub link: https://github.com/lmarena/p2l.

We provide a theoretical framework for Reinforcement Learning with Human Feedback (RLHF). Our analysis shows that when the true reward function is linear, the widely used maximum likelihood estimator (MLE) converges under both the Bradley-Terry-Luce (BTL) model and the Plackett-Luce (PL) model. However, we show that when training a policy based on the learned reward model, MLE fails while a pessimistic MLE provides policies with improved performance under certain coverage assumptions. Additionally, we demonstrate that under the PL model, the true MLE and an alternative MLE that splits the K-wise comparison into pairwise comparisons both converge. Moreover, the true MLE is asymptotically more efficient. Our results validate the empirical success of existing RLHF algorithms in InstructGPT and provide new insights for algorithm design. Furthermore, our results unify the problem of RLHF and max-entropy Inverse Reinforcement Learning (IRL), and provide the first sample complexity bound for max-entropy IRL.

Large language models (LLMs) demonstrate remarkable reasoning capabilities in tasks such as algorithmic coding and mathematical problem-solving. Recent methods have improved reasoning through expanded corpus and multistage training combining reinforcement learning and supervised fine-tuning. Although some methods suggest that small but targeted dataset can incentivize reasoning via only distillation, a reasoning scaling laws is still taking shape, increasing computational costs. To address this, we propose a data-efficient distillation framework (DED) that optimizes the Pareto frontier of reasoning distillation. Inspired by the on-policy learning and diverse roll-out strategies of reinforcement learning, the key idea of our approach is threefold: (1) We identify that benchmark scores alone do not determine an effective teacher model. Through comprehensive comparisons of leading reasoning LLMs, we develop a method to select an optimal teacher model. (2) While scaling distillation can enhance reasoning, it often degrades out-of-domain performance. A carefully curated, smaller corpus achieves a balanced trade-off between in-domain and out-of-domain capabilities. (3) Diverse reasoning trajectories encourage the student model to develop robust reasoning skills. We validate our method through evaluations on mathematical reasoning (AIME 2024/2025, MATH-500) and code generation (LiveCodeBench), achieving state-of-the-art results with only 0.8k carefully curated examples, bypassing the need for extensive scaling. Our systematic analysis demonstrates that DED outperforms existing methods by considering factors beyond superficial hardness, token length, or teacher model capability. This work offers a practical and efficient pathway to advanced reasoning while preserving general capabilities.

Aligning large language models (LLMs) with human preference has recently gained tremendous attention, with the canonical yet costly RLHF-PPO and the simple and straightforward Direct Preference Optimization (DPO) as two examples. Despite the efficiency, DPO has rarely be used in the state-of-the-art production-level LLMs, implying its potential pathologies. In this work, we revisit DPO with a comprehensive examination of its empirical efficacy and a systematic comparison with RLHF-PPO. We identify the 3D-properties of DPO's learning outcomes: the Drastic drop in the likelihood of rejected responses, the Degradation into LLM unlearning, and the Dispersion effect on unseen responses through experiments with both a carefully designed toy model and practical LLMs on tasks including mathematical problem-solving and instruction following. These findings inherently connect to some observations made by related works and we additionally contribute a plausible theoretical explanation for them. Accordingly, we propose easy regularization methods to mitigate the issues caused by 3D-properties, improving the training stability and final performance of DPO. Our contributions also include an investigation into how the distribution of the paired preference data impacts the effectiveness of DPO. We hope this work could offer research directions to narrow the gap between reward-free preference learning methods and reward-based ones.

We introduce an approach aimed at enhancing the reasoning capabilities of Large Language Models (LLMs) through an iterative preference learning process inspired by the successful strategy employed by AlphaZero. Our work leverages Monte Carlo Tree Search (MCTS) to iteratively collect preference data, utilizing its look-ahead ability to break down instance-level rewards into more granular step-level signals. To enhance consistency in intermediate steps, we combine outcome validation and stepwise self-evaluation, continually updating the quality assessment of newly generated data. The proposed algorithm employs Direct Preference Optimization (DPO) to update the LLM policy using this newly generated step-level preference data. Theoretical analysis reveals the importance of using on-policy sampled data for successful self-improving. Extensive evaluations on various arithmetic and commonsense reasoning tasks demonstrate remarkable performance improvements over existing models. For instance, our approach outperforms the Mistral-7B Supervised Fine-Tuning (SFT) baseline on GSM8K, MATH, and ARC-C, with substantial increases in accuracy to 81.8% (+5.9%), 34.7% (+5.8%), and 76.4% (+15.8%), respectively. Additionally, our research delves into the training and inference compute tradeoff, providing insights into how our method effectively maximizes performance gains. Our code is publicly available at https://github.com/YuxiXie/MCTS-DPO.

Recent advancements in reinforcement learning from human feedback have shown that utilizing fine-grained token-level reward models can substantially enhance the performance of Proximal Policy Optimization (PPO) in aligning large language models. However, it is challenging to leverage such token-level reward as guidance for Direct Preference Optimization (DPO), since DPO is formulated as a sequence-level bandit problem. To address this challenge, this work decomposes the sequence-level PPO into a sequence of token-level proximal policy optimization problems and then frames the problem of token-level PPO with token-level reward guidance, from which closed-form optimal token-level policy and the corresponding token-level reward can be derived. Using the obtained reward and Bradley-Terry model, this work establishes a framework of computable loss functions with token-level reward guidance for DPO, and proposes a practical reward guidance based on the induced DPO reward. This formulation enables different tokens to exhibit varying degrees of deviation from reference policy based on their respective rewards. Experiment results demonstrate that our method achieves substantial performance improvements over DPO, with win rate gains of up to 7.5 points on MT-Bench, 6.2 points on AlpacaEval 2, and 4.3 points on Arena-Hard. Code is available at https://github.com/dvlab-research/TGDPO.

This paper studies post-training large language models (LLMs) using preference feedback from a powerful oracle to help a model iteratively improve over itself. The typical approach for post-training LLMs involves Reinforcement Learning from Human Feedback (RLHF), which traditionally separates reward learning and subsequent policy optimization. However, such a reward maximization approach is limited by the nature of "point-wise" rewards (such as Bradley-Terry model), which fails to express complex intransitive or cyclic preference relations. While advances on RLHF show reward learning and policy optimization can be merged into a single contrastive objective for stability, they yet still remain tethered to the reward maximization framework. Recently, a new wave of research sidesteps the reward maximization presumptions in favor of directly optimizing over "pair-wise" or general preferences. In this paper, we introduce Direct Nash Optimization (DNO), a provable and scalable algorithm that marries the simplicity and stability of contrastive learning with theoretical generality from optimizing general preferences. Because DNO is a batched on-policy algorithm using a regression-based objective, its implementation is straightforward and efficient. Moreover, DNO enjoys monotonic improvement across iterations that help it improve even over a strong teacher (such as GPT-4). In our experiments, a resulting 7B parameter Orca-2.5 model aligned by DNO achieves the state-of-the-art win-rate against GPT-4-Turbo of 33% on AlpacaEval 2.0 (even after controlling for response length), an absolute gain of 26% (7% to 33%) over the initializing model. It outperforms models with far more parameters, including Mistral Large, Self-Rewarding LM (70B parameters), and older versions of GPT-4.

In this paper, we present a novel approach, called LogicPro, to enhance Large Language Models (LLMs) complex Logical reasoning through Program Examples. We do this effectively by simply utilizing widely available algorithmic problems and their code solutions. First, we constructed diverse test samples input based on algorithmic questions and code solutions. Then, we designed different complex reasoning questions based on algorithmic problems and test samples. Finally, combining the intermediate variable outputs of the code solutions and the complex reasoning questions, we derived the reasoning process and the final answer. With this approach, we can construct a dataset that is sufficiently difficult (all models are ineffective), diverse (synthesized from 2,360 different algorithmic questions), and scalable (building different test samples and collecting more algorithmic questions). In addition, we obtain a high-quality reasoning process guided by the values of intermediate variables. As a result, our approach achieves significant improvements in multiple models for the BBH^{27}, GSM8K, HellSwag, Logicqa, Reclor, and RTE datasets, outperforming a wide range of existing reasoning datasets.

Reinforcement Learning (RL) has been used to finetune Large Language Models (LLMs) using a reward model trained from preference data, to better align with human judgment. The recently introduced direct alignment methods, which are often simpler, more stable, and computationally lighter, can more directly achieve this. However, these approaches cannot optimize arbitrary rewards, and the preference-based ones are not the only rewards of interest for LLMs (eg., unit tests for code generation or textual entailment for summarization, among others). RL-finetuning is usually done with a variation of policy gradient, which calls for on-policy or near-on-policy samples, requiring costly generations. We introduce Contrastive Policy Gradient, or CoPG, a simple and mathematically principled new RL algorithm that can estimate the optimal policy even from off-policy data. It can be seen as an off-policy policy gradient approach that does not rely on important sampling techniques and highlights the importance of using (the right) state baseline. We show this approach to generalize the direct alignment method IPO (identity preference optimization) and classic policy gradient. We experiment with the proposed CoPG on a toy bandit problem to illustrate its properties, as well as for finetuning LLMs on a summarization task, using a learned reward function considered as ground truth for the purpose of the experiments.

We propose a new class of online learning algorithms, generalized implicit Follow-The-Regularized-Leader (FTRL), that expands the scope of FTRL framework. Generalized implicit FTRL can recover known algorithms, as FTRL with linearized losses and implicit FTRL, and it allows the design of new update rules, as extensions of aProx and Mirror-Prox to FTRL. Our theory is constructive in the sense that it provides a simple unifying framework to design updates that directly improve the worst-case upper bound on the regret. The key idea is substituting the linearization of the losses with a Fenchel-Young inequality. We show the flexibility of the framework by proving that some known algorithms, like the Mirror-Prox updates, are instantiations of the generalized implicit FTRL. Finally, the new framework allows us to recover the temporal variation bound of implicit OMD, with the same computational complexity.

This paper presents Post-Decision Proximal Policy Optimization (PDPPO), a novel variation of the leading deep reinforcement learning method, Proximal Policy Optimization (PPO). The PDPPO state transition process is divided into two steps: a deterministic step resulting in the post-decision state and a stochastic step leading to the next state. Our approach incorporates post-decision states and dual critics to reduce the problem's dimensionality and enhance the accuracy of value function estimation. Lot-sizing is a mixed integer programming problem for which we exemplify such dynamics. The objective of lot-sizing is to optimize production, delivery fulfillment, and inventory levels in uncertain demand and cost parameters. This paper evaluates the performance of PDPPO across various environments and configurations. Notably, PDPPO with a dual critic architecture achieves nearly double the maximum reward of vanilla PPO in specific scenarios, requiring fewer episode iterations and demonstrating faster and more consistent learning across different initializations. On average, PDPPO outperforms PPO in environments with a stochastic component in the state transition. These results support the benefits of using a post-decision state. Integrating this post-decision state in the value function approximation leads to more informed and efficient learning in high-dimensional and stochastic environments.

Large Reasoning Models (LRMs) have shown remarkable capabilities in solving complex problems through reinforcement learning (RL), particularly by generating long reasoning traces. However, these extended outputs often exhibit substantial redundancy, which limits the efficiency of LRMs. In this paper, we investigate RL-based approaches to promote reasoning efficiency. Specifically, we first present a unified framework that formulates various efficient reasoning methods through the lens of length-based reward shaping. Building on this perspective, we propose a novel Length-bAsed StEp Reward shaping method (LASER), which employs a step function as the reward, controlled by a target length. LASER surpasses previous methods, achieving a superior Pareto-optimal balance between performance and efficiency. Next, we further extend LASER based on two key intuitions: (1) The reasoning behavior of the model evolves during training, necessitating reward specifications that are also adaptive and dynamic; (2) Rather than uniformly encouraging shorter or longer chains of thought (CoT), we posit that length-based reward shaping should be difficulty-aware i.e., it should penalize lengthy CoTs more for easy queries. This approach is expected to facilitate a combination of fast and slow thinking, leading to a better overall tradeoff. The resulting method is termed LASER-D (Dynamic and Difficulty-aware). Experiments on DeepSeek-R1-Distill-Qwen-1.5B, DeepSeek-R1-Distill-Qwen-7B, and DeepSeek-R1-Distill-Qwen-32B show that our approach significantly enhances both reasoning performance and response length efficiency. For instance, LASER-D and its variant achieve a +6.1 improvement on AIME2024 while reducing token usage by 63%. Further analysis reveals our RL-based compression produces more concise reasoning patterns with less redundant "self-reflections". Resources are at https://github.com/hkust-nlp/Laser.

Even though large language models are becoming increasingly capable, it is still unreasonable to expect them to excel at tasks that are under-represented on the Internet. Leveraging LLMs for specialized applications, particularly in niche programming languages and private domains, remains challenging and largely unsolved. In this work, we address this gap by presenting a comprehensive, open-source approach for adapting LLMs to the Q programming language, a popular tool in quantitative finance that is much less present on the Internet compared to Python, C, Java, and other ``mainstream" languages and is therefore not a strong suit of general-purpose AI models. We introduce a new Leetcode style evaluation dataset for Q, benchmark major frontier models on the dataset, then do pretraining, supervised fine tuning, and reinforcement learning to train a suite of reasoning and non-reasoning models based on the Qwen-2.5 series, spanning five parameter sizes (1.5B, 3B, 7B, 14B, 32B). Our best model achieves a pass@1 accuracy of 59 percent on our Q benchmark, surpassing the best-performing frontier model, Claude Opus-4 by 29.5 percent. Additionally, all models, even our 1.5B model, outperform GPT-4.1 on this task. In addition to releasing models, code, and data, we provide a detailed blueprint for dataset construction, model pretraining, supervised fine-tuning, and reinforcement learning. Our methodology is broadly applicable, and we discuss how these techniques can be extended to other tasks, including those where evaluation may rely on soft or subjective signals.

The Bourne-Again Shell (Bash) command-line interface for Linux systems has complex syntax and requires extensive specialized knowledge. Using the natural language to Bash command (NL2SH) translation capabilities of large language models (LLMs) for command composition circumvents these issues. However, the NL2SH performance of LLMs is difficult to assess due to inaccurate test data and unreliable heuristics for determining the functional equivalence of Bash commands. We present a manually verified test dataset of 600 instruction-command pairs and a training dataset of 40,939 pairs, increasing the size of previous datasets by 441% and 135%, respectively. Further, we present a novel functional equivalence heuristic that combines command execution with LLM evaluation of command outputs. Our heuristic can determine the functional equivalence of two Bash commands with 95% confidence, a 16% increase over previous heuristics. Evaluation of popular LLMs using our test dataset and heuristic demonstrates that parsing, in-context learning, in-weight learning, and constrained decoding can improve NL2SH accuracy by up to 32%. Our findings emphasize the importance of dataset quality, execution-based evaluation and translation method for advancing NL2SH translation. Our code is available at https://github.com/westenfelder/NL2SH

We present a novel unified bilevel optimization-based framework, PARL, formulated to address the recently highlighted critical issue of policy alignment in reinforcement learning using utility or preference-based feedback. We identify a major gap within current algorithmic designs for solving policy alignment due to a lack of precise characterization of the dependence of the alignment objective on the data generated by policy trajectories. This shortfall contributes to the sub-optimal performance observed in contemporary algorithms. Our framework addressed these concerns by explicitly parameterizing the distribution of the upper alignment objective (reward design) by the lower optimal variable (optimal policy for the designed reward). Interestingly, from an optimization perspective, our formulation leads to a new class of stochastic bilevel problems where the stochasticity at the upper objective depends upon the lower-level variable. To demonstrate the efficacy of our formulation in resolving alignment issues in RL, we devised an algorithm named A-PARL to solve PARL problem, establishing sample complexity bounds of order O(1/T). Our empirical results substantiate that the proposed PARL can address the alignment concerns in RL by showing significant improvements (up to 63\% in terms of required samples) for policy alignment in large-scale environments of the Deepmind control suite and Meta world tasks.

We study methods for efficiently aligning large language models (LLMs) with human preferences given budgeted online feedback. We first formulate the LLM alignment problem in the frame of contextual dueling bandits. This formulation, subsuming recent paradigms such as online RLHF and online DPO, inherently quests for sample-efficient algorithms that incorporate online active exploration. Leveraging insights from bandit theory, we introduce a unified algorithm based on Thompson sampling and highlight its applications in two distinct LLM alignment scenarios. The practical agent that efficiently implements this algorithm, named SEA (Sample-Efficient Alignment), is empirically validated through extensive experiments across three model scales (1B, 2.8B, 6.9B) and three preference learning algorithms (DPO, IPO, SLiC). The results demonstrate that SEA achieves highly sample-efficient alignment with oracle's preferences, outperforming recent active exploration methods for LLMs. Additionally, we release the implementation of SEA together with an efficient codebase designed for online alignment of LLMs, aiming to accelerate future research in this field.

Recent progress in large language models (LLMs) has shown promise in formal theorem proving, yet existing benchmarks remain limited to isolated, static proof tasks, failing to capture the iterative, engineering-intensive workflows of real-world formal mathematics libraries. Motivated by analogous advances in software engineering, we introduce the paradigm of Automated Proof Engineering (APE), which aims to automate proof engineering tasks such as feature addition, proof refactoring, and bug fixing using LLMs. To facilitate research in this direction, we present APE-Bench I, the first realistic benchmark built from real-world commit histories of Mathlib4, featuring diverse file-level tasks described in natural language and verified via a hybrid approach combining the Lean compiler and LLM-as-a-Judge. We further develop Eleanstic, a scalable parallel verification infrastructure optimized for proof checking across multiple versions of Mathlib. Empirical results on state-of-the-art LLMs demonstrate strong performance on localized edits but substantial degradation on handling complex proof engineering. This work lays the foundation for developing agentic workflows in proof engineering, with future benchmarks targeting multi-file coordination, project-scale verification, and autonomous agents capable of planning, editing, and repairing formal libraries.

Reinforcement learning (RL) post-training is crucial for LLM alignment and reasoning, but existing policy-based methods, such as PPO and DPO, can fall short of fixing shortcuts inherited from pre-training. In this work, we introduce Qsharp, a value-based algorithm for KL-regularized RL that guides the reference policy using the optimal regularized Q function. We propose to learn the optimal Q function using distributional RL on an aggregated online dataset. Unlike prior value-based baselines that guide the model using unregularized Q-values, our method is theoretically principled and provably learns the optimal policy for the KL-regularized RL problem. Empirically, Qsharp outperforms prior baselines in math reasoning benchmarks while maintaining a smaller KL divergence to the reference policy. Theoretically, we establish a reduction from KL-regularized RL to no-regret online learning, providing the first bounds for deterministic MDPs under only realizability. Thanks to distributional RL, our bounds are also variance-dependent and converge faster when the reference policy has small variance. In sum, our results highlight Qsharp as an effective approach for post-training LLMs, offering both improved performance and theoretical guarantees. The code can be found at https://github.com/jinpz/q_sharp.

Direct Preference Optimization (DPO) has become a widely used training method for the instruction fine-tuning of large language models (LLMs). In this work, we explore an under-investigated aspect of DPO - its dependency on the reference model or policy. Such reference policies, typically instantiated as the model to be further fine-tuned, are important since they can impose an upper limit on DPO's effectiveness. Therefore, we address three related research questions in this work. First, we explore the optimal strength of the KL-divergence constraint in DPO, which penalizes deviations from the reference policy, and find that DPO is sensitive to this strength. Next, we examine the necessity of reference policies for instruction fine-tuning by providing both theoretical and empirical comparisons between DPO and related learning objectives, demonstrating DPO's superiority. Additionally, we investigate whether DPO benefits from stronger reference policies, finding that a stronger reference policy can lead to improved performance, but only when it is similar to the model being fine-tuned. Our findings highlight the confounding role of reference policies in DPO and offer insights for best practices, while also identifying open research questions for future studies.

This paper presents the second ChatGPT4PCG competition at the 2024 IEEE Conference on Games. In this edition of the competition, we follow the first edition, but make several improvements and changes. We introduce a new evaluation metric along with allowing a more flexible format for participants' submissions and making several improvements to the evaluation pipeline. Continuing from the first edition, we aim to foster and explore the realm of prompt engineering (PE) for procedural content generation (PCG). While the first competition saw success, it was hindered by various limitations; we aim to mitigate these limitations in this edition. We introduce diversity as a new metric to discourage submissions aimed at producing repetitive structures. Furthermore, we allow submission of a Python program instead of a prompt text file for greater flexibility in implementing advanced PE approaches, which may require control flow, including conditions and iterations. We also make several improvements to the evaluation pipeline with a better classifier for similarity evaluation and better-performing function signatures. We thoroughly evaluate the effectiveness of the new metric and the improved classifier. Additionally, we perform an ablation study to select a function signature to instruct ChatGPT for level generation. Finally, we provide implementation examples of various PE techniques in Python and evaluate their preliminary performance. We hope this competition serves as a resource and platform for learning about PE and PCG in general.

Direct Alignment Algorithms (DAAs) simplify language model alignment by replacing reinforcement learning (RL) and reward modeling (RM) in Reinforcement Learning from Human Feedback (RLHF) with direct policy optimization. DAAs can be classified by their ranking losses (pairwise vs. pointwise), by the rewards used in those losses (e.g., likelihood ratios of policy and reference policy, or odds ratios), or by whether a Supervised Fine-Tuning (SFT) phase is required (two-stage vs. one-stage). We first show that one-stage methods underperform two-stage methods. To address this, we incorporate an explicit SFT phase and introduce the beta parameter, controlling the strength of preference optimization, into single-stage ORPO and ASFT. These modifications improve their performance in Alpaca Eval 2 by +3.46 (ORPO) and +8.27 (ASFT), matching two-stage methods like DPO. Further analysis reveals that the key factor is whether the approach uses pairwise or pointwise objectives, rather than the specific implicit reward or loss function. These results highlight the importance of careful evaluation to avoid premature claims of performance gains or overall superiority in alignment algorithms.

We propose TraceRL, a trajectory-aware reinforcement learning framework for diffusion language models (DLMs) that incorporates preferred inference trajectory into post-training, and is applicable across different architectures. Equipped with a diffusion-based value model that enhances training stability, we demonstrate improved reasoning performance on complex math and coding tasks. Besides, it can also be applied to adapt block-specific models to larger blocks, which improves sampling flexibility. Employing TraceRL, we derive a series of state-of-the-art diffusion language models, namely TraDo. Although smaller than 7B-scale AR models, TraDo-4B-Instruct still consistently outperforms them across complex math reasoning tasks. TraDo-8B-Instruct achieves relative accuracy improvements of 6.1% over Qwen2.5-7B-Instruct and 51.3% over Llama3.1-8B-Instruct on mathematical reasoning benchmarks. Through curriculum learning, we also derive the first long-CoT DLM, outperforming Qwen2.5-7B-Instruct on MATH500 with an 18.1% relative accuracy gain. To facilitate reproducible research and practical applications, we release a comprehensive open-source framework for building, training, and deploying diffusion LLMs across diverse architectures. The framework integrates accelerated KV-cache techniques and inference engines for both inference and reinforcement learning, and includes implementations of various supervised fine-tuning and RL methods for mathematics, coding, and general tasks. Code and Models: https://github.com/Gen-Verse/dLLM-RL

A fundamental challenge in formal theorem proving by LLMs is the lack of high-quality training data. Although reinforcement learning or expert iteration partially mitigates this issue by alternating between LLM generating proofs and finetuning them on correctly generated ones, performance quickly plateaus due to the scarcity of correct proofs (sparse rewards). To keep improving the models with limited data, we draw inspiration from mathematicians, who continuously develop new results, partly by proposing novel conjectures or exercises (which are often variants of known results) and attempting to solve them. We design the Self-play Theorem Prover (STP) that simultaneously takes on two roles, conjecturer and prover, each providing training signals to the other. The conjecturer is trained iteratively on previously generated conjectures that are barely provable by the current prover, which incentivizes it to generate increasingly challenging conjectures over time. The prover attempts to prove the conjectures with standard expert iteration. We evaluate STP with both Lean and Isabelle formal versifiers. With 19.8 billion tokens generated during the training in Lean, STP proves 26.3% of the statements in the LeanWorkbook dataset, doubling the previous best result of 13.2% achieved through expert iteration. The final model achieves state-of-the-art performance among whole-proof generation methods on miniF2F-test (61.7%, pass@3200), Proofnet-test (23.1%, pass@3200) and PutnamBench (8/644, pass@3200).

In recent years, Reinforcement Learning (RL) has been applied to real-world problems with increasing success. Such applications often require to put constraints on the agent's behavior. Existing algorithms for constrained RL (CRL) rely on gradient descent-ascent, but this approach comes with a caveat. While these algorithms are guaranteed to converge on average, they do not guarantee last-iterate convergence, i.e., the current policy of the agent may never converge to the optimal solution. In practice, it is often observed that the policy alternates between satisfying the constraints and maximizing the reward, rarely accomplishing both objectives simultaneously. Here, we address this problem by introducing Reinforcement Learning with Optimistic Ascent-Descent (ReLOAD), a principled CRL method with guaranteed last-iterate convergence. We demonstrate its empirical effectiveness on a wide variety of CRL problems including discrete MDPs and continuous control. In the process we establish a benchmark of challenging CRL problems.

Large Language Models (LLMs) exhibit remarkable code generation capabilities but falter when adapting to frequent updates in external library APIs. This critical limitation, stemming from reliance on outdated API knowledge from their training data, even with access to current documentation, impedes reliable code generation in dynamic environments. To tackle this issue, we propose ReCode (rule-based Reinforcement learning for Code Update), a novel framework that mimics human programmer adaptation to API changes. Specifically, we construct a dataset of approximately 2,000 data entries to train the LLMs to perform version migration based on updated information. Then, we introduce a modified string similarity metric for code evaluation as the reward for reinforcement learning. Our experiments demonstrate that ReCode substantially boosts LLMs' code generation performance in dynamic API scenarios, especially on the unseen CodeUpdateArena task. Crucially, compared to supervised fine-tuning, ReCode has less impact on LLMs' general code generation abilities. We apply ReCode on various LLMs and reinforcement learning algorithms (GRPO and DAPO), all achieving consistent improvements. Notably, after training, Qwen2.5-Coder-7B outperforms that of the 32B parameter code instruction-tuned model and the reasoning model with the same architecture. Code is available at https://github.com/zjunlp/ReCode.

The left-corner transformation (Rosenkrantz and Lewis, 1970) is used to remove left recursion from context-free grammars, which is an important step towards making the grammar parsable top-down with simple techniques. This paper generalizes prior left-corner transformations to support semiring-weighted production rules and to provide finer-grained control over which left corners may be moved. Our generalized left-corner transformation (GLCT) arose from unifying the left-corner transformation and speculation transformation (Eisner and Blatz, 2007), originally for logic programming. Our new transformation and speculation define equivalent weighted languages. Yet, their derivation trees are structurally different in an important way: GLCT replaces left recursion with right recursion, and speculation does not. We also provide several technical results regarding the formal relationships between the outputs of GLCT, speculation, and the original grammar. Lastly, we empirically investigate the efficiency of GLCT for left-recursion elimination from grammars of nine languages.

In a compound AI system, components such as an LLM call, a retriever, a code interpreter, or tools are interconnected. The system's behavior is primarily driven by parameters such as instructions or tool definitions. Recent advancements enable end-to-end optimization of these parameters using an LLM. Notably, leveraging an LLM as an optimizer is particularly efficient because it avoids gradient computation and can generate complex code and instructions. This paper presents a survey of the principles and emerging trends in LLM-based optimization of compound AI systems. It covers archetypes of compound AI systems, approaches to LLM-based end-to-end optimization, and insights into future directions and broader impacts. Importantly, this survey uses concepts from program analysis to provide a unified view of how an LLM optimizer is prompted to optimize a compound AI system. The exhaustive list of paper is provided at https://github.com/linyuhongg/LLM-based-Optimization-of-Compound-AI-Systems.

Large Language Models (LLMs) have demonstrated impressive reasoning capabilities, yet their direct application to NP-hard combinatorial problems (CPs) remains underexplored. In this work, we systematically investigate the reasoning abilities of LLMs on a variety of NP-hard combinatorial optimization tasks and introduce ACCORD: Autoregressive Constraint-satisfying generation for COmbinatorial optimization with Routing and Dynamic attention. ACCORD features a novel dataset representation and model architecture that leverage the autoregressive nature of LLMs to dynamically enforce feasibility constraints, coupled with attention-based routing to activate problem-specific LoRA modules. We also present the ACCORD-90k supervised dataset, covering six NP-hard combinatorial problems: TSP, VRP, Knapsack, FlowShop, JSSP, and BinPacking. Extensive experiments demonstrate that our ACCORD model, built on an 8B-parameter Llama backbone, consistently outperforms standard prompting and input-output methods, even when compared to much larger LLMs, such as gpt-4. Ablation studies further show that our output structure enhances solution feasibility. To the best of our knowledge, this is the first large-scale, end-to-end framework for exploring the applications of LLMs to a broad spectrum of combinatorial optimization problems. The codes are publicly available at https://github.com/starjob42/ACCORD

Automating Register Transfer Level (RTL) code generation using Large Language Models (LLMs) offers substantial promise for streamlining digital circuit design and reducing human effort. However, current LLM-based approaches face significant challenges with training data scarcity, poor specification-code alignment, lack of verification mechanisms, and balancing generalization with specialization. Inspired by DeepSeek-R1, we introduce VeriReason, a framework integrating supervised fine-tuning with Guided Reward Proximal Optimization (GRPO) reinforcement learning for RTL generation. Using curated training examples and a feedback-driven reward model, VeriReason combines testbench evaluations with structural heuristics while embedding self-checking capabilities for autonomous error correction. On the VerilogEval Benchmark, VeriReason delivers significant improvements: achieving 83.1% functional correctness on the VerilogEval Machine benchmark, substantially outperforming both comparable-sized models and much larger commercial systems like GPT-4 Turbo. Additionally, our approach demonstrates up to a 2.8X increase in first-attempt functional correctness compared to baseline methods and exhibits robust generalization to unseen designs. To our knowledge, VeriReason represents the first system to successfully integrate explicit reasoning capabilities with reinforcement learning for Verilog generation, establishing a new state-of-the-art for automated RTL synthesis. The models and datasets are available at: https://huggingface.co/collections/AI4EDA-CASE Code is Available at: https://github.com/NellyW8/VeriReason

Partial label learning (PLL) aims to train multiclass classifiers from the examples each annotated with a set of candidate labels where a fixed but unknown candidate label is correct. In the last few years, the instance-independent generation process of candidate labels has been extensively studied, on the basis of which many theoretical advances have been made in PLL. Nevertheless, the candidate labels are always instance-dependent in practice and there is no theoretical guarantee that the model trained on the instance-dependent PLL examples can converge to an ideal one. In this paper, a theoretically grounded and practically effective approach named POP, i.e. PrOgressive Purification for instance-dependent partial label learning, is proposed. Specifically, POP updates the learning model and purifies each candidate label set progressively in every epoch. Theoretically, we prove that POP enlarges the region appropriately fast where the model is reliable, and eventually approximates the Bayes optimal classifier with mild assumptions. Technically, POP is flexible with arbitrary PLL losses and could improve the performance of the previous PLL losses in the instance-dependent case. Experiments on the benchmark datasets and the real-world datasets validate the effectiveness of the proposed method.

Robust Markov Decision Processes (MDPs) and risk-sensitive MDPs are both powerful tools for making decisions in the presence of uncertainties. Previous efforts have aimed to establish their connections, revealing equivalences in specific formulations. This paper introduces a new formulation for risk-sensitive MDPs, which assesses risk in a slightly different manner compared to the classical Markov risk measure (Ruszczy\'nski 2010), and establishes its equivalence with a class of regularized robust MDP (RMDP) problems, including the standard RMDP as a special case. Leveraging this equivalence, we further derive the policy gradient theorem for both problems, proving gradient domination and global convergence of the exact policy gradient method under the tabular setting with direct parameterization. This forms a sharp contrast to the Markov risk measure, known to be potentially non-gradient-dominant (Huang et al. 2021). We also propose a sample-based offline learning algorithm, namely the robust fitted-Z iteration (RFZI), for a specific regularized RMDP problem with a KL-divergence regularization term (or equivalently the risk-sensitive MDP with an entropy risk measure). We showcase its streamlined design and less stringent assumptions due to the equivalence and analyze its sample complexity.

We introduce Probabilistic Dependent Type Systems (PDTS) via a functional language based on a subsystem of intuitionistic type theory including dependent sums and products, which is expanded to include stochastic functions. We provide a sampling-based semantics for the language based on non-deterministic beta reduction. Further, we derive a probabilistic logic from the PDTS introduced as a direct result of the Curry-Howard isomorphism. The probabilistic logic derived is shown to provide a universal representation for finite discrete distributions.

The equivalence of realizable and agnostic learnability is a fundamental phenomenon in learning theory. With variants ranging from classical settings like PAC learning and regression to recent trends such as adversarially robust learning, it's surprising that we still lack a unified theory; traditional proofs of the equivalence tend to be disparate, and rely on strong model-specific assumptions like uniform convergence and sample compression. In this work, we give the first model-independent framework explaining the equivalence of realizable and agnostic learnability: a three-line blackbox reduction that simplifies, unifies, and extends our understanding across a wide variety of settings. This includes models with no known characterization of learnability such as learning with arbitrary distributional assumptions and more general loss functions, as well as a host of other popular settings such as robust learning, partial learning, fair learning, and the statistical query model. More generally, we argue that the equivalence of realizable and agnostic learning is actually a special case of a broader phenomenon we call property generalization: any desirable property of a learning algorithm (e.g. noise tolerance, privacy, stability) that can be satisfied over finite hypothesis classes extends (possibly in some variation) to any learnable hypothesis class.

Despite recent success in large language model (LLM) reasoning, LLMs struggle with hierarchical multi-step reasoning tasks like generating complex programs. For these tasks, humans often start with a high-level algorithmic design and implement each part gradually. We introduce Parsel, a framework enabling automatic implementation and validation of complex algorithms with code LLMs. With Parsel, we automatically decompose algorithmic tasks into hierarchical natural language function descriptions and then search over combinations of possible function implementations using tests. We show that Parsel can be used across domains requiring hierarchical reasoning, including program synthesis and robotic planning. We find that, using Parsel, LLMs solve more competition-level problems in the APPS dataset, resulting in pass rates over 75\% higher than prior results from directly sampling AlphaCode and Codex, while often using a smaller sample budget. Moreover, with automatically generated tests, we find that Parsel can improve the state-of-the-art pass@1 performance on HumanEval from 67\% to 85\%. We also find that LLM-generated robotic plans using Parsel are more than twice as likely to be considered accurate than directly generated plans. Lastly, we explore how Parsel addresses LLM limitations and discuss how Parsel may be useful for human programmers. We release our code at https://github.com/ezelikman/parsel

Following the success of Proximal Policy Optimization (PPO) for Reinforcement Learning from Human Feedback (RLHF), new techniques such as Sequence Likelihood Calibration (SLiC) and Direct Policy Optimization (DPO) have been proposed that are offline in nature and use rewards in an indirect manner. These techniques, in particular DPO, have recently become the tools of choice for LLM alignment due to their scalability and performance. However, they leave behind important features of the PPO approach. Methods such as SLiC or RRHF make use of the Reward Model (RM) only for ranking/preference, losing fine-grained information and ignoring the parametric form of the RM (eg., Bradley-Terry, Plackett-Luce), while methods such as DPO do not use even a separate reward model. In this work, we propose a novel approach, named BRAIn, that re-introduces the RM as part of a distribution matching approach.BRAIn considers the LLM distribution conditioned on the assumption of output goodness and applies Bayes theorem to derive an intractable posterior distribution where the RM is explicitly represented. BRAIn then distills this posterior into an amortized inference network through self-normalized importance sampling, leading to a scalable offline algorithm that significantly outperforms prior art in summarization and AntropicHH tasks. BRAIn also has interesting connections to PPO and DPO for specific RM choices.

Drawing upon recent advances in language model alignment, we formulate offline Reinforcement Learning as a two-stage optimization problem: First pretraining expressive generative policies on reward-free behavior datasets, then fine-tuning these policies to align with task-specific annotations like Q-values. This strategy allows us to leverage abundant and diverse behavior data to enhance generalization and enable rapid adaptation to downstream tasks using minimal annotations. In particular, we introduce Efficient Diffusion Alignment (EDA) for solving continuous control problems. EDA utilizes diffusion models for behavior modeling. However, unlike previous approaches, we represent diffusion policies as the derivative of a scalar neural network with respect to action inputs. This representation is critical because it enables direct density calculation for diffusion models, making them compatible with existing LLM alignment theories. During policy fine-tuning, we extend preference-based alignment methods like Direct Preference Optimization (DPO) to align diffusion behaviors with continuous Q-functions. Our evaluation on the D4RL benchmark shows that EDA exceeds all baseline methods in overall performance. Notably, EDA maintains about 95\% of performance and still outperforms several baselines given only 1\% of Q-labelled data during fine-tuning.

Softmax Loss (SL) is widely applied in recommender systems (RS) and has demonstrated effectiveness. This work analyzes SL from a pairwise perspective, revealing two significant limitations: 1) the relationship between SL and conventional ranking metrics like DCG is not sufficiently tight; 2) SL is highly sensitive to false negative instances. Our analysis indicates that these limitations are primarily due to the use of the exponential function. To address these issues, this work extends SL to a new family of loss functions, termed Pairwise Softmax Loss (PSL), which replaces the exponential function in SL with other appropriate activation functions. While the revision is minimal, we highlight three merits of PSL: 1) it serves as a tighter surrogate for DCG with suitable activation functions; 2) it better balances data contributions; and 3) it acts as a specific BPR loss enhanced by Distributionally Robust Optimization (DRO). We further validate the effectiveness and robustness of PSL through empirical experiments. The code is available at https://github.com/Tiny-Snow/IR-Benchmark.

Reinforcement learning improves LLM reasoning, yet sparse delayed reward over long sequences makes token-level credit assignment the key bottleneck. We study the verifiable-reward setting, where the final answer is checkable and multiple responses can be drawn per prompt. Reasoning tasks in math and medical QA align with this setup, where only a few decision tokens significantly impact the outcome. PPO offers token-level advantages with a learned value model, but it is complex to train both the actor and critic models simultaneously, and it is not easily generalizable, as the token-level values from the critic model can make training prone to overfitting. GRPO is critic-free and supports verifiable rewards, but spreads a single sequence-level return across tokens and ignores branching. We introduce Prefix-to-Tree (P2T), a simple procedure that converts a group of responses into a prefix tree and computes nonparametric prefix values \(V(s)\) by aggregating descendant outcomes. Built on P2T, we propose TEMPO (\textbf{Tree-Estimated Mean Prefix Value for Policy Optimization}), a critic-free algorithm that augments the group-relative outcome signal of GRPO with branch-gated temporal-difference corrections derived from the tree. At non-branch tokens, the temporal-difference (TD) term is zero, so TEMPO reduces to GRPO; at branching tokens, it supplies precise token-level credit without a learned value network or extra judges/teachers. On Qwen3-1.7B/4B, TEMPO outperforms PPO and GRPO on in-distribution (MATH, MedQA) and out-of-distribution (GSM-HARD, AMC23, MedMCQA, MMLU-Medical) benchmarks, and reaches higher validation accuracy with roughly the same wall-clock time.

Language models have become increasingly powerful tools for formal mathematical reasoning. However, most existing approaches rely exclusively on either large general-purpose models or smaller specialized models, each with distinct limitations, while training specialized large models still requires significant computational resources. This paper introduces ProofCompass, a novel hybrid methodology that achieves remarkable computational efficiency by strategically guiding existing specialized prover methods, such as DeepSeek-Prover-v1.5-RL (DSP-v1.5) with a Large Language Model (LLM) without requiring additional model training. The LLM provides natural language proof strategies and analyzes failed attempts to select intermediate lemmas, enabling effective problem decomposition. On the miniF2F benchmark, ProofCompass demonstrates substantial resource efficiency: it outperforms DSP-v1.5 (54.9% rightarrow 55.3%) while using 25x fewer attempts (3200 rightarrow 128). Our synergistic approach paves the way for simultaneously improving computational efficiency and accuracy in formal theorem proving.

Reinforcement learning from human feedback (RLHF) has become essential for improving language model capabilities, but traditional approaches rely on the assumption that human preferences follow a transitive Bradley-Terry model. This assumption fails to capture the non-transitive nature of populational human preferences. Nash learning from human feedback (NLHF), targeting non-transitive preferences, is a problem of computing the Nash equilibrium (NE) of the two-player constant-sum game defined by the human preference. We introduce Extragradient preference optimization (EGPO), a novel algorithm for NLHF achieving last-iterate linear convergence to the NE of KL-regularized games and polynomial convergence to the NE of original games, while being robust to noise. Unlike previous approaches that rely on nested optimization, we derive an equivalent implementation using gradients of an online variant of the identity preference optimization (IPO) loss, enabling more faithful implementation for neural networks. Our empirical evaluations demonstrate EGPO's superior performance over baseline methods when training for the same number of epochs, as measured by pairwise win-rates using the ground truth preference. These results validate both the theoretical strengths and practical advantages of EGPO for language model alignment with non-transitive human preferences.

We show that feedforward neural networks with ReLU activation generalize on low complexity data, suitably defined. Given i.i.d. data generated from a simple programming language, the minimum description length (MDL) feedforward neural network which interpolates the data generalizes with high probability. We define this simple programming language, along with a notion of description length of such networks. We provide several examples on basic computational tasks, such as checking primality of a natural number, and more. For primality testing, our theorem shows the following. Suppose that we draw an i.i.d. sample of Theta(N^{delta}ln N) numbers uniformly at random from 1 to N, where deltain (0,1). For each number x_i, let y_i = 1 if x_i is a prime and 0 if it is not. Then with high probability, the MDL network fitted to this data accurately answers whether a newly drawn number between 1 and N is a prime or not, with test error leq O(N^{-delta}). Note that the network is not designed to detect primes; minimum description learning discovers a network which does so.

Large language models (LLMs) often contain misleading content, emphasizing the need to align them with human values to ensure secur AI systems. Reinforcement learning from human feedback (RLHF) has been employed to achieve this alignment by combining a reward model, typically based on Bradley-Terry paired comparison, with an RL algorithm such as Proximal Policy Optimization (PPO) to optimize LLM responses. However, RLHF exhibits complexity, instability, and sensitivity to hyperparameters. In this paper, we propose Preference Ranking Optimization (PRO) as an alternative to PPO for directly aligning LLMs with the Bradley-Terry comparison. PRO extends the pairwise Bradley-Terry comparison to accommodate preference rankings of any length. By iteratively contrasting the likelihood of generating responses, PRO instructs the LLM to prioritize the best response while progressively ranking the remaining responses. In this manner, PRO effectively transforms human alignment into aligning the probability ranking of n responses generated by LLM with the preference ranking of humans towards these responses. Experiments have shown that PRO outperforms existing alignment algorithms, achieving comparable results to ChatGPT and human responses through automatic-based, reward-based, GPT-4, and human evaluations. Furthermore, we demonstrate that longer, more diverse, and higher-quality preference ranking sequences can consistently enhance the performance of human alignment.

Large language models~(LLMs) are expected to be helpful, harmless, and honest. In alignment scenarios such as safety, confidence, and general preference alignment, binary preference data collection and reward modeling are resource-intensive but essential for transferring human preference. In this work, we explore using the similarity between sampled generations and high-quality reference answers as an alternative reward function choice for LLM alignment. Similarity reward circumvents binary preference data collection and reward modeling when unary high-quality reference answers are available. We introduce RefAlign, a versatile REINFORCE-style alignment algorithm that does not rely on reference or reward models. RefAlign utilizes similarity metrics, such as BERTScore between sampled generations and reference answers as surrogate rewards. Beyond general human preference optimization, RefAlign can be readily extended to diverse scenarios, such as safety and confidence alignment, by incorporating the similarity reward with task-related objectives. In various scenarios, RefAlign demonstrates comparable performance to previous alignment methods without binary preference data and reward models.

Recently, Offline Reinforcement Learning (RL) has achieved remarkable progress with the emergence of various algorithms and datasets. However, these methods usually focus on algorithmic advancements, ignoring that many low-level implementation choices considerably influence or even drive the final performance. As a result, it becomes hard to attribute the progress in Offline RL as these choices are not sufficiently discussed and aligned in the literature. In addition, papers focusing on a dataset (e.g., D4RL) often ignore algorithms proposed on another dataset (e.g., RL Unplugged), causing isolation among the algorithms, which might slow down the overall progress. Therefore, this work aims to bridge the gaps caused by low-level choices and datasets. To this end, we empirically investigate 20 implementation choices using three representative algorithms (i.e., CQL, CRR, and IQL) and present a guidebook for choosing implementations. Following the guidebook, we find two variants CRR+ and CQL+ , achieving new state-of-the-art on D4RL. Moreover, we benchmark eight popular offline RL algorithms across datasets under unified training and evaluation framework. The findings are inspiring: the success of a learning paradigm severely depends on the data distribution, and some previous conclusions are biased by the dataset used. Our code is available at https://github.com/sail-sg/offbench.

Large Language Models (LLMs) have become increasingly popular due to their ability to process and generate natural language. However, as they are trained on massive datasets of text, LLMs can inherit harmful biases and produce outputs that are not aligned with human values. This paper studies two main approaches to LLM alignment: Reinforcement Learning with Human Feedback (RLHF) and contrastive learning-based methods like Direct Preference Optimization (DPO). By analyzing the stability and robustness of RLHF and DPO, we propose MPO (Mixed Preference Optimization), a novel method that mitigates the weaknesses of both approaches. Specifically, we propose a two-stage training procedure: first train DPO on an easy dataset, and then perform RLHF on a difficult set with DPO model being the reference model. Here, the easy and difficult sets are constructed by a well-trained reward model that splits response pairs into those with large gaps of reward (easy), and those with small gaps (difficult). The first stage allows us to obtain a relatively optimal policy (LLM) model quickly, whereas the second stage refines LLM with online RLHF, thus mitigating the distribution shift issue associated with DPO. Experiments are conducted on two public alignment datasets, namely HH-RLHF and TLDR, demonstrating the effectiveness of MPO, both in terms of GPT4 and human evaluation.

Human alignment in large language models (LLMs) is an active area of research. A recent groundbreaking work, direct preference optimization (DPO), has greatly simplified the process from past work in reinforcement learning from human feedback (RLHF) by bypassing the reward learning stage in RLHF. DPO, after training, provides an implicit reward model. In this work, we make a novel observation that this implicit reward model can by itself be used in a bootstrapping fashion to further align the LLM. Our approach is to use the rewards from a current LLM model to construct a preference dataset, which is then used in subsequent DPO rounds. We incorporate refinements that debias the length of the responses and improve the quality of the preference dataset to further improve our approach. Our approach, named self-alignment with DPO ImpliCit rEwards (DICE), shows great improvements in alignment and achieves superior performance than Gemini Pro on AlpacaEval 2, reaching 27.55% length-controlled win rate against GPT-4 Turbo, but with only 8B parameters and no external feedback. Our code is available at https://github.com/sail-sg/dice.

Recent large language models (LLMs) have demonstrated strong reasoning capabilities that benefits from online reinforcement learning (RL). These capabilities have primarily been demonstrated within the left-to-right autoregressive (AR) generation paradigm. In contrast, non-autoregressive paradigms based on diffusion generate text in a coarse-to-fine manner. Although recent diffusion-based large language models (dLLMs) have achieved competitive language modeling performance compared to their AR counterparts, it remains unclear if dLLMs can also leverage recent advances in LLM reasoning. To this end, we propose d1, a framework to adapt pre-trained masked dLLMs into reasoning models via a combination of supervised finetuning (SFT) and RL. Specifically, we develop and extend techniques to improve reasoning in pretrained dLLMs: (a) we utilize a masked SFT technique to distill knowledge and instill self-improvement behavior directly from existing datasets, and (b) we introduce a novel critic-free, policy-gradient based RL algorithm called diffu-GRPO. Through empirical studies, we investigate the performance of different post-training recipes on multiple mathematical and logical reasoning benchmarks. We find that d1 yields the best performance and significantly improves performance of a state-of-the-art dLLM.

Large Language Models (LLMs) have demonstrated remarkable potential in handling complex reasoning tasks by generating step-by-step rationales.Some methods have proven effective in boosting accuracy by introducing extra verifiers to assess these paths. However, existing verifiers, typically trained on binary-labeled reasoning paths, fail to fully utilize the relative merits of intermediate steps, thereby limiting the effectiveness of the feedback provided. To overcome this limitation, we propose Tree-based Preference Learning Verifier (Tree-PLV), a novel approach that constructs reasoning trees via a best-first search algorithm and collects step-level paired data for preference training. Compared to traditional binary classification, step-level preferences more finely capture the nuances between reasoning steps, allowing for a more precise evaluation of the complete reasoning path. We empirically evaluate Tree-PLV across a range of arithmetic and commonsense reasoning tasks, where it significantly outperforms existing benchmarks. For instance, Tree-PLV achieved substantial performance gains over the Mistral-7B self-consistency baseline on GSM8K (67.55% to 82.79%), MATH (17.00% to 26.80%), CSQA (68.14% to 72.97%), and StrategyQA (82.86% to 83.25%).Additionally, our study explores the appropriate granularity for applying preference learning, revealing that step-level guidance provides feedback that better aligns with the evaluation of the reasoning process.

Large language models (LLMs) have shown promise in proving formal theorems using proof assistants such as Lean. However, existing methods are difficult to reproduce or build on, due to private code, data, and large compute requirements. This has created substantial barriers to research on machine learning methods for theorem proving. This paper removes these barriers by introducing LeanDojo: an open-source Lean playground consisting of toolkits, data, models, and benchmarks. LeanDojo extracts data from Lean and enables interaction with the proof environment programmatically. It contains fine-grained annotations of premises in proofs, providing valuable data for premise selection: a key bottleneck in theorem proving. Using this data, we develop ReProver (Retrieval-Augmented Prover): the first LLM-based prover that is augmented with retrieval for selecting premises from a vast math library. It is inexpensive and needs only one GPU week of training. Our retriever leverages LeanDojo's program analysis capability to identify accessible premises and hard negative examples, which makes retrieval much more effective. Furthermore, we construct a new benchmark consisting of 96,962 theorems and proofs extracted from Lean's math library. It features challenging data split requiring the prover to generalize to theorems relying on novel premises that are never used in training. We use this benchmark for training and evaluation, and experimental results demonstrate the effectiveness of ReProver over non-retrieval baselines and GPT-4. We thus provide the first set of open-source LLM-based theorem provers without any proprietary datasets and release it under a permissive MIT license to facilitate further research.

Query rewrite, which aims to generate more efficient queries by altering a SQL query's structure without changing the query result, has been an important research problem. In order to maintain equivalence between the rewritten query and the original one during rewriting, traditional query rewrite methods always rewrite the queries following certain rewrite rules. However, some problems still remain. Firstly, existing methods of finding the optimal choice or sequence of rewrite rules are still limited and the process always costs a lot of resources. Methods involving discovering new rewrite rules typically require complicated proofs of structural logic or extensive user interactions. Secondly, current query rewrite methods usually rely highly on DBMS cost estimators which are often not accurate. In this paper, we address these problems by proposing a novel method of query rewrite named LLM-R2, adopting a large language model (LLM) to propose possible rewrite rules for a database rewrite system. To further improve the inference ability of LLM in recommending rewrite rules, we train a contrastive model by curriculum to learn query representations and select effective query demonstrations for the LLM. Experimental results have shown that our method can significantly improve the query execution efficiency and outperform the baseline methods. In addition, our method enjoys high robustness across different datasets.

Emergency of DeepSeek R1 and QwQ 32B have broken through performance barriers for running frontier large language models (LLMs) on home devices. While consumer hardware is getting stronger and model quantization is improving, existing end-side solutions still demand GPU clusters, large RAM/VRAM, and high bandwidth, far beyond what a common home cluster can handle. This paper introduces prima.cpp, a distributed inference system that runs 70B-scale models on everyday home devices using a mix of CPU/GPU, low RAM/VRAM, Wi-Fi, and cross-platform support. It uses mmap to manage model weights and introduces piped-ring parallelism with prefetching to hide disk loading. By modeling heterogeneity in computation, communication, disk, memory (and its management behavior), and OS, it optimally assigns model layers to each device's CPU and GPU, further reducing token latency. An elegant algorithm named Halda is proposed to solve this NP-hard assignment problem. We evaluate prima.cpp on a common four-node home cluster. It outperforms llama.cpp, exo, and dllama on 30B+ models while keeping memory pressure below 6%. This brings frontier 30B-70B models, such as Llama 3, DeepSeek R1, Qwen 2.5, and QwQ to home assistants, making advanced AI truly accessible to individuals. The code is open source and available at https://github.com/Lizonghang/prima.cpp.

Post-training quantization (PTQ) of large language models (LLMs) to extremely low bit-widths remains challenging due to the fundamental trade-off between computational efficiency and model expressiveness. While existing ultra-low-bit PTQ methods rely on binary approximations or complex compensation mechanisms, they suffer from either limited representational capacity or computational overhead that undermines their efficiency gains. We introduce PTQ to Trit-Planes (PTQTP), the first ternary-weight PTQ framework that decomposes weight matrices into structured ternary {-1, 0, 1} trit-planes using 2x1.58-bit representation. PTQTP achieves multiplication-free inference, identical to 1-bit quantization, while maintaining superior expressiveness through its novel structured decomposition. Our approach provides: (1) a theoretically grounded progressive approximation algorithm ensuring global weight consistency; (2) model-agnostic deployment across diverse modern LLMs without architectural modifications; and (3) uniform ternary operations that eliminate the need for mixed-precision or compensation schemes. Comprehensive experiments across LLaMA3.x and Qwen3 model families (0.6B-70B parameters) demonstrate that PTQTP significantly outperforms existing low-bit PTQ methods, achieving 82.4% mathematical reasoning retention versus 0% for competing approaches. PTQTP approaches and sometimes surpasses 1.58-bit quantization-aware training performance while requiring only single-hour quantization compared to 10-14 GPU days for training-based methods. These results establish PTQTP as a practical solution for efficient LLM deployment in resource-constrained environments.

Quality Estimation (QE) models evaluate the quality of machine translations without reference translations, serving as the reward models for the translation task. Due to the data scarcity, synthetic data generation has emerged as a promising solution. However, synthetic QE data often suffers from distribution shift, which can manifest as discrepancies between pseudo and real translations, or in pseudo labels that do not align with human preferences. To tackle this issue, we introduce DCSQE, a novel framework for alleviating distribution shift in synthetic QE data. To reduce the difference between pseudo and real translations, we employ the constrained beam search algorithm and enhance translation diversity through the use of distinct generation models. DCSQE uses references, i.e., translation supervision signals, to guide both the generation and annotation processes, enhancing the quality of token-level labels. DCSQE further identifies the shortest phrase covering consecutive error tokens, mimicking human annotation behavior, to assign the final phrase-level labels. Specially, we underscore that the translation model can not annotate translations of itself accurately. Extensive experiments demonstrate that DCSQE outperforms SOTA baselines like CometKiwi in both supervised and unsupervised settings. Further analysis offers insights into synthetic data generation that could benefit reward models for other tasks. The code is available at https://github.com/NJUNLP/njuqe.

Well-designed prompts are crucial for enhancing Large language models' (LLMs) reasoning capabilities while aligning their outputs with task requirements across diverse domains. However, manually designed prompts require expertise and iterative experimentation. While existing prompt optimization methods aim to automate this process, they rely heavily on external references such as ground truth or by humans, limiting their applicability in real-world scenarios where such data is unavailable or costly to obtain. To address this, we propose Self-Supervised Prompt Optimization (SPO), a cost-efficient framework that discovers effective prompts for both closed and open-ended tasks without requiring external reference. Motivated by the observations that prompt quality manifests directly in LLM outputs and LLMs can effectively assess adherence to task requirements, we derive evaluation and optimization signals purely from output comparisons. Specifically, SPO selects superior prompts through pairwise output comparisons evaluated by an LLM evaluator, followed by an LLM optimizer that aligns outputs with task requirements. Extensive experiments demonstrate that SPO outperforms state-of-the-art prompt optimization methods, achieving comparable or superior results with significantly lower costs (e.g., 1.1% to 5.6% of existing methods) and fewer samples (e.g., three samples). The code is available at https://github.com/geekan/MetaGPT.

The fine-tuning of pre-trained large language models (LLMs) using reinforcement learning (RL) is generally formulated as direct policy optimization. This approach was naturally favored as it efficiently improves a pretrained LLM, seen as an initial policy. Another RL paradigm, Q-learning methods, has received far less attention in the LLM community while demonstrating major success in various non-LLM RL tasks. In particular, Q-learning effectiveness comes from its sample efficiency and ability to learn offline, which is particularly valuable given the high computational cost of sampling with LLMs. However, naively applying a Q-learning-style update to the model's logits is ineffective due to the specificity of LLMs. Our core contribution is to derive theoretically grounded loss functions from Bellman equations to adapt Q-learning methods to LLMs. To do so, we carefully adapt insights from the RL literature to account for LLM-specific characteristics, ensuring that the logits become reliable Q-value estimates. We then use this loss to build a practical algorithm, ShiQ for Shifted-Q, that supports off-policy, token-wise learning while remaining simple to implement. Finally, we evaluate ShiQ on both synthetic data and real-world benchmarks, e.g., UltraFeedback and BFCL-V3, demonstrating its effectiveness in both single-turn and multi-turn LLM settings

Continual Pre-Training (CPT) on Large Language Models (LLMs) has been widely used to expand the model's fundamental understanding of specific downstream domains (e.g., math and code). For the CPT on domain-specific LLMs, one important question is how to choose the optimal mixture ratio between the general-corpus (e.g., Dolma, Slim-pajama) and the downstream domain-corpus. Existing methods usually adopt laborious human efforts by grid-searching on a set of mixture ratios, which require high GPU training consumption costs. Besides, we cannot guarantee the selected ratio is optimal for the specific domain. To address the limitations of existing methods, inspired by the Scaling Law for performance prediction, we propose to investigate the Scaling Law of the Domain-specific Continual Pre-Training (D-CPT Law) to decide the optimal mixture ratio with acceptable training costs for LLMs of different sizes. Specifically, by fitting the D-CPT Law, we can easily predict the general and downstream performance of arbitrary mixture ratios, model sizes, and dataset sizes using small-scale training costs on limited experiments. Moreover, we also extend our standard D-CPT Law on cross-domain settings and propose the Cross-Domain D-CPT Law to predict the D-CPT law of target domains, where very small training costs (about 1% of the normal training costs) are needed for the target domains. Comprehensive experimental results on six downstream domains demonstrate the effectiveness and generalizability of our proposed D-CPT Law and Cross-Domain D-CPT Law.

We present semantic correctness proofs of Automatic Differentiation (AD). We consider a forward-mode AD method on a higher order language with algebraic data types, and we characterise it as the unique structure preserving macro given a choice of derivatives for basic operations. We describe a rich semantics for differentiable programming, based on diffeological spaces. We show that it interprets our language, and we phrase what it means for the AD method to be correct with respect to this semantics. We show that our characterisation of AD gives rise to an elegant semantic proof of its correctness based on a gluing construction on diffeological spaces. We explain how this is, in essence, a logical relations argument. Finally, we sketch how the analysis extends to other AD methods by considering a continuation-based method.

Verifiable formal languages like Lean have profoundly impacted mathematical reasoning, particularly through the use of large language models (LLMs) for automated reasoning. A significant challenge in training LLMs for these formal languages is the lack of parallel datasets that align natural language with formal language proofs. To address this challenge, this paper introduces a novel framework for translating the Mathlib4 corpus (a unified library of mathematics in formal language Lean 4) into natural language. Building upon this, we employ a dual augmentation strategy that combines tactic-based and informal-based approaches, leveraging the Lean-jixia system, a Lean 4 analyzer. We present the results of this pipeline on Mathlib4 as Herald (Hierarchy and Retrieval-based Translated Lean Dataset). We also propose the Herald Translator, which is fine-tuned on Herald. Herald translator achieves a 93.2% accuracy (Pass@128) on formalizing statements in the miniF2F-test and a 22.5% accuracy on our internal graduate-level textbook dataset, outperforming InternLM2-Math-Plus-7B (74.0% and 7.5%) and TheoremLlama (50.1% and 4.0%). Furthermore, we propose a section-level translation framework for real-world applications. As a direct application of Herald translator, we have successfully translated a template section in the Stack project, marking a notable progress in the automatic formalization of graduate-level mathematical literature. Our model, along with the datasets, will be open-sourced to the public soon.

LLMs exhibit advanced reasoning capabilities, offering the potential to transform natural language questions into mathematical models. However, existing open-source datasets in operations research domain lack detailed annotations of the modeling process, such as variable definitions, focusing solely on objective values, which hinders reinforcement learning applications. To address this, we release the StructuredOR dataset, annotated with comprehensive labels that capture the complete mathematical modeling process. We further propose BPP-Search, a algorithm that integrates reinforcement learning into a tree-of-thought structure using Beam search, a Process reward model, and a pairwise Preference algorithm. This approach enables efficient exploration of tree structures, avoiding exhaustive search while improving accuracy. Extensive experiments on StructuredOR, NL4OPT, and MAMO-ComplexLP datasets show that BPP-Search significantly outperforms state-of-the-art methods. In tree-based reasoning, BPP-Search excels in accuracy and efficiency, enabling faster retrieval of correct solutions.

The recent success and openness of DeepSeek-R1 have brought widespread attention to Group Relative Policy Optimization (GRPO) as a reinforcement learning method for large reasoning models (LRMs). In this work, we analyze the GRPO objective under a binary reward setting and reveal an inherent limitation of question-level difficulty bias. We also identify a connection between GRPO and traditional discriminative methods in supervised learning. Motivated by these insights, we introduce a new Discriminative Constrained Optimization (DisCO) framework for reinforcing LRMs, grounded in the principle of discriminative learning. The main differences between DisCO and GRPO and its recent variants are: (1) it replaces the group relative objective with a discriminative objective defined by a scoring function; (2) it abandons clipping-based surrogates in favor of non-clipping RL surrogate objectives used as scoring functions; (3) it employs a simple yet effective constrained optimization approach to enforce the KL divergence constraint, ensuring stable training. As a result, DisCO offers notable advantages over GRPO and its variants: (i) it completely eliminates difficulty bias by adopting discriminative objectives; (ii) it addresses the entropy instability in GRPO and its variants through the use of non-clipping scoring functions and a constrained optimization approach; (iii) it allows the incorporation of advanced discriminative learning techniques to address data imbalance, where a significant number of questions have more negative than positive generated answers during training. Our experiments on enhancing the mathematical reasoning capabilities of SFT-finetuned models show that DisCO significantly outperforms GRPO and its improved variants such as DAPO, achieving average gains of 7\% over GRPO and 6\% over DAPO across six benchmark tasks for an 1.5B model.

In this paper, we introduce PolyMath, a multilingual mathematical reasoning benchmark covering 18 languages and 4 easy-to-hard difficulty levels. Our benchmark ensures difficulty comprehensiveness, language diversity, and high-quality translation, making it a highly discriminative multilingual mathematical benchmark in the era of reasoning LLMs. We conduct a comprehensive evaluation for advanced LLMs and find that even Deepseek-R1-671B and Qwen-QwQ-32B, achieve only 43.4 and 41.8 benchmark scores, with less than 30% accuracy under the highest level. From a language perspective, our benchmark reveals several key challenges of LLMs in multilingual reasoning: (1) Reasoning performance varies widely across languages for current LLMs; (2) Input-output language consistency is low in reasoning LLMs and may be correlated with performance; (3) The thinking length differs significantly by language for current LLMs. Additionally, we demonstrate that controlling the output language in the instructions has the potential to affect reasoning performance, especially for some low-resource languages, suggesting a promising direction for improving multilingual capabilities in LLMs.

Mixed integer linear programs are commonly solved by Branch and Bound algorithms. A key factor of the efficiency of the most successful commercial solvers is their fine-tuned heuristics. In this paper, we leverage patterns in real-world instances to learn from scratch a new branching strategy optimised for a given problem and compare it with a commercial solver. We propose FMSTS, a novel Reinforcement Learning approach specifically designed for this task. The strength of our method lies in the consistency between a local value function and a global metric of interest. In addition, we provide insights for adapting known RL techniques to the Branch and Bound setting, and present a new neural network architecture inspired from the literature. To our knowledge, it is the first time Reinforcement Learning has been used to fully optimise the branching strategy. Computational experiments show that our method is appropriate and able to generalise well to new instances.

Twenty-seven years ago, E. Freuder highlighted that "Constraint programming represents one of the closest approaches computer science has yet made to the Holy Grail of programming: the user states the problem, the computer solves it". Nowadays, CP users have great modeling tools available (like Minizinc and CPMpy), allowing them to formulate the problem and then let a solver do the rest of the job, getting closer to the stated goal. However, this still requires the CP user to know the formalism and respect it. Another significant challenge lies in the expertise required to effectively model combinatorial problems. All this limits the wider adoption of CP. In this position paper, we investigate a possible approach to leverage pre-trained Large Language Models to extract models from textual problem descriptions. More specifically, we take inspiration from the Natural Language Processing for Optimization (NL4OPT) challenge and present early results with a decomposition-based prompting approach to GPT Models.

Agents based on large language models (LLMs) have demonstrated effectiveness in solving a wide range of tasks by integrating LLMs with key modules such as planning, memory, and tool usage. Increasingly, customers are adopting LLM agents across a variety of commercial applications critical to reliability, including support for mental well-being, chemical synthesis, and software development. Nevertheless, our observations and daily use of LLM agents indicate that they are prone to making erroneous plans, especially when the tasks are complex and require long-term planning. In this paper, we propose PDoctor, a novel and automated approach to testing LLM agents and understanding their erroneous planning. As the first work in this direction, we formulate the detection of erroneous planning as a constraint satisfiability problem: an LLM agent's plan is considered erroneous if its execution violates the constraints derived from the user inputs. To this end, PDoctor first defines a domain-specific language (DSL) for user queries and synthesizes varying inputs with the assistance of the Z3 constraint solver. These synthesized inputs are natural language paragraphs that specify the requirements for completing a series of tasks. Then, PDoctor derives constraints from these requirements to form a testing oracle. We evaluate PDoctor with three mainstream agent frameworks and two powerful LLMs (GPT-3.5 and GPT-4). The results show that PDoctor can effectively detect diverse errors in agent planning and provide insights and error characteristics that are valuable to both agent developers and users. We conclude by discussing potential alternative designs and directions to extend PDoctor.

We present Ring-lite, a Mixture-of-Experts (MoE)-based large language model optimized via reinforcement learning (RL) to achieve efficient and robust reasoning capabilities. Built upon the publicly available Ling-lite model, a 16.8 billion parameter model with 2.75 billion activated parameters, our approach matches the performance of state-of-the-art (SOTA) small-scale reasoning models on challenging benchmarks (e.g., AIME, LiveCodeBench, GPQA-Diamond) while activating only one-third of the parameters required by comparable models. To accomplish this, we introduce a joint training pipeline integrating distillation with RL, revealing undocumented challenges in MoE RL training. First, we identify optimization instability during RL training, and we propose Constrained Contextual Computation Policy Optimization(C3PO), a novel approach that enhances training stability and improves computational throughput via algorithm-system co-design methodology. Second, we empirically demonstrate that selecting distillation checkpoints based on entropy loss for RL training, rather than validation metrics, yields superior performance-efficiency trade-offs in subsequent RL training. Finally, we develop a two-stage training paradigm to harmonize multi-domain data integration, addressing domain conflicts that arise in training with mixed dataset. We will release the model, dataset, and code.

Reinforcement learning with human feedback for aligning large language models (LLMs) trains a reward model typically using ranking loss with comparison pairs.However, the training procedure suffers from an inherent problem: the uncontrolled scaling of reward scores during reinforcement learning due to the lack of constraints while training the reward model.This paper proposes a Prior Constraints-based Reward Model (namely PCRM) training method to mitigate this problem. PCRM incorporates prior constraints, specifically, length ratio and cosine similarity between outputs of each comparison pair, during reward model training to regulate optimization magnitude and control score margins. We comprehensively evaluate PCRM by examining its rank correlation with human preferences and its effectiveness in aligning LLMs via RL. Experimental results demonstrate that PCRM significantly improves alignment performance by effectively constraining reward score scaling. As another bonus, our method is easily integrated into arbitrary rank-based alignment methods, such as direct preference optimization, and can yield consistent improvement.

We investigate the logical reasoning capabilities of large language models (LLMs) and their scalability in complex non-monotonic reasoning. To this end, we introduce ZebraLogic, a comprehensive evaluation framework for assessing LLM reasoning performance on logic grid puzzles derived from constraint satisfaction problems (CSPs). ZebraLogic enables the generation of puzzles with controllable and quantifiable complexity, facilitating a systematic study of the scaling limits of models such as Llama, o1 models, and DeepSeek-R1. By encompassing a broad range of search space complexities and diverse logical constraints, ZebraLogic provides a structured environment to evaluate reasoning under increasing difficulty. Our results reveal a significant decline in accuracy as problem complexity grows -- a phenomenon we term the curse of complexity. This limitation persists even with larger models and increased inference-time computation, suggesting inherent constraints in current LLM reasoning capabilities. Additionally, we explore strategies to enhance logical reasoning, including Best-of-N sampling, backtracking mechanisms, and self-verification prompts. Our findings offer critical insights into the scalability of LLM reasoning, highlight fundamental limitations, and outline potential directions for improvement.

Machine learning is becoming an increasingly valuable tool in mathematics, enabling one to identify subtle patterns across collections of examples so vast that they would be impossible for a single researcher to feasibly review and analyze. In this work, we use graph neural networks to investigate quiver mutation -- an operation that transforms one quiver (or directed multigraph) into another -- which is central to the theory of cluster algebras with deep connections to geometry, topology, and physics. In the study of cluster algebras, the question of mutation equivalence is of fundamental concern: given two quivers, can one efficiently determine if one quiver can be transformed into the other through a sequence of mutations? In this paper, we use graph neural networks and AI explainability techniques to independently discover mutation equivalence criteria for quivers of type D. Along the way, we also show that even without explicit training to do so, our model captures structure within its hidden representation that allows us to reconstruct known criteria from type D, adding to the growing evidence that modern machine learning models are capable of learning abstract and parsimonious rules from mathematical data.

In the field of large language models (LLMs), Knowledge Distillation (KD) is a critical technique for transferring capabilities from teacher models to student models. However, existing KD methods face limitations and challenges in distillation of LLMs, including efficiency and insufficient measurement capabilities of traditional KL divergence. It is shown that LLMs can serve as an implicit reward function, which we define as a supplement to KL divergence. In this work, we propose Direct Preference Knowledge Distillation (DPKD) for LLMs. DPKD utilizes distribution divergence to represent the preference loss and implicit reward function. We re-formulate KD of LLMs into two stages: first optimizing and objective consisting of implicit reward and reverse KL divergence and then improving the preference probability of teacher outputs over student outputs. We conducted experiments and analysis on various datasets with LLM parameters ranging from 120M to 13B and demonstrate the broad applicability and effectiveness of our DPKD approach. Meanwhile, we prove the value and effectiveness of the introduced implicit reward and output preference in KD through experiments and theoretical analysis. The DPKD method outperforms the baseline method in both output response precision and exact match percentage. Code and data are available at https://aka.ms/dpkd.

Direct Alignment Algorithms (DAAs), such as Direct Preference Optimisation (DPO) and Identity Preference Optimisation (IPO), have emerged as alternatives to online Reinforcement Learning from Human Feedback (RLHF) algorithms such as Proximal Policy Optimisation (PPO) for aligning language models to human preferences, without the need for explicit reward modelling. These methods generally aim to increase the likelihood of generating better (preferred) completions while discouraging worse (non-preferred) ones, while staying close to the original model's behaviour. In this work, we explore the relationship between completion likelihood and model performance in state-of-the-art DAAs, and identify a critical issue of likelihood over-optimisation. Contrary to expectations, we find that higher likelihood of better completions and larger margins between better and worse completion likelihoods do not necessarily lead to better performance, and may even degrade it. Our analysis reveals that while higher likelihood correlates with better memorisation of factual knowledge patterns, a slightly lower completion likelihood tends to improve output diversity, thus leading to better generalisation to unseen scenarios. Moreover, we identify two key indicators that signal when over-optimised output diversity begins to harm performance: Decreasing Entropy over Top-k Tokens and Diminishing Top-k Probability Mass. Our experimental results validate that these indicators are reliable signs of declining performance under different regularisations, helping prevent over-optimisation and improve alignment with human preferences.

Existing math datasets evaluate the reasoning abilities of large language models (LLMs) by either using the final answer or the intermediate reasoning steps derived from static examples. However, the former approach fails to surface model's uses of shortcuts and wrong reasoning while the later poses challenges in accommodating alternative solutions. In this work, we seek to use symbolic programs as a means for automated evaluation if a model can consistently produce correct final answers across various inputs to the program. We begin by extracting programs for popular math datasets (GSM8K and MATH) using GPT4-o. For those executable programs verified using the original input-output pairs, they are found to encapsulate the proper reasoning required to solve the original text questions. We then prompt GPT4-o to generate new questions using alternative input-output pairs based the extracted program. We apply the resulting datasets to evaluate a collection of LLMs. In our experiments, we observe significant accuracy drops using our proposed evaluation compared with original static examples, suggesting the fragility of math reasoning in state-of-the-art LLMs.

Recent advances in large language model (LLM) post-training have leveraged two distinct paradigms to enhance reasoning capabilities: reinforcement learning (RL) and knowledge distillation (KD). While RL enables the emergence of complex reasoning behaviors, it often suffers from low sample efficiency when the initial policy struggles to explore high-reward trajectories. Conversely, KD improves learning efficiency via mimicking the teacher model but tends to generalize poorly to out-of-domain scenarios. In this work, we present KDRL, a unified post-training framework that jointly optimizes a reasoning model through teacher supervision (KD) and self-exploration (RL). Specifically, KDRL leverages policy gradient optimization to simultaneously minimize the reverse Kullback-Leibler divergence (RKL) between the student and teacher distributions while maximizing the expected rule-based rewards. We first formulate a unified objective that integrates GRPO and KD, and systematically explore how different KL approximations, KL coefficients, and reward-guided KD strategies affect the overall post-training dynamics and performance. Empirical results on multiple reasoning benchmarks demonstrate that KDRL outperforms GRPO and various KD baselines while achieving a favorable balance between performance and reasoning token efficiency. These findings indicate that integrating KD and RL serves as an effective and efficient strategy to train reasoning LLMs.

We study the classic Text-to-Pattern Hamming Distances problem: given a pattern P of length m and a text T of length n, both over a polynomial-size alphabet, compute the Hamming distance between P and T[i, ., . , i+m-1] for every shift i, under the standard Word-RAM model with Theta(log n)-bit words. - We provide an O(nm) time Las Vegas randomized algorithm for this problem, beating the decades-old O(n m log m) running time [Abrahamson, SICOMP 1987]. We also obtain a deterministic algorithm, with a slightly higher O(nm(log mloglog m)^{1/4}) running time. Our randomized algorithm extends to the k-bounded setting, with running time Obig(n+nk{m}big), removing all the extra logarithmic factors from earlier algorithms [Gawrychowski and Uzna\'{n}ski, ICALP 2018; Chan, Golan, Kociumaka, Kopelowitz and Porat, STOC 2020]. - For the (1+epsilon)-approximate version of Text-to-Pattern Hamming Distances, we give an O(epsilon^{-0.93}n) time Monte Carlo randomized algorithm, beating the previous O(epsilon^{-1}n) running time [Kopelowitz and Porat, FOCS 2015; Kopelowitz and Porat, SOSA 2018]. Our approximation algorithm exploits a connection with 3SUM, and uses a combination of Fredman's trick, equality matrix product, and random sampling; in particular, we obtain new results on approximate counting versions of 3SUM and Exact Triangle, which may be of independent interest. Our exact algorithms use a novel combination of hashing, bit-packed FFT, and recursion; in particular, we obtain a faster algorithm for computing the sumset of two integer sets, in the regime when the universe size is close to quadratic in the number of elements. We also prove a fine-grained equivalence between the exact Text-to-Pattern Hamming Distances problem and a range-restricted, counting version of 3SUM.

Mathematical reasoning is an important capability of large language models~(LLMs) for real-world applications. To enhance this capability, existing work either collects large-scale math-related texts for pre-training, or relies on stronger LLMs (\eg GPT-4) to synthesize massive math problems. Both types of work generally lead to large costs in training or synthesis. To reduce the cost, based on open-source available texts, we propose an efficient way that trains a small LLM for math problem synthesis, to efficiently generate sufficient high-quality pre-training data. To achieve it, we create a dataset using GPT-4 to distill its data synthesis capability into the small LLM. Concretely, we craft a set of prompts based on human education stages to guide GPT-4, to synthesize problems covering diverse math knowledge and difficulty levels. Besides, we adopt the gradient-based influence estimation method to select the most valuable math-related texts. The both are fed into GPT-4 for creating the knowledge distillation dataset to train the small LLM. We leverage it to synthesize 6 million math problems for pre-training our JiuZhang3.0 model, which only needs to invoke GPT-4 API 9.3k times and pre-train on 4.6B data. Experimental results have shown that JiuZhang3.0 achieves state-of-the-art performance on several mathematical reasoning datasets, under both natural language reasoning and tool manipulation settings. Our code and data will be publicly released in https://github.com/RUCAIBox/JiuZhang3.0.

Multi-agent pathfinding (MAPF) is a common abstraction of multi-robot trajectory planning problems, where multiple homogeneous robots simultaneously move in the shared environment. While solving MAPF optimally has been proven to be NP-hard, scalable, and efficient, solvers are vital for real-world applications like logistics, search-and-rescue, etc. To this end, decentralized suboptimal MAPF solvers that leverage machine learning have come on stage. Building on the success of the recently introduced MAPF-GPT, a pure imitation learning solver, we introduce MAPF-GPT-DDG. This novel approach effectively fine-tunes the pre-trained MAPF model using centralized expert data. Leveraging a novel delta-data generation mechanism, MAPF-GPT-DDG accelerates training while significantly improving performance at test time. Our experiments demonstrate that MAPF-GPT-DDG surpasses all existing learning-based MAPF solvers, including the original MAPF-GPT, regarding solution quality across many testing scenarios. Remarkably, it can work with MAPF instances involving up to 1 million agents in a single environment, setting a new milestone for scalability in MAPF domains.

Large language models (LLMs) have shown promising performance across diverse domains. Many practical applications of LLMs, such as code completion and structured data extraction, require adherence to syntactic constraints specified by a formal language. Yet, due to their probabilistic nature, LLM output is not guaranteed to adhere to such formal languages. Prior work has proposed constrained decoding as a means to restrict LLM generation to particular formal languages. However, existing works are not applicable to the emerging paradigm of diffusion LLMs, when used in practical scenarios such as the generation of formally correct C++ or JSON output. In this paper we address this challenge and present the first constrained decoding method for diffusion models, one that can handle formal languages captured by context-free grammars. We begin by reducing constrained decoding to the more general additive infilling problem, which asks whether a partial output can be completed to a valid word in the target language. This problem also naturally subsumes the previously unaddressed multi-region infilling constrained decoding. We then reduce this problem to the task of deciding whether the intersection of the target language and a regular language is empty and present an efficient algorithm to solve it for context-free languages. Empirical results on various applications, such as C++ code infilling and structured data extraction in JSON, demonstrate that our method achieves near-perfect syntactic correctness while consistently preserving or improving functional correctness. Importantly, our efficiency optimizations ensure that the computational overhead remains practical.

The increasing capabilities of large language models (LLMs) raise opportunities for artificial general intelligence but concurrently amplify safety concerns, such as potential misuse of AI systems, necessitating effective AI alignment. Reinforcement Learning from Human Feedback (RLHF) has emerged as a promising pathway towards AI alignment but brings forth challenges due to its complexity and dependence on a separate reward model. Direct Preference Optimization (DPO) has been proposed as an alternative, and it remains equivalent to RLHF under the reverse KL regularization constraint. This paper presents f-DPO, a generalized approach to DPO by incorporating diverse divergence constraints. We show that under certain f-divergences, including Jensen-Shannon divergence, forward KL divergences and alpha-divergences, the complex relationship between the reward and optimal policy can also be simplified by addressing the Karush-Kuhn-Tucker conditions. This eliminates the need for estimating the normalizing constant in the Bradley-Terry model and enables a tractable mapping between the reward function and the optimal policy. Our approach optimizes LLMs to align with human preferences in a more efficient and supervised manner under a broad set of divergence constraints. Empirically, adopting these divergences ensures a balance between alignment performance and generation diversity. Importantly, f-DPO outperforms PPO-based methods in divergence efficiency, and divergence constraints directly influence expected calibration error (ECE).

Large language models (LLMs) have achieved remarkable performance in various evaluation benchmarks. However, concerns are raised about potential data contamination in their considerable volume of training corpus. Moreover, the static nature and fixed complexity of current benchmarks may inadequately gauge the advancing capabilities of LLMs. In this paper, we introduce DyVal, a general and flexible protocol for dynamic evaluation of LLMs. Based on our framework, we build graph-informed DyVal by leveraging the structural advantage of directed acyclic graphs to dynamically generate evaluation samples with controllable complexities. DyVal generates challenging evaluation sets on reasoning tasks including mathematics, logical reasoning, and algorithm problems. We evaluate various LLMs ranging from Flan-T5-large to GPT-3.5-Turbo and GPT-4. Experiments show that LLMs perform worse in DyVal-generated evaluation samples with different complexities, highlighting the significance of dynamic evaluation. We also analyze the failure cases and results of different prompting methods. Moreover, DyVal-generated samples are not only evaluation sets, but also helpful data for fine-tuning to improve the performance of LLMs on existing benchmarks. We hope that DyVal can shed light on future evaluation research of LLMs. Code is available at: https://github.com/microsoft/promptbench.

Reinforcement learning (RL) has emerged as a powerful paradigm for fine-tuning Large Language Models (LLMs) for conditional text generation. In particular, recent LLMs such as ChatGPT and GPT-4 can engage in fluent conversations with users by incorporating RL and feedback from humans. Inspired by learning-to-search algorithms and capitalizing on key properties of text generation, we seek to investigate reinforcement learning algorithms beyond general purpose algorithms such as Proximal policy optimization (PPO). In particular, we extend RL algorithms to allow them to interact with a dynamic black-box guide LLM such as GPT-3 and propose RL with guided feedback (RLGF), a suite of RL algorithms for LLM fine-tuning. We experiment on the IMDB positive review and CommonGen text generation task from the GRUE benchmark. We show that our RL algorithms achieve higher performance than supervised learning (SL) and default PPO baselines, demonstrating the benefit of interaction with the guide LLM. On CommonGen, we not only outperform our SL baselines but also improve beyond PPO across a variety of lexical and semantic metrics beyond the one we optimized for. Notably, on the IMDB dataset, we show that our GPT-2 based policy outperforms the zero-shot GPT-3 oracle, indicating that our algorithms can learn from a powerful, black-box GPT-3 oracle with a simpler, cheaper, and publicly available GPT-2 model while gaining performance.

It is crucial for large language models (LLMs) to follow instructions that involve multiple constraints. However, it is an unexplored area to enhance LLMs' ability to follow soft constraints. To bridge the gap, we initially design a pipeline to construct datasets with high-quality outputs automatically. Additionally, to fully utilize the positive and negative samples generated during the data construction process, we choose Direct Preference Optimization (DPO) as the training method. Furthermore, taking into account the difficulty of soft constraints indicated by the number of constraints, we design a curriculum learning training paradigm based on the constraint quantity. We experimentally evaluate the effectiveness of our methods in improving LLMs' soft constraint following ability and analyze the factors driving the improvements.The datasets and code are publicly available at https://github.com/Rainier-rq/FollowSoftConstraint.

Reward finetuning has emerged as a promising approach to aligning foundation models with downstream objectives. Remarkable success has been achieved in the language domain by using reinforcement learning (RL) to maximize rewards that reflect human preference. However, in the vision domain, existing RL-based reward finetuning methods are limited by their instability in large-scale training, rendering them incapable of generalizing to complex, unseen prompts. In this paper, we propose Proximal Reward Difference Prediction (PRDP), enabling stable black-box reward finetuning for diffusion models for the first time on large-scale prompt datasets with over 100K prompts. Our key innovation is the Reward Difference Prediction (RDP) objective that has the same optimal solution as the RL objective while enjoying better training stability. Specifically, the RDP objective is a supervised regression objective that tasks the diffusion model with predicting the reward difference of generated image pairs from their denoising trajectories. We theoretically prove that the diffusion model that obtains perfect reward difference prediction is exactly the maximizer of the RL objective. We further develop an online algorithm with proximal updates to stably optimize the RDP objective. In experiments, we demonstrate that PRDP can match the reward maximization ability of well-established RL-based methods in small-scale training. Furthermore, through large-scale training on text prompts from the Human Preference Dataset v2 and the Pick-a-Pic v1 dataset, PRDP achieves superior generation quality on a diverse set of complex, unseen prompts whereas RL-based methods completely fail.

Fine-tuning pre-trained Large Language Models (LLMs) is essential to align them with human values and intentions. This process often utilizes methods like pairwise comparisons and KL divergence against a reference LLM, focusing on the evaluation of full answers generated by the models. However, the generation of these responses occurs in a token level, following a sequential, auto-regressive fashion. In this paper, we introduce Token-level Direct Preference Optimization (TDPO), a novel approach to align LLMs with human preferences by optimizing policy at the token level. Unlike previous methods, which face challenges in divergence efficiency, TDPO incorporates forward KL divergence constraints for each token, improving alignment and diversity. Utilizing the Bradley-Terry model for a token-based reward system, TDPO enhances the regulation of KL divergence, while preserving simplicity without the need for explicit reward modeling. Experimental results across various text tasks demonstrate TDPO's superior performance in balancing alignment with generation diversity. Notably, fine-tuning with TDPO strikes a better balance than DPO in the controlled sentiment generation and single-turn dialogue datasets, and significantly improves the quality of generated responses compared to both DPO and PPO-based RLHF methods. Our code is open-sourced at https://github.com/Vance0124/Token-level-Direct-Preference-Optimization.

Large Language Models (LLMs) struggle with reliably generating highly structured outputs, such as program code, mathematical formulas, or well-formed markup. Constrained decoding approaches mitigate this problem by greedily restricting what tokens an LLM can output at each step to guarantee that the output matches a given constraint. Specifically, in grammar-constrained decoding (GCD), the LLM's output must follow a given grammar. In this paper, we demonstrate that GCD techniques (and in general constrained decoding techniques) can distort the LLM's distribution, leading to outputs that are grammatical but appear with likelihoods that are not proportional to the ones given by the LLM, and so ultimately are low-quality. We call the problem of aligning sampling with a grammar constraint, grammar-aligned decoding (GAD), and propose adaptive sampling with approximate expected futures (ASAp), a decoding algorithm that guarantees the output to be grammatical while provably producing outputs that match the conditional probability of the LLM's distribution conditioned on the given grammar constraint. Our algorithm uses prior sample outputs to soundly overapproximate the future grammaticality of different output prefixes. Our evaluation on code generation and structured NLP tasks shows how ASAp often produces outputs with higher likelihood (according to the LLM's distribution) than existing GCD techniques, while still enforcing the desired grammatical constraints.

Large Language Models (LLMs) have exhibited exceptional performance across a broad range of tasks and domains. However, they still encounter difficulties in solving mathematical problems due to the rigorous and logical nature of mathematics. Previous studies have employed techniques such as supervised fine-tuning (SFT), prompt engineering, and search-based methods to improve the mathematical problem-solving abilities of LLMs. Despite these efforts, their performance remains suboptimal and demands substantial computational resources. To address this issue, we propose a novel approach, BEATS, to enhance mathematical problem-solving abilities. Our method leverages newly designed prompts that guide the model to iteratively rewrite, advance by one step, and generate answers based on previous steps. Additionally, we introduce a new back-verification technique that uses LLMs to validate the correctness of the generated answers. Furthermore, we employ a pruning tree search to optimize search time while achieving strong performance. Notably, our method improves Qwen2-7b-Instruct's score from 36.94 to 61.52, outperforming GPT4's 42.5 on the MATH benchmark.

The generative power of diffusion models (DMs) has recently enabled high-performing decision-making algorithms in offline reinforcement learning (RL), achieving state-of-the-art results across standard benchmarks. Among them, Diffusion Q-Learning (DQL) stands out as a leading method for its consistently strong performance. Nevertheless, DQL remains limited in practice due to its reliance on multi-step denoising for action generation during both training and inference. Although one-step denoising is desirable, simply applying it to DQL leads to a drastic performance drop. In this work, we revisit DQL and identify its core limitations. We then propose One-Step Flow Q-Learning (OFQL), a novel framework that enables efficient one-step action generation during both training and inference, without requiring auxiliary models, distillation, or multi-phase training. Specifically, OFQL reformulates DQL within the sample-efficient Flow Matching (FM) framework. While conventional FM induces curved generative trajectories that impede one-step generation, OFQL instead learns an average velocity field that facilitates direct, accurate action generation. Collectively, OFQL eliminates the need for multi-step sampling and recursive gradient updates in DQL, resulting in faster and more robust training and inference. Extensive experiments on the D4RL benchmark demonstrate that OFQL outperforms DQL and other diffusion-based baselines, while substantially reducing both training and inference time compared to DQL.

Many methods in differentially private model training rely on computing the similarity between a query point (such as public or synthetic data) and private data. We abstract out this common subroutine and study the following fundamental algorithmic problem: Given a similarity function f and a large high-dimensional private dataset X subset R^d, output a differentially private (DP) data structure which approximates sum_{x in X} f(x,y) for any query y. We consider the cases where f is a kernel function, such as f(x,y) = e^{-|x-y|_2^2/sigma^2} (also known as DP kernel density estimation), or a distance function such as f(x,y) = |x-y|_2, among others. Our theoretical results improve upon prior work and give better privacy-utility trade-offs as well as faster query times for a wide range of kernels and distance functions. The unifying approach behind our results is leveraging `low-dimensional structures' present in the specific functions f that we study, using tools such as provable dimensionality reduction, approximation theory, and one-dimensional decomposition of the functions. Our algorithms empirically exhibit improved query times and accuracy over prior state of the art. We also present an application to DP classification. Our experiments demonstrate that the simple methodology of classifying based on average similarity is orders of magnitude faster than prior DP-SGD based approaches for comparable accuracy.

Learning from human preference data has emerged as the dominant paradigm for fine-tuning large language models (LLMs). The two most common families of techniques -- online reinforcement learning (RL) such as Proximal Policy Optimization (PPO) and offline contrastive methods such as Direct Preference Optimization (DPO) -- were positioned as equivalent in prior work due to the fact that both have to start from the same offline preference dataset. To further expand our theoretical understanding of the similarities and differences between online and offline techniques for preference fine-tuning, we conduct a rigorous analysis through the lens of dataset coverage, a concept that captures how the training data covers the test distribution and is widely used in RL. We prove that a global coverage condition is both necessary and sufficient for offline contrastive methods to converge to the optimal policy, but a weaker partial coverage condition suffices for online RL methods. This separation provides one explanation of why online RL methods can perform better than offline methods, especially when the offline preference data is not diverse enough. Finally, motivated by our preceding theoretical observations, we derive a hybrid preference optimization (HyPO) algorithm that uses offline data for contrastive-based preference optimization and online data for KL regularization. Theoretically and empirically, we demonstrate that HyPO is more performant than its pure offline counterpart DPO, while still preserving its computation and memory efficiency.

Large Language Models (LLMs) are widely adopted for assisting in software development tasks, yet their performance evaluations have narrowly focused on the functional correctness of generated code. Human programmers, however, require LLM-generated code to be not only correct but also optimally efficient. We propose PerfCodeGen, a training-free framework that enhances the performance of LLM-generated code by incorporating feedback based on runtime during test case execution into the self-refinement iterations. With PerfCodeGen, we achieve speedups for a significantly higher proportion of problems compared to using the base LLM with sophisticated prompting techniques. Applied to open language models like Phi-3-mini, PerfCodeGen achieves runtime efficiency comparable to prompting powerful closed models like GPT-4. We achieve state-of-the-art runtime efficiency on benchmarks such as HumanEval, MBPP, and APPS, frequently surpassing the ground truth reference solutions with PerfCodeGen using GPT-3.5 and GPT-4. Additionally, we demonstrate the effectiveness of our approach in enhancing code quality across a range of open LLMs of varying sizes including Phi-3-mini, Llama 3 8B, Mixtral 8x7B, Command R, and Llama 3 70B.

Evaluating the mathematical capability of Large Language Models (LLMs) is a critical yet challenging frontier. Existing benchmarks fall short, particularly for proof-centric problems, as manual creation is unscalable and costly, leaving the true mathematical abilities of LLMs largely unassessed. To overcome these barriers, we propose Proof2Hybrid, the first fully automated framework that synthesizes high-quality, proof-centric benchmarks from natural language mathematical corpora. The key novelty of our solution is Proof2X, a roadmap of converting mathematical proofs into various kinds of questions that are easy to verify. Instructed by this roadmap, we propose a new type of hybrid-formatted questions, named ``m-out-of-n multiple judge questions'', specifically designed to enable robust, automatic evaluation while being resilient to guessing and superficial pattern matching inherent in traditional formats. As a demonstration of our framework, we introduce AlgGeoTest, a benchmark for algebraic geometry--a frontier domain of modern mathematics--comprising 456 challenging items. Our extensive evaluations on state-of-the-art LLMs using AlgGeoTest reveal profound deficits in their comprehension of algebraic geometry, providing a more precise measure of their true mathematical capabilities. Our framework and benchmark pave the way for a new wave of in-depth research into the mathematical intelligence of AI systems.

In this paper, we present Jellyfish, an open-source LLM as a universal task solver for DP. Built on the Llama 2 13B model, Jellyfish is instruction-tuned with the datasets of several typical DP tasks including error detection, data imputation, schema matching, and entity matching, and delivers generalizability to other tasks. Remarkably, Jellyfish can operate on a local, single, and low-priced GPU with its 13 billion parameters, ensuring data security and enabling further tuning. Its proficiency in understanding natural language allows users to manually craft instructions for DP tasks. Unlike many existing methods that heavily rely on prior knowledge, Jellyfish acquires domain knowledge during its tuning process and integrates optional knowledge injection during inference. A distinctive feature of Jellyfish is its interpreter, which elucidates its output decisions. To construct Jellyfish, we develop a series of pre-tuning and DP-tuning techniques. Jellyfish is equipped with an instance serializer, which automatically translates raw data into model prompts, and a knowledge injector, which optionally introduces task- and dataset-specific knowledge to enhance DP performance. Our evaluation of Jellyfish, using a range of real datasets, shows its competitiveness compared to state-of-the-art methods and its strong generalizability to unseen tasks. Jellyfish's performance rivals that of GPT series models, and its interpreter offers enhanced reasoning capabilities compared to GPT-3.5. Furthermore, our evaluation highlights the effectiveness of the techniques employed in constructing Jellyfish. Our model is available at Hugging Face: https://huggingface.co/NECOUDBFM/Jellyfish .

Reinforcement learning (RL) with tree search has demonstrated superior performance in traditional reasoning tasks. Compared to conventional independent chain sampling strategies with outcome supervision, tree search enables better exploration of the reasoning space and provides dense, on-policy process rewards during RL training but remains under-explored in On-Policy LLM RL. We propose TreeRL, a reinforcement learning framework that directly incorporates on-policy tree search for RL training. Our approach includes intermediate supervision and eliminates the need for a separate reward model training. Existing approaches typically train a separate process reward model, which can suffer from distribution mismatch and reward hacking. We also introduce a cost-effective tree search approach that achieves higher search efficiency under the same generation token budget by strategically branching from high-uncertainty intermediate steps rather than using random branching. Experiments on challenging math and code reasoning benchmarks demonstrate that TreeRL achieves superior performance compared to traditional ChainRL, highlighting the potential of tree search for LLM. TreeRL is open-sourced at https://github.com/THUDM/TreeRL.

Recent advancements in large language models (LLMs) have sparked considerable interest in automated theorem proving and a prominent line of research integrates stepwise LLM-based provers into tree search. In this paper, we introduce a novel proof-state exploration approach for training data synthesis, designed to produce diverse tactics across a wide range of intermediate proof states, thereby facilitating effective one-shot fine-tuning of LLM as the policy model. We also propose an adaptive beam size strategy, which effectively takes advantage of our data synthesis method and achieves a trade-off between exploration and exploitation during tree search. Evaluations on the MiniF2F and ProofNet benchmarks demonstrate that our method outperforms strong baselines under the stringent Pass@1 metric, attaining an average pass rate of 60.74% on MiniF2F and 21.18% on ProofNet. These results underscore the impact of large-scale synthetic data in advancing automated theorem proving.

In practical settings, differentially private Federated learning (DP-FL) is the dominant method for training models from private, on-device client data. Recent work has suggested that DP-FL may be enhanced or outperformed by methods that use DP synthetic data (Wu et al., 2024; Hou et al., 2024). The primary algorithms for generating DP synthetic data for FL applications require careful prompt engineering based on public information and/or iterative private client feedback. Our key insight is that the private client feedback collected by prior DP synthetic data methods (Hou et al., 2024; Xie et al., 2024) can be viewed as a preference ranking. Our algorithm, Preference Optimization for Private Client Data (POPri) harnesses client feedback using preference optimization algorithms such as Direct Preference Optimization (DPO) to fine-tune LLMs to generate high-quality DP synthetic data. To evaluate POPri, we release LargeFedBench, a new federated text benchmark for uncontaminated LLM evaluations on federated client data. POPri substantially improves the utility of DP synthetic data relative to prior work on LargeFedBench datasets and an existing benchmark from Xie et al. (2024). POPri closes the gap between next-token prediction accuracy in the fully-private and non-private settings by up to 68%, compared to 52% for prior synthetic data methods, and 10% for state-of-the-art DP federated learning methods. The code and data are available at https://github.com/meiyuw/POPri.

Large language models (LLMs) show strong performance across natural language processing (NLP), mathematical reasoning, and programming, and recent large reasoning models (LRMs) further emphasize explicit reasoning. Yet their computational limits, particularly spatial complexity constrained by finite context windows, remain poorly understood. While recent works often focus on problems within the NP complexity class, we push the boundary by introducing a novel benchmark grounded in two PSPACE-complete regular expression (regex) problems: equivalence decision (RegexEQ) and minimization (RegexMin). PSPACE-complete problems serve as a more rigorous standard for assessing computational capacity, as their solutions require massive search space exploration. We perform a double-exponential space exploration to construct a labeled dataset of over a million regex instances with a sound filtering process to build the benchmark. We conduct extensive evaluations on 6 LLMs and 5 LRMs of varying scales, revealing common failure patterns such as verbosity and repetition. With its well-defined structure and quantitative evaluation metrics, this work presents the first empirical investigation into the spatial computational limitations of LLMs and LRMs, offering a new framework for evaluating their advanced reasoning capabilities. Our code is available at https://github.com/hyundong98/RegexPSPACE .

Recent years have seen considerable advancements in multi-step reasoning with Large Language Models (LLMs). The previous studies have elucidated the merits of integrating feedback or search mechanisms during model inference to improve the reasoning accuracy. The Process-Supervised Reward Model (PRM), typically furnishes LLMs with step-by-step feedback during the training phase, akin to Proximal Policy Optimization (PPO) or reject sampling. Our objective is to examine the efficacy of PRM in the inference phase to help discern the optimal solution paths for multi-step tasks such as mathematical reasoning and code generation. To this end, we propose a heuristic greedy search algorithm that employs the step-level feedback from PRM to optimize the reasoning pathways explored by LLMs. This tailored PRM demonstrated enhanced results compared to the Chain of Thought (CoT) on mathematical benchmarks like GSM8K and MATH. Additionally, to explore the versatility of our approach, we develop a novel method to automatically generate step-level reward dataset for coding tasks and observed similar improved performance in the code generation tasks. Thus highlighting the robust nature of our reward-model-based approach to inference for reasoning tasks.

With the growing utilization of large language models (LLMs) across domains, alignment towards human preferences has become one of the most critical aspects of training models. At the forefront of state-of-the-art human alignment methods are preference optimization methods (*PO). However, prior research has often concentrated on identifying the best-performing method, typically involving a grid search over hyperparameters, which can be impractical for general practitioners. In this paper, we aim to identify the algorithm that, while being performant, is simultaneously more robust to varying hyperparameters, thereby increasing the likelihood of achieving better results. We focus on a realistic out-of-distribution (OOD) scenario that mirrors real-world applications of human alignment, offering practical insights into the strengths and weaknesses of these methods. Furthermore, to better understand the shortcomings of generations from the different methods, we analyze the model generations through the lens of KL divergence of the SFT model and the response length statistics. Our analysis reveals that the widely adopted DPO method consistently produces lengthy responses of inferior quality that are very close to the SFT responses. Motivated by these findings, we propose an embarrassingly simple extension to the DPO algorithm, LN-DPO, resulting in more concise responses without sacrificing quality compared to the policy obtained by vanilla DPO.

We introduce a novel framework for analyzing sorting algorithms in pairwise ranking prompting (PRP), re-centering the cost model around LLM inferences rather than traditional pairwise comparisons. While classical metrics based on comparison counts have traditionally been used to gauge efficiency, our analysis reveals that expensive LLM inferences overturn these predictions; accordingly, our framework encourages strategies such as batching and caching to mitigate inference costs. We show that algorithms optimal in the classical setting can lose efficiency when LLM inferences dominate the cost under certain optimizations.

Compared to the wide array of advanced Monte Carlo methods supported by modern probabilistic programming languages (PPLs), PPL support for variational inference (VI) is less developed: users are typically limited to a predefined selection of variational objectives and gradient estimators, which are implemented monolithically (and without formal correctness arguments) in PPL backends. In this paper, we propose a more modular approach to supporting variational inference in PPLs, based on compositional program transformation. In our approach, variational objectives are expressed as programs, that may employ first-class constructs for computing densities of and expected values under user-defined models and variational families. We then transform these programs systematically into unbiased gradient estimators for optimizing the objectives they define. Our design enables modular reasoning about many interacting concerns, including automatic differentiation, density accumulation, tracing, and the application of unbiased gradient estimation strategies. Additionally, relative to existing support for VI in PPLs, our design increases expressiveness along three axes: (1) it supports an open-ended set of user-defined variational objectives, rather than a fixed menu of options; (2) it supports a combinatorial space of gradient estimation strategies, many not automated by today's PPLs; and (3) it supports a broader class of models and variational families, because it supports constructs for approximate marginalization and normalization (previously introduced only for Monte Carlo inference). We implement our approach in an extension to the Gen probabilistic programming system (genjax.vi, implemented in JAX), and evaluate on several deep generative modeling tasks, showing minimal performance overhead vs. hand-coded implementations and performance competitive with well-established open-source PPLs.

Integer Linear Programs (ILPs) are powerful tools for modeling and solving a large number of combinatorial optimization problems. Recently, it has been shown that Large Neighborhood Search (LNS), as a heuristic algorithm, can find high quality solutions to ILPs faster than Branch and Bound. However, how to find the right heuristics to maximize the performance of LNS remains an open problem. In this paper, we propose a novel approach, CL-LNS, that delivers state-of-the-art anytime performance on several ILP benchmarks measured by metrics including the primal gap, the primal integral, survival rates and the best performing rate. Specifically, CL-LNS collects positive and negative solution samples from an expert heuristic that is slow to compute and learns a new one with a contrastive loss. We use graph attention networks and a richer set of features to further improve its performance.

Recent advancements in large language models (LLMs) have spurred growing interest in automatic theorem proving using Lean4, where effective tree search methods are crucial for navigating proof search spaces. While the existing approaches primarily rely on value functions and Monte Carlo Tree Search (MCTS), the potential of simpler methods like Best-First Search (BFS) remains underexplored. This paper investigates whether BFS can achieve competitive performance in large-scale theorem proving tasks. We present BFS-Prover, a scalable expert iteration framework, featuring three key innovations. First, we implement strategic data filtering at each expert iteration round, excluding problems solvable via beam search node expansion to focus on harder cases. Second, we improve the sample efficiency of BFS through Direct Preference Optimization (DPO) applied to state-tactic pairs automatically annotated with compiler error feedback, refining the LLM's policy to prioritize productive expansions. Third, we employ length normalization in BFS to encourage exploration of deeper proof paths. BFS-Prover achieves a score of 71.31 on the MiniF2F test set and therefore challenges the perceived necessity of complex tree search methods, demonstrating that BFS can achieve competitive performance when properly scaled.

Modern Electronic Design Automation (EDA) workflows, especially the RTL-to-GDSII flow, require heavily manual scripting and demonstrate a multitude of tool-specific interactions which limits scalability and efficiency. While LLMs introduces strides for automation, existing LLM solutions require expensive fine-tuning and do not contain standardized frameworks for integration and evaluation. We introduce AutoEDA, a framework for EDA automation that leverages paralleled learning through the Model Context Protocol (MCP) specific for standardized and scalable natural language experience across the entire RTL-to-GDSII flow. AutoEDA limits fine-tuning through structured prompt engineering, implements intelligent parameter extraction and task decomposition, and provides an extended CodeBLEU metric to evaluate the quality of TCL scripts. Results from experiments over five previously curated benchmarks show improvements in automation accuracy and efficiency, as well as script quality when compared to existing methods. AutoEDA is released open-sourced to support reproducibility and the EDA community. Available at: https://github.com/AndyLu666/MCP-EDA-Server

Despite significant advances in long-context reasoning by large language models (LLMs), primarily through Online Reinforcement Learning (RL) methods, these approaches incur substantial computational costs and complexity. In contrast, simpler and more economical Offline RL methods remain underexplored. To address this gap, we investigate the effectiveness of Offline RL methods, specifically Direct Preference Optimization (DPO) and its length-desensitized variant LD-DPO, in enhancing the reasoning capabilities of LLMs. Extensive experiments across multiple reasoning benchmarks demonstrate that these simpler Offline RL methods substantially improve model performance, achieving an average enhancement of 3.3\%, with a particularly notable increase of 10.1\% on the challenging Arena-Hard benchmark. Furthermore, we analyze DPO's sensitivity to output length, emphasizing that increasing reasoning length should align with semantic richness, as indiscriminate lengthening may adversely affect model performance. We provide comprehensive descriptions of our data processing and training methodologies, offering empirical evidence and practical insights for developing more cost-effective Offline RL approaches.

We propose a methodology that allows communication with Piping and Instrumentation Diagrams (P&IDs) using natural language. In particular, we represent P&IDs through the DEXPI data model as labeled property graphs and integrate them with Large Language Models (LLMs). The approach consists of three main parts: 1) P&IDs are cast into a graph representation from the DEXPI format using our pyDEXPI Python package. 2) A tool for generating P&ID knowledge graphs from pyDEXPI. 3) Integration of the P&ID knowledge graph to LLMs using graph-based retrieval augmented generation (graph-RAG). This approach allows users to communicate with P&IDs using natural language. It extends LLM's ability to retrieve contextual data from P&IDs and mitigate hallucinations. Leveraging the LLM's large corpus, the model is also able to interpret process information in PIDs, which could help engineers in their daily tasks. In the future, this work will also open up opportunities in the context of other generative Artificial Intelligence (genAI) solutions on P&IDs, and AI-assisted HAZOP studies.

Recent advances in reinforcement learning (RL)-based post-training have led to notable improvements in large language models (LLMs), particularly in enhancing their reasoning capabilities to handle complex tasks. However, most existing methods treat the training data as a unified whole, overlooking the fact that modern LLM training often involves a mixture of data from diverse distributions-varying in both source and difficulty. This heterogeneity introduces a key challenge: how to adaptively schedule training across distributions to optimize learning efficiency. In this paper, we present a principled curriculum learning framework grounded in the notion of distribution-level learnability. Our core insight is that the magnitude of policy advantages reflects how much a model can still benefit from further training on a given distribution. Based on this, we propose a distribution-level curriculum learning framework for RL-based LLM post-training, which leverages the Upper Confidence Bound (UCB) principle to dynamically adjust sampling probabilities for different distrubutions. This approach prioritizes distributions with either high average advantage (exploitation) or low sample count (exploration), yielding an adaptive and theoretically grounded training schedule. We instantiate our curriculum learning framework with GRPO as the underlying RL algorithm and demonstrate its effectiveness on logic reasoning datasets with multiple difficulties and sources. Our experiments show that our framework significantly improves convergence speed and final performance, highlighting the value of distribution-aware curriculum strategies in LLM post-training. Code: https://github.com/ZhentingWang/DUMP.

We introduce Goedel-Prover, an open-source large language model (LLM) that achieves the state-of-the-art (SOTA) performance in automated formal proof generation for mathematical problems. The key challenge in this field is the scarcity of formalized math statements and proofs, which we tackle in the following ways. We train statement formalizers to translate the natural language math problems from Numina into formal language (Lean 4), creating a dataset of 1.64 million formal statements. LLMs are used to check that the formal statements accurately preserve the content of the original natural language problems. We then iteratively build a large dataset of formal proofs by training a series of provers. Each prover succeeds in proving many statements that the previous ones could not, and these new proofs are added to the training set for the next prover. The final prover outperforms all existing open-source models in whole-proof generation. On the miniF2F benchmark, it achieves a 57.6% success rate (Pass@32), exceeding the previous best open-source model by 7.6%. On PutnamBench, Goedel-Prover successfully solves 7 problems (Pass@512), ranking first on the leaderboard. Furthermore, it generates 29.7K formal proofs for Lean Workbook problems, nearly doubling the 15.7K produced by earlier works.

We present a simple yet theoretically motivated improvement to Supervised Fine-Tuning (SFT) for the Large Language Model (LLM), addressing its limited generalization compared to reinforcement learning (RL). Through mathematical analysis, we reveal that standard SFT gradients implicitly encode a problematic reward structure that may severely restrict the generalization capabilities of model. To rectify this, we propose Dynamic Fine-Tuning (DFT), stabilizing gradient updates for each token by dynamically rescaling the objective function with the probability of this token. Remarkably, this single-line code change significantly outperforms standard SFT across multiple challenging benchmarks and base models, demonstrating greatly improved generalization. Additionally, our approach shows competitive results in offline RL settings, offering an effective yet simpler alternative. This work bridges theoretical insight and practical solutions, substantially advancing SFT performance. The code will be available at https://github.com/yongliang-wu/DFT.

Generative models, particularly Large Language Models (LLMs), produce fluent outputs yet lack verifiable guarantees. We adapt Design by Contract (DbC) and type-theoretic principles to introduce a contract layer that mediates every LLM call. Contracts stipulate semantic and type requirements on inputs and outputs, coupled with probabilistic remediation to steer generation toward compliance. The layer exposes the dual view of LLMs as semantic parsers and probabilistic black-box components. Contract satisfaction is probabilistic and semantic validation is operationally defined through programmer-specified conditions on well-typed data structures. More broadly, this work postulates that any two agents satisfying the same contracts are functionally equivalent with respect to those contracts.

We consider a fair division model in which agents have positive, zero and negative utilities for items. For this model, we analyse one existing fairness property - EFX - and three new and related properties - EFX_0, EFX^3 and EF1^3 - in combination with Pareto-optimality. With general utilities, we give a modified version of an existing algorithm for computing an EF1^3 allocation. With -alpha/0/alpha utilities, this algorithm returns an EFX^3 and PO allocation. With absolute identical utilities, we give a new algorithm for an EFX and PO allocation. With -alpha/0/beta utilities, this algorithm also returns such an allocation. We report some new impossibility results as well.

Recent advancements in Large Language Models (LLMs) have demonstrated their potential in planning and reasoning tasks, offering a flexible alternative to classical pathfinding algorithms. However, most existing studies focus on LLMs' independent reasoning capabilities and overlook the potential synergy between LLMs and traditional algorithms. To fill this gap, we propose a comprehensive evaluation benchmark GridRoute to assess how LLMs can take advantage of traditional algorithms. We also propose a novel hybrid prompting technique called Algorithm of Thought (AoT), which introduces traditional algorithms' guidance into prompting. Our benchmark evaluates six LLMs ranging from 7B to 72B parameters across various map sizes, assessing their performance in correctness, optimality, and efficiency in grid environments with varying sizes. Our results show that AoT significantly boosts performance across all model sizes, particularly in larger or more complex environments, suggesting a promising approach to addressing path planning challenges. Our code is open-sourced at https://github.com/LinChance/GridRoute.

Reinforcement Learning (RL) plays a crucial role in aligning large language models (LLMs) with human preferences and improving their ability to perform complex tasks. However, current approaches either require significant computational resources due to the use of multiple models and extensive online sampling for training (e.g., PPO) or are framed as bandit problems (e.g., DPO, DRO), which often struggle with multi-step reasoning tasks, such as math problem-solving and complex reasoning that involve long chains of thought. To overcome these limitations, we introduce Direct Q-function Optimization (DQO), which formulates the response generation process as a Markov Decision Process (MDP) and utilizes the soft actor-critic (SAC) framework to optimize a Q-function directly parameterized by the language model. The MDP formulation of DQO offers structural advantages over bandit-based methods, enabling more effective process supervision. Experimental results on two math problem-solving datasets, GSM8K and MATH, demonstrate that DQO outperforms previous methods, establishing it as a promising offline reinforcement learning approach for aligning language models.

Circuit Satisfiability (CSAT) plays a pivotal role in Electronic Design Automation. The standard workflow for solving CSAT problems converts circuits into Conjunctive Normal Form (CNF) and employs generic SAT solvers powered by Conflict-Driven Clause Learning (CDCL). However, this process inherently discards rich structural and functional information, leading to suboptimal solver performance. To address this limitation, we introduce CASCAD, a novel circuit-aware SAT solving framework that directly leverages circuit-level conditional probabilities computed via Graph Neural Networks (GNNs). By explicitly modeling gate-level conditional probabilities, CASCAD dynamically guides two critical CDCL heuristics -- variable phase selection and clause managementto significantly enhance solver efficiency. Extensive evaluations on challenging real-world Logical Equivalence Checking (LEC) benchmarks demonstrate that CASCAD reduces solving times by up to 10x compared to state-of-the-art CNF-based approaches, achieving an additional 23.5% runtime reduction via our probability-guided clause filtering strategy. Our results underscore the importance of preserving circuit-level structural insights within SAT solvers, providing a robust foundation for future improvements in SAT-solving efficiency and EDA tool design.

Reinforcement Learning (RL) has shown remarkable success in enhancing the reasoning capabilities of Large Language Models (LLMs). Process-Supervised RL (PSRL) has emerged as a more effective paradigm compared to outcome-based RL. However, existing PSRL approaches suffer from limited exploration efficiency, both in terms of branching positions and sampling. In this paper, we introduce a novel PSRL framework (AttnRL), which enables efficient exploration for reasoning models. Motivated by preliminary observations that steps exhibiting high attention scores correlate with reasoning behaviors, we propose to branch from positions with high values. Furthermore, we develop an adaptive sampling strategy that accounts for problem difficulty and historical batch size, ensuring that the whole training batch maintains non-zero advantage values. To further improve sampling efficiency, we design a one-step off-policy training pipeline for PSRL. Extensive experiments on multiple challenging mathematical reasoning benchmarks demonstrate that our method consistently outperforms prior approaches in terms of performance and sampling and training efficiency.

Recent progress in o1-like models has significantly enhanced the reasoning abilities of Large Language Models (LLMs), empowering them to tackle increasingly complex tasks through reflection capabilities, such as making assumptions, backtracking, and self-refinement. However, effectively evaluating such reflection capabilities remains challenging due to the lack of appropriate benchmarks. To bridge this gap, we introduce LR^2Bench, a novel benchmark designed to evaluate the Long-chain Reflective Reasoning capabilities of LLMs. LR^2Bench comprises 850 samples across six Constraint Satisfaction Problems (CSPs) where reflective reasoning is crucial for deriving solutions that meet all given constraints. Each type of task focuses on distinct constraint patterns, such as knowledge-based, logical, and spatial constraints, providing a comprehensive evaluation of diverse problem-solving scenarios. We conduct extensive evaluation on both conventional models and o1-like models. Our experimental results reveal that even the most advanced reasoning-specific models, such as DeepSeek-R1 and OpenAI o1-preview, struggle with tasks in LR^2Bench, achieving an average Exact Match score of only 20.0% and 23.6%, respectively. These findings underscore the significant room for improvement in the reflective reasoning capabilities of current LLMs. The leaderboard of our benchmark is available at https://huggingface.co/spaces/UltraRonin/LR2Bench

While recent advancements in reasoning optimization have significantly enhanced the capabilities of large language models (LLMs), existing efforts to improve reasoning have been limited to solving mathematical problems and focusing on visual graphical inputs, neglecting broader applications in general video understanding.This paper proposes video-SALMONN-o1, the first open-source reasoning-enhanced audio-visual LLM designed for general video understanding tasks. To enhance its reasoning abilities, we develop a reasoning-intensive dataset featuring challenging audio-visual questions with step-by-step solutions. We also propose process direct preference optimization (pDPO), which leverages contrastive step selection to achieve efficient step-level reward modelling tailored for multimodal inputs. Additionally, we introduce RivaBench, the first reasoning-intensive video understanding benchmark, featuring over 4,000 high-quality, expert-curated question-answer pairs across scenarios such as standup comedy, academic presentations, and synthetic video detection. video-SALMONN-o1 achieves 3-8% accuracy improvements over the LLaVA-OneVision baseline across different video reasoning benchmarks. Besides, pDPO achieves 6-8% improvements compared to the supervised fine-tuning model on RivaBench. Enhanced reasoning enables video-SALMONN-o1 zero-shot synthetic video detection capabilities.

Persona-driven role-playing (PRP) aims to build AI characters that can respond to user queries by faithfully sticking with all persona statements. Unfortunately, existing faithfulness criteria for PRP are limited to coarse-grained LLM-based scoring without a clear definition or formulation. This paper presents a pioneering exploration to quantify PRP faithfulness as a fine-grained and explainable criterion, which also serves as a reliable reference for optimization. Our criterion first discriminates persona statements into active and passive constraints by identifying the query-statement relevance. Then, we incorporate all constraints following the principle that the AI character's response should be (a) entailed by active (relevant) constraints and (b) not contradicted by passive (irrelevant) constraints. We translate this principle mathematically into a novel Active-Passive-Constraint (APC) score, a constraint-wise sum of natural language inference (NLI) scores weighted by relevance scores. In practice, we build the APC scoring system by symbolically distilling small discriminators from GPT-4 for efficiency. We validate the quality of the APC score against human evaluation based on example personas with tens of statements, and the results show a high correlation. We further leverage it as a reward system in direct preference optimization (DPO) for better AI characters. Our experiments offer a fine-grained and explainable comparison between existing PRP techniques, revealing their advantages and limitations. We further find APC-based DPO to be one of the most competitive techniques for sticking with all constraints and can be well incorporated with other techniques. We then extend the scale of the experiments to real persons with hundreds of statements and reach a consistent conclusion.

Large language models (LLMs) have shown increasing in-context learning capabilities through scaling up model and data size. Despite this progress, LLMs are still unable to solve algorithmic reasoning problems. While providing a rationale with the final answer has led to further improvements in multi-step reasoning problems, Anil et al. 2022 showed that even simple algorithmic reasoning tasks such as parity are far from solved. In this work, we identify and study four key stages for successfully teaching algorithmic reasoning to LLMs: (1) formulating algorithms as skills, (2) teaching multiple skills simultaneously (skill accumulation), (3) teaching how to combine skills (skill composition) and (4) teaching how to use skills as tools. We show that it is possible to teach algorithmic reasoning to LLMs via in-context learning, which we refer to as algorithmic prompting. We evaluate our approach on a variety of arithmetic and quantitative reasoning tasks, and demonstrate significant boosts in performance over existing prompting techniques. In particular, for long parity, addition, multiplication and subtraction, we achieve an error reduction of approximately 10x, 9x, 5x and 2x respectively compared to the best available baselines.

We propose Delta L Normalization, a simple yet effective loss aggregation method tailored to the characteristic of dynamic generation lengths in Reinforcement Learning with Verifiable Rewards (RLVR). Recently, RLVR has demonstrated strong potential in improving the reasoning capabilities of large language models (LLMs), but a major challenge lies in the large variability of response lengths during training, which leads to high gradient variance and unstable optimization. Although previous methods such as GRPO, DAPO, and Dr. GRPO introduce different loss normalization terms to address this issue, they either produce biased estimates or still suffer from high gradient variance. By analyzing the effect of varying lengths on policy loss both theoretically and empirically, we reformulate the problem as finding a minimum-variance unbiased estimator. Our proposed Delta L Normalization not only provides an unbiased estimate of the true policy loss but also minimizes gradient variance in theory. Extensive experiments show that it consistently achieves superior results across different model sizes, maximum lengths, and tasks. Our code will be made public at https://github.com/zerolllin/Delta-L-Normalization.

Enhancing the mathematical reasoning capabilities of LLMs has garnered significant attention in both the mathematical and computer science communities. Recent works have made substantial progress in both Natural Language (NL) reasoning and Formal Language (FL) reasoning by leveraging the potential of pure Reinforcement Learning (RL) methods on base models. However, RL approaches struggle to impart new capabilities not presented in the base model, highlighting the need to integrate more knowledge like FL into NL math reasoning effectively. Yet, this integration is challenging due to inherent disparities in problem structure and reasoning format between NL and FL. To address these challenges, we introduce **NL-FL HybridReasoning**, an end-to-end framework designed to incorporate the FL expert into NL math problem-solving. To bridge the NL and FL input format gap, we propose the *NL-FL Problem Alignment* method, which reformulates the Question-Answering (QA) problems in NL as existence theorems in FL. Subsequently, the *Mixed Problem Input* technique we provide enables the FL reasoner to handle both QA and existence problems concurrently. Lastly, we mitigate the NL and FL output format gap in reasoning through an LLM-based *Answer Extraction* mechanism. Comprehensive experiments demonstrate that the **HybridReasoning** framework achieves **89.80%** and **84.34%** accuracy rates on the MATH-500 and the AMC benchmarks, surpassing the NL baseline by 4.60% and 4.82%, respectively. Notably, some problems resolved by our framework remain unsolved by the NL baseline model even under a larger number of trials.

We introduce LeetCodeDataset, a high-quality benchmark for evaluating and training code-generation models, addressing two key challenges in LLM research: the lack of reasoning-focused coding benchmarks and self-contained training testbeds. By curating LeetCode Python problems with rich metadata, broad coverage, 100+ test cases per problem, and temporal splits (pre/post July 2024), our dataset enables contamination-free evaluation and efficient supervised fine-tuning (SFT). Experiments show reasoning models significantly outperform non-reasoning counterparts, while SFT with only 2.6K model-generated solutions achieves performance comparable to 110K-sample counterparts. The dataset and evaluation framework are available on Hugging Face and Github.

Reinforcement learning, such as PPO and GRPO, has powered recent breakthroughs in LLM reasoning. Scaling rollout to sample more prompts enables models to selectively use higher-quality data for training, which can stabilize RL training and improve model performance. However, this comes at the cost of significant computational overhead. In this paper, we show that a substantial portion of this overhead can be avoided by skipping uninformative prompts before rollout. Our analysis of reward dynamics reveals a strong temporal consistency in prompt value: prompts that are uninformative in one epoch of training are likely to remain uninformative in future epochs. Based on these insights, we propose GRESO (GRPO with Efficient Selective Rollout), an online, lightweight pre-rollout filtering algorithm that predicts and skips uninformative prompts using reward training dynamics. By evaluating GRESO on a broad range of math reasoning benchmarks and models, such as Qwen2.5-Math-1.5B, DeepSeek-R1-Distill-Qwen-1.5B, and Qwen2.5-Math-7B, we show that GRESO achieves up to 2.4x wall-clock time speedup in rollout and up to 2.0x speedup in total training time without accuracy degradation.

Large Language Models (LLMs) have made significant strides in mathematical reasoning, underscoring the need for a comprehensive and fair evaluation of their capabilities. However, existing benchmarks often fall short, either lacking extensive coverage of undergraduate-level mathematical problems or probably suffering from test-set contamination. To address these issues, we introduce UGMathBench, a diverse and dynamic benchmark specifically designed for evaluating undergraduate-level mathematical reasoning with LLMs. UGMathBench comprises 5,062 problems across 16 subjects and 111 topics, featuring 10 distinct answer types. Each problem includes three randomized versions, with additional versions planned for release as leading open-source LLMs become saturated in UGMathBench. Furthermore, we propose two key metrics: effective accuracy (EAcc), which measures the percentage of correctly solved problems across all three versions, and reasoning gap (Delta), which assesses reasoning robustness by calculating the difference between the average accuracy across all versions and EAcc. Our extensive evaluation of 23 leading LLMs reveals that the highest EAcc achieved is 56.3\% by OpenAI-o1-mini, with large Delta values observed across different models. This highlights the need for future research aimed at developing "large reasoning models" with high EAcc and Delta = 0. We anticipate that the release of UGMathBench, along with its detailed evaluation codes, will serve as a valuable resource to advance the development of LLMs in solving mathematical problems.

We present a novel application of evolutionary algorithms to automate the creation of powerful foundation models. While model merging has emerged as a promising approach for LLM development due to its cost-effectiveness, it currently relies on human intuition and domain knowledge, limiting its potential. Here, we propose an evolutionary approach that overcomes this limitation by automatically discovering effective combinations of diverse open-source models, harnessing their collective intelligence without requiring extensive additional training data or compute. Our approach operates in both parameter space and data flow space, allowing for optimization beyond just the weights of the individual models. This approach even facilitates cross-domain merging, generating models like a Japanese LLM with Math reasoning capabilities. Surprisingly, our Japanese Math LLM achieved state-of-the-art performance on a variety of established Japanese LLM benchmarks, even surpassing models with significantly more parameters, despite not being explicitly trained for such tasks. Furthermore, a culturally-aware Japanese VLM generated through our approach demonstrates its effectiveness in describing Japanese culture-specific content, outperforming previous Japanese VLMs. This work not only contributes new state-of-the-art models back to the open-source community, but also introduces a new paradigm for automated model composition, paving the way for exploring alternative, efficient approaches to foundation model development.

We propose a novel approach to scaling LLM inference for code generation. We frame code generation as a black box optimization problem within the code space, and employ optimization-inspired techniques to enhance exploration. Specifically, we introduce Scattered Forest Search to enhance solution diversity while searching for solutions. Our theoretical analysis illustrates how these methods avoid local optima during optimization. Extensive experiments on HumanEval, MBPP, APPS, CodeContests, and Leetcode reveal significant performance improvements. For instance, our method achieves a pass@1 rate of 67.1% on HumanEval+ and 87.2% on HumanEval with GPT-3.5, marking improvements of 8.6% and 4.3% over the state-of-the-art, while also halving the iterations needed to find the correct solution. Furthermore, our method scales more efficiently than existing search techniques, including tree search, line search, and repeated sampling.