Daily Papers

Understanding properties of deep neural networks is an important challenge in deep learning. In this paper, we take a step in this direction by proposing a rigorous way of verifying properties of a popular class of neural networks, Binarized Neural Networks, using the well-developed means of Boolean satisfiability. Our main contribution is a construction that creates a representation of a binarized neural network as a Boolean formula. Our encoding is the first exact Boolean representation of a deep neural network. Using this encoding, we leverage the power of modern SAT solvers along with a proposed counterexample-guided search procedure to verify various properties of these networks. A particular focus will be on the critical property of robustness to adversarial perturbations. For this property, our experimental results demonstrate that our approach scales to medium-size deep neural networks used in image classification tasks. To the best of our knowledge, this is the first work on verifying properties of deep neural networks using an exact Boolean encoding of the network.

Query rewriting is one of the most effective techniques for coping with poorly written queries before passing them down to the query optimizer. Manual rewriting is not scalable, as it is error-prone and requires deep expertise. Similarly, traditional query rewriting algorithms can only handle a small subset of queries: rule-based techniques do not generalize to new query patterns and synthesis-based techniques cannot handle complex queries. Fortunately, the rise of Large Language Models (LLMs), equipped with broad general knowledge and advanced reasoning capabilities, has created hopes for solving some of these previously open problems. In this paper, we present GenRewrite, the first holistic system that leverages LLMs for query rewriting. We introduce the notion of Natural Language Rewrite Rules (NLR2s), and use them as hints to the LLM but also a means for transferring knowledge from rewriting one query to another, and thus becoming smarter and more effective over time. We present a novel counterexample-guided technique that iteratively corrects the syntactic and semantic errors in the rewritten query, significantly reducing the LLM costs and the manual effort required for verification. GenRewrite speeds up 22 out of 99 TPC queries (the most complex public benchmark) by more than 2x, which is 2.5x--3.2x higher coverage than state-of-the-art traditional query rewriting and 2.1x higher than the out-of-the-box LLM baseline.

There is growing excitement about the potential of Language Models (LMs) to accelerate scientific discovery. Falsifying hypotheses is key to scientific progress, as it allows claims to be iteratively refined over time. This process requires significant researcher effort, reasoning, and ingenuity. Yet current benchmarks for LMs predominantly assess their ability to generate solutions rather than challenge them. We advocate for developing benchmarks that evaluate this inverse capability - creating counterexamples for subtly incorrect solutions. To demonstrate this approach, we start with the domain of algorithmic problem solving, where counterexamples can be evaluated automatically using code execution. Specifically, we introduce REFUTE, a dynamically updating benchmark that includes recent problems and incorrect submissions from programming competitions, where human experts successfully identified counterexamples. Our analysis finds that the best reasoning agents, even OpenAI o3-mini (high) with code execution feedback, can create counterexamples for only <9% of incorrect solutions in REFUTE, even though ratings indicate its ability to solve up to 48% of these problems from scratch. We hope our work spurs progress in evaluating and enhancing LMs' ability to falsify incorrect solutions - a capability that is crucial for both accelerating research and making models self-improve through reliable reflective reasoning.

Counterexample-guided repair aims at creating neural networks with mathematical safety guarantees, facilitating the application of neural networks in safety-critical domains. However, whether counterexample-guided repair is guaranteed to terminate remains an open question. We approach this question by showing that counterexample-guided repair can be viewed as a robust optimisation algorithm. While termination guarantees for neural network repair itself remain beyond our reach, we prove termination for more restrained machine learning models and disprove termination in a general setting. We empirically study the practical implications of our theoretical results, demonstrating the suitability of common verifiers and falsifiers for repair despite a disadvantageous theoretical result. Additionally, we use our theoretical insights to devise a novel algorithm for repairing linear regression models based on quadratic programming, surpassing existing approaches.

We introduce HunyuanProver, an language model finetuned from the Hunyuan 7B for interactive automatic theorem proving with LEAN4. To alleviate the data sparsity issue, we design a scalable framework to iterative synthesize data with low cost. Besides, guided tree search algorithms are designed to enable effective ``system 2 thinking`` of the prover. HunyuanProver achieves state-of-the-art (SOTA) performances on major benchmarks. Specifically, it achieves a pass of 68.4% on the miniF2F-test compared to 65.9%, the current SOTA results. It proves 4 IMO statements (imo_1960_p2, imo_1962_p2}, imo_1964_p2 and imo_1983_p6) in miniF2F-test. To benefit the community, we will open-source a dataset of 30k synthesized instances, where each instance contains the original question in natural language, the converted statement by autoformalization, and the proof by HunyuanProver.

Despite the critical need to align search targets with users' intention, retrievers often only prioritize query information without delving into the users' intended search context. Enhancing the capability of retrievers to understand intentions and preferences of users, akin to language model instructions, has the potential to yield more aligned search targets. Prior studies restrict the application of instructions in information retrieval to a task description format, neglecting the broader context of diverse and evolving search scenarios. Furthermore, the prevailing benchmarks utilized for evaluation lack explicit tailoring to assess instruction-following ability, thereby hindering progress in this field. In response to these limitations, we propose a novel benchmark,INSTRUCTIR, specifically designed to evaluate instruction-following ability in information retrieval tasks. Our approach focuses on user-aligned instructions tailored to each query instance, reflecting the diverse characteristics inherent in real-world search scenarios. Through experimental analysis, we observe that retrievers fine-tuned to follow task-style instructions, such as INSTRUCTOR, can underperform compared to their non-instruction-tuned counterparts. This underscores potential overfitting issues inherent in constructing retrievers trained on existing instruction-aware retrieval datasets.

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.

Large language models (LLMs) struggle with multi-step reasoning, where inference-time scaling has emerged as a promising strategy for performance improvement. Verifier-guided search outperforms repeated sampling when sample size is limited by selecting and prioritizing valid reasoning paths. However, we identify a critical limitation: scaling flaws, prevalent across different models (Mistral 7B and DeepSeekMath 7B), benchmarks (GSM8K and MATH), and verifiers (outcome value models and process reward models). As sample size increases, verifier-guided search exhibits diminishing advantages and eventually underperforms repeated sampling. Our analysis attributes this to verifier failures, where imperfect verifiers misrank candidates and erroneously prune all valid paths. These issues are further exacerbated in challenging and out-of-distribution problems, restricting search effectiveness. To mitigate verifier failures, we explore reducing reliance on verifiers and conduct preliminary investigations using two simple methods. Our findings reveal fundamental limitations in verifier-guided search and suggest future directions.

Among the most important properties of algorithms investigated in computer science are soundness, completeness, and complexity. These properties, however, are rarely analyzed for the vast collection of recently proposed methods for planning with large language models. In this work, we alleviate this gap. We analyse these properties of using LLMs for planning and highlight that recent trends abandon both soundness and completeness for the sake of inefficiency. We propose a significantly more efficient approach that can, at the same time, maintain both soundness and completeness. We exemplify on four representative search problems, comparing to the LLM-based solutions from the literature that attempt to solve these problems. We show that by using LLMs to produce the code for the search components we can solve the entire datasets with 100\% accuracy with only a few calls to the LLM. We argue for a responsible use of compute resources; urging research community to investigate sound and complete LLM-based approaches that uphold efficiency.

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.

In this paper we study how to effectively exploit implicit feedback in Dense Retrievers (DRs). We consider the specific case in which click data from a historic click log is available as implicit feedback. We then exploit such historic implicit interactions to improve the effectiveness of a DR. A key challenge that we study is the effect that biases in the click signal, such as position bias, have on the DRs. To overcome the problems associated with the presence of such bias, we propose the Counterfactual Rocchio (CoRocchio) algorithm for exploiting implicit feedback in Dense Retrievers. We demonstrate both theoretically and empirically that dense query representations learnt with CoRocchio are unbiased with respect to position bias and lead to higher retrieval effectiveness. We make available the implementations of the proposed methods and the experimental framework, along with all results at https://github.com/ielab/Counterfactual-DR.

Programming-by-example is the task of synthesizing a program that is consistent with a set of user-provided input-output examples. As examples are often an under-specification of one's intent, a good synthesizer must choose the intended program from the many that are consistent with the given set of examples. Prior work frames program synthesis as a cooperative game between a listener (that synthesizes programs) and a speaker (a user choosing examples), and shows that models of computational pragmatic inference are effective in choosing the user intended programs. However, these models require counterfactual reasoning over a large set of programs and examples, which is infeasible in realistic program spaces. In this paper, we propose a novel way to amortize this search with neural networks. We sample pairs of programs and examples via self-play between listener and speaker models, and use pragmatic inference to choose informative training examples from this sample.We then use the informative dataset to train models to improve the synthesizer's ability to disambiguate user-provided examples without human supervision. We validate our method on the challenging task of synthesizing regular expressions from example strings, and find that our method (1) outperforms models trained without choosing pragmatic examples by 23% (a 51% relative increase) (2) matches the performance of supervised learning on a dataset of pragmatic examples provided by humans, despite using no human data in training.

Instruction-following is a fundamental capability of language models, requiring the model to recognize even the most subtle requirements in the instructions and accurately reflect them in its output. Such an ability is well-suited for and often optimized by preference learning. However, existing methods often directly sample multiple independent responses from the model when creating preference pairs. Such practice can introduce content variations irrelevant to whether the instruction is precisely followed (e.g., different expressions about the same semantic), interfering with the goal of teaching models to recognize the key differences that lead to improved instruction following. In light of this, we introduce SPaR, a self-play framework integrating tree-search self-refinement to yield valid and comparable preference pairs free from distractions. By playing against itself, an LLM employs a tree-search strategy to refine its previous responses with respect to the instruction while minimizing unnecessary variations. Our experiments show that a LLaMA3-8B model, trained over three iterations guided by SPaR, surpasses GPT-4-Turbo on the IFEval benchmark without losing general capabilities. Furthermore, SPaR demonstrates promising scalability and transferability, greatly enhancing models like GLM-4-9B and LLaMA3-70B. We also identify how inference scaling in tree search would impact model performance. Our code and data are publicly available at https://github.com/thu-coai/SPaR.

Large language models (LLMs) have shown impressive capabilities in real-world applications. The capability of in-context learning (ICL) allows us to adapt an LLM to downstream tasks by including input-label exemplars in the prompt without model fine-tuning. However, the quality of these exemplars in the prompt greatly impacts performance, highlighting the need for an effective automated exemplar selection method. Recent studies have explored retrieval-based approaches to select exemplars tailored to individual test queries, which can be undesirable due to extra test-time computation and an increased risk of data exposure. Moreover, existing methods fail to adequately account for the impact of exemplar ordering on the performance. On the other hand, the impact of the instruction, another essential component in the prompt given to the LLM, is often overlooked in existing exemplar selection methods. To address these challenges, we propose a novel method named EASE, which leverages the hidden embedding from a pre-trained language model to represent ordered sets of exemplars and uses a neural bandit algorithm to optimize the sets of exemplars while accounting for exemplar ordering. Our EASE can efficiently find an ordered set of exemplars that performs well for all test queries from a given task, thereby eliminating test-time computation. Importantly, EASE can be readily extended to jointly optimize both the exemplars and the instruction. Through extensive empirical evaluations (including novel tasks), we demonstrate the superiority of EASE over existing methods, and reveal practical insights about the impact of exemplar selection on ICL, which may be of independent interest. Our code is available at https://github.com/ZhaoxuanWu/EASE-Prompt-Optimization.

In common law jurisdictions, legal practitioners rely on precedents to construct arguments, in line with the doctrine of stare decisis. As the number of cases grow over the years, prior case retrieval (PCR) has garnered significant attention. Besides lacking real-world scale, existing PCR datasets do not simulate a realistic setting, because their queries use complete case documents while only masking references to prior cases. The query is thereby exposed to legal reasoning not yet available when constructing an argument for an undecided case as well as spurious patterns left behind by citation masks, potentially short-circuiting a comprehensive understanding of case facts and legal principles. To address these limitations, we introduce a PCR dataset based on judgements from the European Court of Human Rights (ECtHR), which explicitly separate facts from arguments and exhibit precedential practices, aiding us to develop this PCR dataset to foster systems' comprehensive understanding. We benchmark different lexical and dense retrieval approaches with various negative sampling strategies, adapting them to deal with long text sequences using hierarchical variants. We found that difficulty-based negative sampling strategies were not effective for the PCR task, highlighting the need for investigation into domain-specific difficulty criteria. Furthermore, we observe performance of the dense models degrade with time and calls for further research into temporal adaptation of retrieval models. Additionally, we assess the influence of different views , Halsbury's and Goodhart's, in practice in ECtHR jurisdiction using PCR task.

Current literature, aiming to surpass the "Chain-of-Thought" approach, often resorts to an external modus operandi involving halting, modifying, and then resuming the generation process to boost Large Language Models' (LLMs) reasoning capacities. This mode escalates the number of query requests, leading to increased costs, memory, and computational overheads. Addressing this, we propose the Algorithm of Thoughts -- a novel strategy that propels LLMs through algorithmic reasoning pathways, pioneering a new mode of in-context learning. By employing algorithmic examples, we exploit the innate recurrence dynamics of LLMs, expanding their idea exploration with merely one or a few queries. Our technique outperforms earlier single-query methods and stands on par with a recent multi-query strategy that employs an extensive tree search algorithm. Intriguingly, our results suggest that instructing an LLM using an algorithm can lead to performance surpassing that of the algorithm itself, hinting at LLM's inherent ability to weave its intuition into optimized searches. We probe into the underpinnings of our method's efficacy and its nuances in application.

Collecting ground truth task completion rewards or human demonstrations for multi-step reasoning tasks is often cost-prohibitive and time-consuming, especially in interactive domains like web tasks. To address this bottleneck, we present self-taught lookahead, a self-supervised method that leverages state-transition dynamics to train a value model capable of effectively guiding language model-controlled search. We find that moderately sized (8 billion parameters) open-weight value models improved with self-taught lookahead can match the performance of using a frontier LLM such as gpt-4o as the value model. Furthermore, we find that self-taught lookahead improves performance by 20% while reducing costs 37x compared to previous LLM-based tree search, without relying on ground truth rewards.

Code generation with large language models has shown significant promise, especially when employing retrieval-augmented generation (RAG) with few-shot examples. However, selecting effective examples that enhance generation quality remains a challenging task, particularly when the target programming language (PL) is underrepresented. In this study, we present two key findings: (1) retrieving examples whose presented algorithmic plans can be referenced for generating the desired behavior significantly improves generation accuracy, and (2) converting code into pseudocode effectively captures such algorithmic plans, enhancing retrieval quality even when the source and the target PLs are different. Based on these findings, we propose Plan-as-query Example Retrieval for few-shot prompting in Code generation (PERC), a novel framework that utilizes algorithmic plans to identify and retrieve effective examples. We validate the effectiveness of PERC through extensive experiments on the CodeContests, HumanEval and MultiPL-E benchmarks: PERC consistently outperforms the state-of-the-art RAG methods in code generation, both when the source and target programming languages match or differ, highlighting its adaptability and robustness in diverse coding environments.

We present Lean Finder, a semantic search engine for Lean and mathlib that understands and aligns with the intents of mathematicians. Progress in formal theorem proving is often hindered by the difficulty of locating relevant theorems and the steep learning curve of the Lean 4 language, making advancement slow and labor-intensive. Existing Lean search engines, though helpful, rely primarily on informalizations (natural language translation of the formal statements), while largely overlooking the mismatch with real-world user queries. In contrast, we propose a user-centered semantic search tailored to the needs of mathematicians. Our approach begins by analyzing and clustering the semantics of public Lean discussions, then fine-tuning text embeddings on synthesized queries that emulate user intents. We further align Lean Finder with mathematicians' preferences using diverse feedback signals, encoding it with a rich awareness of their goals from multiple perspectives. Evaluations on real-world queries, informalized statements, and proof states demonstrate that our Lean Finder achieves over 30% relative improvement compared to previous search engines and GPT-4o. In addition, Lean Finder is compatible with LLM-based theorem provers, bridging retrieval with formal reasoning. Lean Finder is available at: https://leanfinder.github.io

We propose an online training procedure for a transformer-based automated theorem prover. Our approach leverages a new search algorithm, HyperTree Proof Search (HTPS), inspired by the recent success of AlphaZero. Our model learns from previous proof searches through online training, allowing it to generalize to domains far from the training distribution. We report detailed ablations of our pipeline's main components by studying performance on three environments of increasing complexity. In particular, we show that with HTPS alone, a model trained on annotated proofs manages to prove 65.4% of a held-out set of Metamath theorems, significantly outperforming the previous state of the art of 56.5% by GPT-f. Online training on these unproved theorems increases accuracy to 82.6%. With a similar computational budget, we improve the state of the art on the Lean-based miniF2F-curriculum dataset from 31% to 42% proving accuracy.

Prompt-based learning has been an effective paradigm for large pretrained language models (LLM), enabling few-shot or even zero-shot learning. Black-box prompt search has received growing interest recently for its distinctive properties of gradient-free optimization, proven particularly useful and powerful for model-as-a-service usage. However, the discrete nature and the complexity of combinatorial optimization hinder the efficiency of modern black-box approaches. Despite extensive research on search algorithms, the crucial aspect of search space design and optimization has been largely overlooked. In this paper, we first conduct a sensitivity analysis by prompting LLM, revealing that only a small number of tokens exert a disproportionate amount of influence on LLM predictions. Leveraging this insight, we propose the Clustering and Pruning for Efficient Black-box Prompt Search (ClaPS), a simple black-box search method that first clusters and prunes the search space to focus exclusively on influential prompt tokens. By employing even simple search methods within the pruned search space, ClaPS achieves state-of-the-art performance across various tasks and LLMs, surpassing the performance of complex approaches while significantly reducing search costs. Our findings underscore the critical role of search space design and optimization in enhancing both the usefulness and the efficiency of black-box prompt-based learning.

Despite their remarkable capabilities, large language models often struggle with tasks requiring complex reasoning and planning. While existing approaches like Chain-of-Thought prompting and tree search techniques show promise, they are limited by their reliance on predefined heuristics and computationally expensive exploration strategies. We propose Policy-Guided Tree Search (PGTS), a framework that combines reinforcement learning with structured tree exploration to efficiently navigate reasoning paths. Our key innovation is a learned policy that dynamically decides between expanding, branching, backtracking, or terminating exploration, eliminating the need for manual heuristics or exhaustive search. Experiments across mathematical reasoning, logical deduction, and planning benchmarks demonstrate that PGTS achieves superior reasoning performance while significantly reducing computational costs compared to existing methods. These results establish PGTS as a scalable and effective solution for tackling complex reasoning tasks with LLMs.

Despite the rapid progress in the capabilities of Large Language Models (LLMs), they continue to have difficulty following relatively simple, unambiguous instructions, especially when compositions are involved. In this paper, we take inspiration from recent work that suggests that models may follow instructions better when they are expressed in pseudo-code. However, writing pseudo-code programs can be tedious and using few-shot demonstrations to craft code representations for use in inference can be unnatural for non-expert users of LLMs. To overcome these limitations, we propose fine-tuning LLMs with instruction-tuning data that additionally includes instructions re-expressed in pseudo-code along with the final response. We evaluate models trained using our method on 11 publicly available benchmarks comprising of tasks related to instruction-following, mathematics, and common-sense reasoning. We conduct rigorous experiments with 5 different models and find that not only do models follow instructions better when trained with pseudo-code, they also retain their capabilities on the other tasks related to mathematical and common sense reasoning. Specifically, we observe a relative gain of 3--19% on instruction-following benchmark, and an average gain of upto 14% across all tasks.

RAG (Retrieval-Augmented Generation) systems and web agents are increasingly evaluated on multi-hop deep search tasks, yet current practice suffers from two major limitations. First, most benchmarks leak the reasoning path in the question text, allowing models to follow surface cues rather than discover reasoning chains autonomously. Second, evaluation is typically reduced to a single pass rate, which collapses diverse behaviours into one score and obscures whether failures stem from inadequate search, poor knowledge use, or inappropriate refusal. To address these issues, we present WebDetective, a benchmark of hint-free multi-hop questions paired with a controlled Wikipedia sandbox that ensures full traceability of model actions, and a holistic evaluation framework that separates search sufficiency, knowledge utilisation, and refusal behaviour. Our evaluation of 25 state-of-the-art models reveals systematic weaknesses across all architectures: models struggle with knowledge utilisation despite having sufficient evidence and demonstrate near-absent appropriate refusal when evidence is lacking. These patterns expose a fundamental gap: today's systems excel at executing given reasoning paths but fail when required to discover them. We develop an agentic workflow, EvidenceLoop, that explicitly targets the challenges our benchmark identifies, incorporating verification loops and systematic evidence tracking that improve both search and synthesis capabilities. This baseline demonstrates that WebDetective's diagnostic framework can guide concrete architectural improvements, establishing our benchmark as a critical tool for developing genuinely autonomous reasoning systems rather than pattern-following agents.

Although counterfactual reasoning is a fundamental aspect of intelligence, the lack of large-scale counterfactual open-domain question-answering (QA) benchmarks makes it difficult to evaluate and improve models on this ability. To address this void, we introduce the first such dataset, named IfQA, where each question is based on a counterfactual presupposition via an "if" clause. For example, if Los Angeles was on the east coast of the U.S., what would be the time difference between Los Angeles and Paris? Such questions require models to go beyond retrieving direct factual knowledge from the Web: they must identify the right information to retrieve and reason about an imagined situation that may even go against the facts built into their parameters. The IfQA dataset contains over 3,800 questions that were annotated annotated by crowdworkers on relevant Wikipedia passages. Empirical analysis reveals that the IfQA dataset is highly challenging for existing open-domain QA methods, including supervised retrieve-then-read pipeline methods (EM score 36.2), as well as recent few-shot approaches such as chain-of-thought prompting with GPT-3 (EM score 27.4). The unique challenges posed by the IfQA benchmark will push open-domain QA research on both retrieval and counterfactual reasoning fronts.

Automated Theorem Proving (ATP) in formal languages remains a formidable challenge in AI, demanding rigorous logical deduction and navigating vast search spaces. While large language models (LLMs) have shown promising performance, existing stepwise provers often suffer from biased search guidance, leading to inefficiencies and suboptimal proof strategies. This paper introduces the Multi-Perspective Search Prover (MPS-Prover), a novel stepwise ATP system designed to overcome these limitations. MPS-Prover incorporates two key innovations: a highly effective post-training data curation strategy that prunes approximately 40% of redundant training data without sacrificing performance, and a multi-perspective tree search mechanism. This search integrates a learned critic model with strategically designed heuristic rules to diversify tactic selection, prevent getting trapped in unproductive states, and enhance search robustness. Extensive evaluations demonstrate that MPS-Prover achieves state-of-the-art performance on multiple challenging benchmarks, including miniF2F and ProofNet, outperforming prior 7B parameter models. Furthermore, our analyses reveal that MPS-Prover generates significantly shorter and more diverse proofs compared to existing stepwise and whole-proof methods, highlighting its efficiency and efficacy. Our work advances the capabilities of LLM-based formal reasoning and offers a robust framework and a comprehensive analysis for developing more powerful theorem provers.

Vector embeddings have been tasked with an ever-increasing set of retrieval tasks over the years, with a nascent rise in using them for reasoning, instruction-following, coding, and more. These new benchmarks push embeddings to work for any query and any notion of relevance that could be given. While prior works have pointed out theoretical limitations of vector embeddings, there is a common assumption that these difficulties are exclusively due to unrealistic queries, and those that are not can be overcome with better training data and larger models. In this work, we demonstrate that we may encounter these theoretical limitations in realistic settings with extremely simple queries. We connect known results in learning theory, showing that the number of top-k subsets of documents capable of being returned as the result of some query is limited by the dimension of the embedding. We empirically show that this holds true even if we restrict to k=2, and directly optimize on the test set with free parameterized embeddings. We then create a realistic dataset called LIMIT that stress tests models based on these theoretical results, and observe that even state-of-the-art models fail on this dataset despite the simple nature of the task. Our work shows the limits of embedding models under the existing single vector paradigm and calls for future research to develop methods that can resolve this fundamental limitation.

Program synthesis is challenging largely because of the difficulty of search in a large space of programs. Human programmers routinely tackle the task of writing complex programs by writing sub-programs and then analyzing their intermediate results to compose them in appropriate ways. Motivated by this intuition, we present a new synthesis approach that leverages learning to guide a bottom-up search over programs. In particular, we train a model to prioritize compositions of intermediate values during search conditioned on a given set of input-output examples. This is a powerful combination because of several emergent properties. First, in bottom-up search, intermediate programs can be executed, providing semantic information to the neural network. Second, given the concrete values from those executions, we can exploit rich features based on recent work on property signatures. Finally, bottom-up search allows the system substantial flexibility in what order to generate the solution, allowing the synthesizer to build up a program from multiple smaller sub-programs. Overall, our empirical evaluation finds that the combination of learning and bottom-up search is remarkably effective, even with simple supervised learning approaches. We demonstrate the effectiveness of our technique on two datasets, one from the SyGuS competition and one of our own creation.

This paper presents first successful steps in designing search agents that learn meta-strategies for iterative query refinement in information-seeking tasks. Our approach uses machine reading to guide the selection of refinement terms from aggregated search results. Agents are then empowered with simple but effective search operators to exert fine-grained and transparent control over queries and search results. We develop a novel way of generating synthetic search sessions, which leverages the power of transformer-based language models through (self-)supervised learning. We also present a reinforcement learning agent with dynamically constrained actions that learns interactive search strategies from scratch. Our search agents obtain retrieval and answer quality performance comparable to recent neural methods, using only a traditional term-based BM25 ranking function and interpretable discrete reranking and filtering actions.

This work proposes a procedure for designing algorithms for specific adaptive data collection tasks like active learning and pure-exploration multi-armed bandits. Unlike the design of traditional adaptive algorithms that rely on concentration of measure and careful analysis to justify the correctness and sample complexity of the procedure, our adaptive algorithm is learned via adversarial training over equivalence classes of problems derived from information theoretic lower bounds. In particular, a single adaptive learning algorithm is learned that competes with the best adaptive algorithm learned for each equivalence class. Our procedure takes as input just the available queries, set of hypotheses, loss function, and total query budget. This is in contrast to existing meta-learning work that learns an adaptive algorithm relative to an explicit, user-defined subset or prior distribution over problems which can be challenging to define and be mismatched to the instance encountered at test time. This work is particularly focused on the regime when the total query budget is very small, such as a few dozen, which is much smaller than those budgets typically considered by theoretically derived algorithms. We perform synthetic experiments to justify the stability and effectiveness of the training procedure, and then evaluate the method on tasks derived from real data including a noisy 20 Questions game and a joke recommendation task.

Language models contain ranking-based knowledge and are powerful solvers of in-context ranking tasks. For instance, they may have parametric knowledge about the ordering of countries by size or may be able to rank reviews by sentiment. Recent work focuses on pairwise, pointwise, and listwise prompting techniques to elicit a language model's ranking knowledge. However, we find that even with careful calibration and constrained decoding, prompting-based techniques may not always be self-consistent in the rankings they produce. This motivates us to explore an alternative approach that is inspired by an unsupervised probing method called Contrast-Consistent Search (CCS). The idea is to train a probing model guided by a logical constraint: a model's representation of a statement and its negation must be mapped to contrastive true-false poles consistently across multiple statements. We hypothesize that similar constraints apply to ranking tasks where all items are related via consistent pairwise or listwise comparisons. To this end, we extend the binary CCS method to Contrast-Consistent Ranking (CCR) by adapting existing ranking methods such as the Max-Margin Loss, Triplet Loss, and Ordinal Regression objective. Our results confirm that, for the same language model, CCR probing outperforms prompting and even performs on a par with prompting much larger language models.

Code search is an important task that has seen many developments in recent years. However, previous attempts have mostly considered the problem of searching for code by a text query. We argue that using a code snippet (and possibly an associated traceback) as a query and looking for answers with bugfixing instructions and code samples is a natural use case that is not covered by existing approaches. Moreover, existing datasets use comments extracted from code rather than full-text descriptions as text, making them unsuitable for this use case. We present a new SearchBySnippet dataset implementing the search-by-code use case based on StackOverflow data; it turns out that in this setting, existing architectures fall short of the simplest BM25 baseline even after fine-tuning. We present a new single encoder model SnippeR that outperforms several strong baselines on the SearchBySnippet dataset with a result of 0.451 Recall@10; we propose the SearchBySnippet dataset and SnippeR as a new important benchmark for code search evaluation.

Recovering causal relationships from data is an important problem. Using observational data, one can typically only recover causal graphs up to a Markov equivalence class and additional assumptions or interventional data are needed for complete recovery. In this work, under some standard assumptions, we study causal graph discovery via adaptive interventions with node-dependent interventional costs. For this setting, we show that no algorithm can achieve an approximation guarantee that is asymptotically better than linear in the number of vertices with respect to the verification number; a well-established benchmark for adaptive search algorithms. Motivated by this negative result, we define a new benchmark that captures the worst-case interventional cost for any search algorithm. Furthermore, with respect to this new benchmark, we provide adaptive search algorithms that achieve logarithmic approximations under various settings: atomic, bounded size interventions and generalized cost objectives.

Language models are rarely shown fruitful mistakes while training. They then struggle to look beyond the next token, suffering from a snowballing of errors and struggling to predict the consequence of their actions several steps ahead. In this paper, we show how language models can be taught to search by representing the process of search in language, as a flattened string -- a stream of search (SoS). We propose a unified language for search that captures an array of different symbolic search strategies. We demonstrate our approach using the simple yet difficult game of Countdown, where the goal is to combine input numbers with arithmetic operations to reach a target number. We pretrain a transformer-based language model from scratch on a dataset of streams of search generated by heuristic solvers. We find that SoS pretraining increases search accuracy by 25% over models trained to predict only the optimal search trajectory. We further finetune this model with two policy improvement methods: Advantage-Induced Policy Alignment (APA) and Self-Taught Reasoner (STaR). The finetuned SoS models solve 36% of previously unsolved problems, including problems that cannot be solved by any of the heuristic solvers. Our results indicate that language models can learn to solve problems via search, self-improve to flexibly use different search strategies, and potentially discover new ones.

Large language models (LLMs) have demonstrated impressive capability in reasoning and planning when integrated with tree-search-based prompting methods. However, since these methods ignore the previous search experiences, they often make the same mistakes in the search process. To address this issue, we introduce Reflection on search Trees (RoT), an LLM reflection framework designed to improve the performance of tree-search-based prompting methods. It uses a strong LLM to summarize guidelines from previous tree search experiences to enhance the ability of a weak LLM. The guidelines are instructions about solving this task through tree search which can prevent the weak LLMs from making similar mistakes in the past search process. In addition, we proposed a novel state selection method, which identifies the critical information from historical search processes to help RoT generate more specific and meaningful guidelines. In our extensive experiments, we find that RoT significantly improves the performance of LLMs in reasoning or planning tasks with various tree-search-based prompting methods (e.g., BFS and MCTS). Non-tree-search-based prompting methods such as Chain-of-Thought (CoT) can also benefit from RoT guidelines since RoT can provide task-specific knowledge collected from the search experience.

The remarkable capability of large language models (LLMs) for in-context learning (ICL) needs to be activated by demonstration examples. Prior work has extensively explored the selection of examples for ICL, predominantly following the "select then organize" paradigm, such approaches often neglect the internal relationships between examples and exist an inconsistency between the training and inference. In this paper, we formulate the problem as a sequential selection problem and introduce Se^2, a sequential-aware method that leverages the LLM's feedback on varying context, aiding in capturing inter-relationships and sequential information among examples, significantly enriching the contextuality and relevance of ICL prompts. Meanwhile, we utilize beam search to seek and construct example sequences, enhancing both quality and diversity. Extensive experiments across 23 NLP tasks from 8 distinct categories illustrate that Se^2 markedly surpasses competitive baselines and achieves 42% relative improvement over random selection. Further in-depth analysis show the effectiveness of proposed strategies, highlighting Se^2's exceptional stability and adaptability across various scenarios. Our code will be released to facilitate future research.

Large language models (LLMs) have been significantly improved by instruction fine-tuning, but still lack transparency and the ability to utilize up-to-date knowledge and information. In this work, we propose search-augmented instruction learning (SAIL), which grounds the language generation and instruction following abilities on complex search results generated by in-house and external search engines. With an instruction tuning corpus, we collect search results for each training case from different search APIs and domains, and construct a new search-grounded training set containing (instruction, grounding information, response) triplets. We then fine-tune the LLaMA-7B model on the constructed training set. Since the collected results contain unrelated and disputing languages, the model needs to learn to ground on trustworthy search results, filter out distracting passages, and generate the target response. The search result-denoising process entails explicit trustworthy information selection and multi-hop reasoning, since the retrieved passages might be informative but not contain the instruction-following answer. Experiments show that the fine-tuned SAIL-7B model has a strong instruction-following ability, and it performs significantly better on transparency-sensitive tasks, including open-ended question answering and fact checking.

While language models have demonstrated impressive capabilities across a range of tasks, they still struggle with tasks that require complex planning and reasoning. Recent studies have proposed training language models on search processes rather than optimal solutions, resulting in better generalization performance even though search processes are noisy and even suboptimal. However, these studies overlook the value of optimal solutions, which can serve as step-by-step landmarks to guide more effective search. In this work, we explore how to leverage optimal solutions to enhance the search and planning abilities of language models. To this end, we propose guided stream of search (GSoS), which seamlessly incorporates optimal solutions into the self-generation process in a progressive manner, producing high-quality search trajectories. These trajectories are then distilled into the pre-trained model via supervised fine-tuning. Our approach significantly enhances the search and planning abilities of language models on Countdown, a simple yet challenging mathematical reasoning task. Notably, combining our method with RL fine-tuning yields further improvements, whereas previous supervised fine-tuning methods do not benefit from RL. Furthermore, our approach exhibits greater effectiveness than leveraging optimal solutions in the form of subgoal rewards.

We define and investigate the problem of c-approximate window search: approximate nearest neighbor search where each point in the dataset has a numeric label, and the goal is to find nearest neighbors to queries within arbitrary label ranges. Many semantic search problems, such as image and document search with timestamp filters, or product search with cost filters, are natural examples of this problem. We propose and theoretically analyze a modular tree-based framework for transforming an index that solves the traditional c-approximate nearest neighbor problem into a data structure that solves window search. On standard nearest neighbor benchmark datasets equipped with random label values, adversarially constructed embeddings, and image search embeddings with real timestamps, we obtain up to a 75times speedup over existing solutions at the same level of recall.

Query expansion, pivotal in search engines, enhances the representation of user information needs with additional terms. While existing methods expand queries using retrieved or generated contextual documents, each approach has notable limitations. Retrieval-based methods often fail to accurately capture search intent, particularly with brief or ambiguous queries. Generation-based methods, utilizing large language models (LLMs), generally lack corpus-specific knowledge and entail high fine-tuning costs. To address these gaps, we propose a novel zero-shot query expansion framework utilizing LLMs for mutual verification. Specifically, we first design a query-query-document generation method, leveraging LLMs' zero-shot reasoning ability to produce diverse sub-queries and corresponding documents. Then, a mutual verification process synergizes generated and retrieved documents for optimal expansion. Our proposed method is fully zero-shot, and extensive experiments on three public benchmark datasets are conducted to demonstrate its effectiveness over existing methods. Our code is available online at https://github.com/Applied-Machine-Learning-Lab/MILL to ease reproduction.

Formulating selective information needs results in queries that implicitly specify set operations, such as intersection, union, and difference. For instance, one might search for "shorebirds that are not sandpipers" or "science-fiction films shot in England". To study the ability of retrieval systems to meet such information needs, we construct QUEST, a dataset of 3357 natural language queries with implicit set operations, that map to a set of entities corresponding to Wikipedia documents. The dataset challenges models to match multiple constraints mentioned in queries with corresponding evidence in documents and correctly perform various set operations. The dataset is constructed semi-automatically using Wikipedia category names. Queries are automatically composed from individual categories, then paraphrased and further validated for naturalness and fluency by crowdworkers. Crowdworkers also assess the relevance of entities based on their documents and highlight attribution of query constraints to spans of document text. We analyze several modern retrieval systems, finding that they often struggle on such queries. Queries involving negation and conjunction are particularly challenging and systems are further challenged with combinations of these operations.

Recent advancements in large language models have significantly improved their reasoning abilities, particularly through techniques involving search and backtracking. Backtracking naturally scales test-time compute by enabling sequential, linearized exploration via long chain-of-thought (CoT) generation. However, this is not the only strategy for scaling test-time compute: parallel sampling with best-of-n selection provides an alternative that generates diverse solutions simultaneously. Despite the growing adoption of sequential search, its advantages over parallel sampling--especially under a fixed compute budget remain poorly understood. In this paper, we systematically compare these two approaches on two challenging reasoning tasks: CountDown and Sudoku. Surprisingly, we find that sequential search underperforms parallel sampling on CountDown but outperforms it on Sudoku, suggesting that backtracking is not universally beneficial. We identify two factors that can cause backtracking to degrade performance: (1) training on fixed search traces can lock models into suboptimal strategies, and (2) explicit CoT supervision can discourage "implicit" (non-verbalized) reasoning. Extending our analysis to reinforcement learning (RL), we show that models with backtracking capabilities benefit significantly from RL fine-tuning, while models without backtracking see limited, mixed gains. Together, these findings challenge the assumption that backtracking universally enhances LLM reasoning, instead revealing a complex interaction between task structure, training data, model scale, and learning paradigm.

The problem of designing NLP solvers for math word problems (MWP) has seen sustained research activity and steady gains in the test accuracy. Since existing solvers achieve high performance on the benchmark datasets for elementary level MWPs containing one-unknown arithmetic word problems, such problems are often considered "solved" with the bulk of research attention moving to more complex MWPs. In this paper, we restrict our attention to English MWPs taught in grades four and lower. We provide strong evidence that the existing MWP solvers rely on shallow heuristics to achieve high performance on the benchmark datasets. To this end, we show that MWP solvers that do not have access to the question asked in the MWP can still solve a large fraction of MWPs. Similarly, models that treat MWPs as bag-of-words can also achieve surprisingly high accuracy. Further, we introduce a challenge dataset, SVAMP, created by applying carefully chosen variations over examples sampled from existing datasets. The best accuracy achieved by state-of-the-art models is substantially lower on SVAMP, thus showing that much remains to be done even for the simplest of the MWPs.

Instruction-following retrievers have been widely adopted alongside LLMs in real-world applications, but little work has investigated the safety risks surrounding their increasing search capabilities. We empirically study the ability of retrievers to satisfy malicious queries, both when used directly and when used in a retrieval augmented generation-based setup. Concretely, we investigate six leading retrievers, including NV-Embed and LLM2Vec, and find that given malicious requests, most retrievers can (for >50% of queries) select relevant harmful passages. For example, LLM2Vec correctly selects passages for 61.35% of our malicious queries. We further uncover an emerging risk with instruction-following retrievers, where highly relevant harmful information can be surfaced by exploiting their instruction-following capabilities. Finally, we show that even safety-aligned LLMs, such as Llama3, can satisfy malicious requests when provided with harmful retrieved passages in-context. In summary, our findings underscore the malicious misuse risks associated with increasing retriever capability.

In dense retrieval, effective training hinges on selecting high quality hard negatives while avoiding false negatives. Recent methods apply heuristics based on positive document scores to identify hard negatives, improving both performance and interpretability. However, these global, example agnostic strategies often miss instance specific false negatives. To address this, we propose a learnable adapter module that monitors Bi-Encoder representations to estimate the likelihood that a hard negative is actually a false negative. This probability is modeled dynamically and contextually, enabling fine-grained, query specific judgments. The predicted scores are used in two downstream components: (1) resampling, where negatives are reweighted during training, and (2) reranking, where top-k retrieved documents are reordered at inference. Empirical results on standard benchmarks show that our adapter-enhanced framework consistently outperforms strong Bi-Encoder baselines, underscoring the benefit of explicit false negative modeling in dense retrieval.

LLMs cannot reliably recognize their parametric knowledge boundaries and often hallucinate answers to outside-of-boundary questions. In contrast, humans recognize their limitations and can either seek external help for such questions or abstain. In this paper, we introduce MASH (Modeling Abstention via Selective Help-seeking), a training framework that readily extracts abstentions from LLMs. Our key idea is that any external help-seeking by an LLM, i.e. search tool use, can serve as a proxy for abstention if the external help (search) is appropriately penalized while simultaneously rewarding answer accuracy. MASH operationalizes this idea using reinforcement learning with a pay-per-search reward. We run experiments on three knowledge-intensive QA datasets. Our results show that MASH substantially improves upon the selective help-seeking performance of prior efficient search approaches; on multi-hop datasets, MASH improves answer accuracy by 7.6%. Furthermore, MASH demonstrates strong off-the-shelf abstention -- it can distinguish between unanswerable/answerable questions and selectively generate responses for answerable questions -- showcasing behavior analogous to specialized abstention approaches. We emphasize that contrary to prior abstention methods, MASH does not require pre-determining knowledge boundaries to construct training data. Instead, MASH's abstentions are a by-product of training for the auxiliary selective help-seeking task. Overall, we show that MASH training effectively aligns search tool use with parametric knowledge, which can be successfully leveraged for making abstention decisions.

Translating natural language mathematical statements into formal, executable code is a fundamental challenge in automated theorem proving. While prior work has focused on generation and compilation success, little attention has been paid to the critic phase-the evaluation of whether generated formalizations truly capture the semantic intent of the original problem. In this paper, we introduce CriticLean, a novel critic-guided reinforcement learning framework that elevates the role of the critic from a passive validator to an active learning component. Specifically, first, we propose the CriticLeanGPT, trained via supervised fine-tuning and reinforcement learning, to rigorously assess the semantic fidelity of Lean 4 formalizations. Then, we introduce CriticLeanBench, a benchmark designed to measure models' ability to distinguish semantically correct from incorrect formalizations, and demonstrate that our trained CriticLeanGPT models can significantly outperform strong open- and closed-source baselines. Building on the CriticLean framework, we construct FineLeanCorpus, a dataset comprising over 285K problems that exhibits rich domain diversity, broad difficulty coverage, and high correctness based on human evaluation. Overall, our findings highlight that optimizing the critic phase is essential for producing reliable formalizations, and we hope our CriticLean will provide valuable insights for future advances in formal mathematical reasoning.

Large Language Models (LLMs) can comply with harmful instructions, raising serious safety concerns despite their impressive capabilities. Recent work has leveraged probing-based approaches to study the separability of malicious and benign inputs in LLMs' internal representations, and researchers have proposed using such probing methods for safety detection. We systematically re-examine this paradigm. Motivated by poor out-of-distribution performance, we hypothesize that probes learn superficial patterns rather than semantic harmfulness. Through controlled experiments, we confirm this hypothesis and identify the specific patterns learned: instructional patterns and trigger words. Our investigation follows a systematic approach, progressing from demonstrating comparable performance of simple n-gram methods, to controlled experiments with semantically cleaned datasets, to detailed analysis of pattern dependencies. These results reveal a false sense of security around current probing-based approaches and highlight the need to redesign both models and evaluation protocols, for which we provide further discussions in the hope of suggesting responsible further research in this direction. We have open-sourced the project at https://github.com/WangCheng0116/Why-Probe-Fails.

Query expansion (QE) enhances retrieval by incorporating relevant terms, with large language models (LLMs) offering an effective alternative to traditional rule-based and statistical methods. However, LLM-based QE suffers from a fundamental limitation: it often fails to generate relevant knowledge, degrading search performance. Prior studies have focused on hallucination, yet its underlying cause--LLM knowledge deficiencies--remains underexplored. This paper systematically examines two failure cases in LLM-based QE: (1) when the LLM lacks query knowledge, leading to incorrect expansions, and (2) when the query is ambiguous, causing biased refinements that narrow search coverage. We conduct controlled experiments across multiple datasets, evaluating the effects of knowledge and query ambiguity on retrieval performance using sparse and dense retrieval models. Our results reveal that LLM-based QE can significantly degrade the retrieval effectiveness when knowledge in the LLM is insufficient or query ambiguity is high. We introduce a framework for evaluating QE under these conditions, providing insights into the limitations of LLM-based retrieval augmentation.

Dense retrieval, which aims to encode the semantic information of arbitrary text into dense vector representations or embeddings, has emerged as an effective and efficient paradigm for text retrieval, consequently becoming an essential component in various natural language processing systems. These systems typically focus on optimizing the embedding space by attending to the relevance of text pairs, while overlooking the Boolean logic inherent in language, which may not be captured by current training objectives. In this work, we first investigate whether current retrieval systems can comprehend the Boolean logic implied in language. To answer this question, we formulate the task of Boolean Dense Retrieval and collect a benchmark dataset, BoolQuestions, which covers complex queries containing basic Boolean logic and corresponding annotated passages. Through extensive experimental results on the proposed task and benchmark dataset, we draw the conclusion that current dense retrieval systems do not fully understand Boolean logic in language, and there is a long way to go to improve our dense retrieval systems. Furthermore, to promote further research on enhancing the understanding of Boolean logic for language models, we explore Boolean operation on decomposed query and propose a contrastive continual training method that serves as a strong baseline for the research community.

We consider the task of mapping pseudocode to long programs that are functionally correct. Given test cases as a mechanism to validate programs, we search over the space of possible translations of the pseudocode to find a program that passes the validation. However, without proper credit assignment to localize the sources of program failures, it is difficult to guide search toward more promising programs. We propose to perform credit assignment based on signals from compilation errors, which constitute 88.7% of program failures. Concretely, we treat the translation of each pseudocode line as a discrete portion of the program, and whenever a synthesized program fails to compile, an error localization method tries to identify the portion of the program responsible for the failure. We then focus search over alternative translations of the pseudocode for those portions. For evaluation, we collected the SPoC dataset (Search-based Pseudocode to Code) containing 18,356 programs with human-authored pseudocode and test cases. Under a budget of 100 program compilations, performing search improves the synthesis success rate over using the top-one translation of the pseudocode from 25.6% to 44.7%.

We introduce Multi-Objective Counterfactuals for Design (MCD), a novel method for counterfactual optimization in design problems. Counterfactuals are hypothetical situations that can lead to a different decision or choice. In this paper, the authors frame the counterfactual search problem as a design recommendation tool that can help identify modifications to a design, leading to better functional performance. MCD improves upon existing counterfactual search methods by supporting multi-objective queries, which are crucial in design problems, and by decoupling the counterfactual search and sampling processes, thus enhancing efficiency and facilitating objective tradeoff visualization. The paper demonstrates MCD's core functionality using a two-dimensional test case, followed by three case studies of bicycle design that showcase MCD's effectiveness in real-world design problems. In the first case study, MCD excels at recommending modifications to query designs that can significantly enhance functional performance, such as weight savings and improvements to the structural safety factor. The second case study demonstrates that MCD can work with a pre-trained language model to suggest design changes based on a subjective text prompt effectively. Lastly, the authors task MCD with increasing a query design's similarity to a target image and text prompt while simultaneously reducing weight and improving structural performance, demonstrating MCD's performance on a complex multimodal query. Overall, MCD has the potential to provide valuable recommendations for practitioners and design automation researchers looking for answers to their ``What if'' questions by exploring hypothetical design modifications and their impact on multiple design objectives. The code, test problems, and datasets used in the paper are available to the public at decode.mit.edu/projects/counterfactuals/.

Retriever-augmented instruction-following models are attractive alternatives to fine-tuned approaches for information-seeking tasks such as question answering (QA). By simply prepending retrieved documents in its input along with an instruction, these models can be adapted to various information domains and tasks without additional fine-tuning. While the model responses tend to be natural and fluent, the additional verbosity makes traditional QA evaluation metrics such as exact match (EM) and F1 unreliable for accurately quantifying model performance. In this work, we investigate the performance of instruction-following models across three information-seeking QA tasks. We use both automatic and human evaluation to evaluate these models along two dimensions: 1) how well they satisfy the user's information need (correctness), and 2) whether they produce a response based on the provided knowledge (faithfulness). Guided by human evaluation and analysis, we highlight the shortcomings of traditional metrics for both correctness and faithfulness. We then propose simple token-overlap based and model-based metrics that reflect the true performance of these models. Our analysis reveals that instruction-following models are competitive, and sometimes even outperform fine-tuned models for correctness. However, these models struggle to stick to the provided knowledge and often hallucinate in their responses. We hope our work encourages a more holistic evaluation of instruction-following models for QA. Our code and data is available at https://github.com/McGill-NLP/instruct-qa

We automate deep step-by step reasoning in an LLM dialog thread by recursively exploring alternatives (OR-nodes) and expanding details (AND-nodes) up to a given depth. Starting from a single succinct task-specific initiator we steer the automated dialog thread to stay focussed on the task by synthesizing a prompt that summarizes the depth-first steps taken so far. Our algorithm is derived from a simple recursive descent implementation of a Horn Clause interpreter, except that we accommodate our logic engine to fit the natural language reasoning patterns LLMs have been trained on. Semantic similarity to ground-truth facts or oracle advice from another LLM instance is used to restrict the search space and validate the traces of justification steps returned as answers. At the end, the unique minimal model of a generated Horn Clause program collects the results of the reasoning process. As applications, we sketch implementations of consequence predictions, causal explanations, recommendation systems and topic-focussed exploration of scientific literature.

In this work, we aim to connect two research areas: instruction models and retrieval-based models. While instruction-tuned Large Language Models (LLMs) excel at extracting information from text, they are not suitable for semantic retrieval. Similarity search over embedding vectors allows to index and query vectors, but the similarity reflected in the embedding is sub-optimal for many use cases. We identify the task of retrieving sentences based on abstract descriptions of their content. We demonstrate the inadequacy of current text embeddings and propose an alternative model that significantly improves when used in standard nearest neighbor search. The model is trained using positive and negative pairs sourced through prompting an a large language model (LLM). While it is easy to source the training material from an LLM, the retrieval task cannot be performed by the LLM directly. This demonstrates that data from LLMs can be used not only for distilling more efficient specialized models than the original LLM, but also for creating new capabilities not immediately possible using the original model.

We study the ability of state-of-the art models to answer constraint satisfaction queries for information retrieval (e.g., 'a list of ice cream shops in San Diego'). In the past, such queries were considered to be tasks that could only be solved via web-search or knowledge bases. More recently, large language models (LLMs) have demonstrated initial emergent abilities in this task. However, many current retrieval benchmarks are either saturated or do not measure constraint satisfaction. Motivated by rising concerns around factual incorrectness and hallucinations of LLMs, we present KITAB, a new dataset for measuring constraint satisfaction abilities of language models. KITAB consists of book-related data across more than 600 authors and 13,000 queries, and also offers an associated dynamic data collection and constraint verification approach for acquiring similar test data for other authors. Our extended experiments on GPT4 and GPT3.5 characterize and decouple common failure modes across dimensions such as information popularity, constraint types, and context availability. Results show that in the absence of context, models exhibit severe limitations as measured by irrelevant information, factual errors, and incompleteness, many of which exacerbate as information popularity decreases. While context availability mitigates irrelevant information, it is not helpful for satisfying constraints, identifying fundamental barriers to constraint satisfaction. We open source our contributions to foster further research on improving constraint satisfaction abilities of future models.

Causal explanations of the predictions of NLP systems are essential to ensure safety and establish trust. Yet, existing methods often fall short of explaining model predictions effectively or efficiently and are often model-specific. In this paper, we address model-agnostic explanations, proposing two approaches for counterfactual (CF) approximation. The first approach is CF generation, where a large language model (LLM) is prompted to change a specific text concept while keeping confounding concepts unchanged. While this approach is demonstrated to be very effective, applying LLM at inference-time is costly. We hence present a second approach based on matching, and propose a method that is guided by an LLM at training-time and learns a dedicated embedding space. This space is faithful to a given causal graph and effectively serves to identify matches that approximate CFs. After showing theoretically that approximating CFs is required in order to construct faithful explanations, we benchmark our approaches and explain several models, including LLMs with billions of parameters. Our empirical results demonstrate the excellent performance of CF generation models as model-agnostic explainers. Moreover, our matching approach, which requires far less test-time resources, also provides effective explanations, surpassing many baselines. We also find that Top-K techniques universally improve every tested method. Finally, we showcase the potential of LLMs in constructing new benchmarks for model explanation and subsequently validate our conclusions. Our work illuminates new pathways for efficient and accurate approaches to interpreting NLP systems.

Supervised Fine-Tuning (SFT) is essential for training large language models (LLMs), significantly enhancing critical capabilities such as instruction following and in-context learning. Nevertheless, creating suitable training datasets tailored for specific domains remains challenging due to unique domain constraints and data scarcity. In this paper, we propose SearchInstruct, an innovative method explicitly designed to construct high quality instruction datasets for SFT. Our approach begins with a limited set of domain specific, human generated questions, which are systematically expanded using a large language model. Subsequently, domain relevant resources are dynamically retrieved to generate accurate and contextually appropriate answers for each augmented question. Experimental evaluation demonstrates that SearchInstruct enhances both the diversity and quality of SFT datasets, leading to measurable improvements in LLM performance within specialized domains. Additionally, we show that beyond dataset generation, the proposed method can also effectively facilitate tasks such as model editing, enabling efficient updates to existing models. To facilitate reproducibility and community adoption, we provide full implementation details, the complete set of generated instruction response pairs, and the source code in a publicly accessible Git repository: [https://github.com/mostafaamiri/SearchInstruct](https://github.com/mostafaamiri/SearchInstruct)

Large language models (LLMs) are becoming increasingly important for machine learning applications. However, it can be challenging to align LLMs with our intent, particularly when we want to generate content that is preferable over others or when we want the LLM to respond in a certain style or tone that is hard to describe. To address this challenge, we propose an approach that uses contrastive examples to better describe our intent. This involves providing positive examples that illustrate the true intent, along with negative examples that show what characteristics we want LLMs to avoid. The negative examples can be retrieved from labeled data, written by a human, or generated by the LLM itself. Before generating an answer, we ask the model to analyze the examples to teach itself what to avoid. This reasoning step provides the model with the appropriate articulation of the user's need and guides it towards generting a better answer. We tested our approach on both synthesized and real-world datasets, including StackExchange and Reddit, and found that it significantly improves performance compared to standard few-shot prompting

One well motivated explanation method for classifiers leverages counterfactuals which are hypothetical events identical to real observations in all aspects except for one categorical feature. Constructing such counterfactual poses specific challenges for texts, however, as some attribute values may not necessarily align with plausible real-world events. In this paper we propose a simple method for generating counterfactuals by intervening in the space of text representations which bypasses this limitation. We argue that our interventions are minimally disruptive and that they are theoretically sound as they align with counterfactuals as defined in Pearl's causal inference framework. To validate our method, we first conduct experiments on a synthetic dataset of counterfactuals, allowing for a direct comparison between classifier predictions based on ground truth counterfactuals (obtained through explicit text interventions) and our counterfactuals, derived through interventions in the representation space. Second, we study a real world scenario where our counterfactuals can be leveraged both for explaining a classifier and for bias mitigation.

Large reasoning models exhibit remarkable reasoning capabilities via long, elaborate reasoning trajectories. Supervised fine-tuning on such reasoning traces, also known as distillation, can be a cost-effective way to boost reasoning capabilities of student models. However, empirical observations reveal that these reasoning trajectories are often suboptimal, switching excessively between different lines of thought, resulting in under-thinking, over-thinking, and even degenerate responses. We introduce Retro-Search, an MCTS-inspired search algorithm, for distilling higher quality reasoning paths from large reasoning models. Retro-Search retrospectively revises reasoning paths to discover better, yet shorter traces, which can then lead to student models with enhanced reasoning capabilities with shorter, thus faster inference. Our approach can enable two use cases: self-improvement, where models are fine-tuned on their own Retro-Search-ed thought traces, and weak-to-strong improvement, where a weaker model revises stronger model's thought traces via Retro-Search. For self-improving, R1-distill-7B, fine-tuned on its own Retro-Search-ed traces, reduces the average reasoning length by 31.2% while improving performance by 7.7% across seven math benchmarks. For weak-to-strong improvement, we retrospectively revise R1-671B's traces from the OpenThoughts dataset using R1-distill-32B as the Retro-Search-er, a model 20x smaller. Qwen2.5-32B, fine-tuned on this refined data, achieves performance comparable to R1-distill-32B, yielding an 11.3% reduction in reasoning length and a 2.4% performance improvement compared to fine-tuning on the original OpenThoughts data. Our work counters recently emergent viewpoints that question the relevance of search algorithms in the era of large reasoning models, by demonstrating that there are still opportunities for algorithmic advancements, even for frontier models.

Proof-oriented programs mix computational content with proofs of program correctness. However, the human effort involved in programming and proving is still substantial, despite the use of Satisfiability Modulo Theories (SMT) solvers to automate proofs in languages such as F*. Seeking to spur research on using AI to automate the construction of proof-oriented programs, we curate a dataset of 600K lines of open-source F* programs and proofs, including software used in production systems ranging from Windows and Linux, to Python and Firefox. Our dataset includes around 32K top-level F* definitions, each representing a type-directed program and proof synthesis problem -- producing a definition given a formal specification expressed as an F* type. We provide a program-fragment checker that queries F* to check the correctness of candidate solutions. We believe this is the largest corpus of SMT-assisted program proofs coupled with a reproducible program-fragment checker. Grounded in this dataset, we investigate the use of AI to synthesize programs and their proofs in F*, with promising results. Our main finding in that the performance of fine-tuned smaller language models (such as Phi-2 or StarCoder) compare favorably with large language models (such as GPT-4), at a much lower computational cost. We also identify various type-based retrieval augmentation techniques and find that they boost performance significantly. With detailed error analysis and case studies, we identify potential strengths and weaknesses of models and techniques and suggest directions for future improvements.

Large language models (LLMs) have demonstrated impressive performance on reasoning tasks, including mathematical reasoning. However, the current evaluation mostly focuses on carefully constructed benchmarks and neglects the consideration of real-world reasoning problems that present missing or contradictory conditions, known as ill-defined problems. To further study this problem, we develop a largescale benchmark called Problems with Missing and Contradictory conditions ( PMC) containing over 5,000 validated ill-defined mathematical problems. Our preliminary experiments through PMC reveal two challenges about existing methods: (1) traditional methods exhibit a trade-off between solving accuracy and rejection capabilities, and (2) formal methods struggle with modeling complex problems. To address these challenges, We develop Variable-Constraint Search (VCSEARCH), a trainingfree framework that leverages formal language to detect ill-defined problems, where a variableconstraint pair search strategy is incorporated to improve the modeling capability of formal language. Extensive experiments demonstrate that VCSEARCH improves the accuracy of identifying unsolvable problems by at least 12% across different LLMs, thus achieving stronger robust mathematical reasoning ability.

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 .

Context: Recent research indicates that Web queries written by software developers are not very successful in retrieving relevant results, performing measurably worse compared to general purpose Web queries. Most approaches up to this point have addressed this problem with software engineering-specific automated query reformulation techniques, which work without developer involvement but are limited by the content of the original query. In other words, these techniques automatically improve the existing query but can not contribute new, previously unmentioned, concepts. Objective: In this paper, we propose a technique to guide software developers in manually improving their own Web search queries. We examine a conversational approach that follows unsuccessful queries with a clarification question aimed at eliciting additional query terms, thus providing to the developer a clear dimension along which the query could be improved. Methods: We describe a set of clarification questions derived from a corpus of software developer queries and a neural approach to recommending them for a newly issued query. Results: Our evaluation indicates that the recommendation technique is accurate, predicting a valid clarification question 80% of the time and outperforms simple baselines, as well as, state-of-the-art Learning To Rank (LTR) baselines. Conclusion: As shown in the experimental results, the described approach is capable at recommending appropriate clarification questions to software developers and considered useful by a sample of developers ranging from novices to experienced professionals.

State-of-the-art large language models (LLMs) exhibit impressive problem-solving capabilities but may struggle with complex reasoning and factual correctness. Existing methods harness the strengths of chain-of-thought and retrieval-augmented generation (RAG) to decompose a complex problem into simpler steps and apply retrieval to improve factual correctness. These methods work well on straightforward reasoning tasks but often falter on challenging tasks such as competitive programming and mathematics, due to frequent reasoning errors and irrelevant knowledge retrieval. To address this, we introduce Critic-guided planning with Retrieval-augmentation, CR-Planner, a novel framework that leverages fine-tuned critic models to guide both reasoning and retrieval processes through planning. CR-Planner solves a problem by iteratively selecting and executing sub-goals. Initially, it identifies the most promising sub-goal from reasoning, query generation, and retrieval, guided by rewards given by a critic model named sub-goal critic. It then executes this sub-goal through sampling and selecting the optimal output based on evaluations from another critic model named execution critic. This iterative process, informed by retrieved information and critic models, enables CR-Planner to effectively navigate the solution space towards the final answer. We employ Monte Carlo Tree Search to collect the data for training the critic models, allowing for a systematic exploration of action sequences and their long-term impacts. We validate CR-Planner on challenging domain-knowledge-intensive and reasoning-heavy tasks, including competitive programming, theorem-driven math reasoning, and complex domain retrieval problems. Our experiments demonstrate that CR-Planner significantly outperforms baselines, highlighting its effectiveness in addressing challenging problems by improving both reasoning and retrieval.

Prompt engineering is a challenging yet crucial task for optimizing the performance of large language models (LLMs). It requires complex reasoning to examine the model's errors, hypothesize what is missing or misleading in the current prompt, and communicate the task with clarity. While recent works indicate that LLMs can be meta-prompted to perform automatic prompt engineering, their potentials may not be fully untapped due to the lack of sufficient guidance to elicit complex reasoning capabilities in LLMs in the meta-prompt. In this work, we investigate the problem of "prompt engineering a prompt engineer" -- constructing a meta-prompt that more effectively guides LLMs to perform automatic prompt engineering. We introduce and analyze key components, such as a step-by-step reasoning template and context specification, which lead to improved performance. In addition, inspired by common optimization concepts such as batch size, step size and momentum, we introduce their verbalized counterparts to the meta-prompt and investigate their effects. Our final method, named PE2, finds a prompt that outperforms "let's think step by step" by 6.3% on the MultiArith dataset and 3.1% on the GSM8K dataset. To demonstrate its versatility, we apply PE2 to the Instruction Induction benchmark, a suite of counterfactual tasks, and a lengthy, real-world industrial prompt. In these settings, PE2 achieves strong performance and outperforms prior automatic prompt engineering baselines. Further, we show that PE2 makes meaningful and targeted prompt edits, amends erroneous or incomplete prompts, and presents non-trivial counterfactual reasoning abilities.

We provide a reproducible, end-to-end demonstration of vector search with OpenAI embeddings using Lucene on the popular MS MARCO passage ranking test collection. The main goal of our work is to challenge the prevailing narrative that a dedicated vector store is necessary to take advantage of recent advances in deep neural networks as applied to search. Quite the contrary, we show that hierarchical navigable small-world network (HNSW) indexes in Lucene are adequate to provide vector search capabilities in a standard bi-encoder architecture. This suggests that, from a simple cost-benefit analysis, there does not appear to be a compelling reason to introduce a dedicated vector store into a modern "AI stack" for search, since such applications have already received substantial investments in existing, widely deployed infrastructure.

Answering counterfactual queries has many important applications such as knowledge discovery and explainability, but is challenging when causal variables are unobserved and we only see a projection onto an observation space, for instance, image pixels. One approach is to recover the latent Structural Causal Model (SCM), but this typically needs unrealistic assumptions, such as linearity of the causal mechanisms. Another approach is to use na\"ive ML approximations, such as generative models, to generate counterfactual samples; however, these lack guarantees of accuracy. In this work, we strive to strike a balance between practicality and theoretical guarantees by focusing on a specific type of causal query called domain counterfactuals, which hypothesizes what a sample would have looked like if it had been generated in a different domain (or environment). Concretely, by only assuming invertibility, sparse domain interventions and access to observational data from different domains, we aim to improve domain counterfactual estimation both theoretically and practically with less restrictive assumptions. We define domain counterfactually equivalent models and prove necessary and sufficient properties for equivalent models that provide a tight characterization of the domain counterfactual equivalence classes. Building upon this result, we prove that every equivalence class contains a model where all intervened variables are at the end when topologically sorted by the causal DAG. This surprising result suggests that a model design that only allows intervention in the last k latent variables may improve model estimation for counterfactuals. We then test this model design on extensive simulated and image-based experiments which show the sparse canonical model indeed improves counterfactual estimation over baseline non-sparse models.

Rerankers play a critical role in multimodal Retrieval-Augmented Generation (RAG) by refining ranking of an initial set of retrieved documents. Rerankers are typically trained using hard negative mining, whose goal is to select pages for each query which rank high, but are actually irrelevant. However, this selection process is typically passive and restricted to what the retriever can find in the available corpus, leading to several inherent limitations. These include: limited diversity, negative examples which are often not hard enough, low controllability, and frequent false negatives which harm training. Our paper proposes an alternative approach: Single-Page Hard Negative Query Generation, which goes the other way around. Instead of retrieving negative pages per query, we generate hard negative queries per page. Using an automated LLM-VLM pipeline, and given a page and its positive query, we create hard negatives by rephrasing the query to be as similar as possible in form and context, yet not answerable from the page. This paradigm enables fine-grained control over the generated queries, resulting in diverse, hard, and targeted negatives. It also supports efficient false negative verification. Our experiments show that rerankers trained with data generated using our approach outperform existing models and significantly improve retrieval performance.

Learning to search is the task of building artificial agents that learn to autonomously use a search box to find information. So far, it has been shown that current language models can learn symbolic query reformulation policies, in combination with traditional term-based retrieval, but fall short of outperforming neural retrievers. We extend the previous learning to search setup to a hybrid environment, which accepts discrete query refinement operations, after a first-pass retrieval step via a dual encoder. Experiments on the BEIR task show that search agents, trained via behavioral cloning, outperform the underlying search system based on a combined dual encoder retriever and cross encoder reranker. Furthermore, we find that simple heuristic Hybrid Retrieval Environments (HRE) can improve baseline performance by several nDCG points. The search agent based on HRE (HARE) matches state-of-the-art performance, balanced in both zero-shot and in-domain evaluations, via interpretable actions, and at twice the speed.

The hallucinations of large language models (LLMs) are increasingly mitigated by allowing LLMs to search for information and to ground their answers in real sources. Unfortunately, LLMs often struggle with posing the right search queries, especially when dealing with complex or otherwise indirect topics. Observing that LLMs can learn to search for relevant facts by trying different queries and learning to up-weight queries that successfully produce relevant results, we introduce Learning to Retrieve by Trying (LeReT), a reinforcement learning framework that explores search queries and uses preference-based optimization to improve their quality. LeReT can improve the absolute retrieval accuracy by up to 29% and the downstream generator evaluations by 17%. The simplicity and flexibility of LeReT allows it to be applied to arbitrary off-the-shelf retrievers and makes it a promising technique for improving general LLM pipelines. Project website: http://sherylhsu.com/LeReT/.

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.

Formulating effective search queries remains a challenging task, particularly when users lack expertise in a specific domain or are not proficient in the language of the content. Providing example documents of interest might be easier for a user. However, such query-by-example scenarios are prone to concept drift, and the retrieval effectiveness is highly sensitive to the query generation method, without a clear way to incorporate user feedback. To enable exploration and to support Human-In-The-Loop experiments we propose QueryExplorer -- an interactive query generation, reformulation, and retrieval interface with support for HuggingFace generation models and PyTerrier's retrieval pipelines and datasets, and extensive logging of human feedback. To allow users to create and modify effective queries, our demo supports complementary approaches of using LLMs interactively, assisting the user with edits and feedback at multiple stages of the query formulation process. With support for recording fine-grained interactions and user annotations, QueryExplorer can serve as a valuable experimental and research platform for annotation, qualitative evaluation, and conducting Human-in-the-Loop (HITL) experiments for complex search tasks where users struggle to formulate queries.

Effective information searching is essential for enhancing the reasoning and generation capabilities of large language models (LLMs). Recent research has explored using reinforcement learning (RL) to improve LLMs' search capabilities by interacting with live search engines in real-world environments. While these approaches show promising results, they face two major challenges: (1) Uncontrolled Document Quality: The quality of documents returned by search engines is often unpredictable, introducing noise and instability into the training process. (2) Prohibitively High API Costs: RL training requires frequent rollouts, potentially involving hundreds of thousands of search requests, which incur substantial API expenses and severely constrain scalability. To address these challenges, we introduce ZeroSearch, a reinforcement learning framework that incentivizes the search capabilities of LLMs without interacting with real search engines. Our approach begins with lightweight supervised fine-tuning to transform the LLM into a retrieval module capable of generating both relevant and noisy documents in response to a query. During RL training, we employ a curriculum-based rollout strategy that incrementally degrades the quality of generated documents, progressively eliciting the model's reasoning ability by exposing it to increasingly challenging retrieval scenarios. Extensive experiments demonstrate that ZeroSearch effectively incentivizes the search capabilities of LLMs using a 3B LLM as the retrieval module. Remarkably, a 7B retrieval module achieves comparable performance to the real search engine, while a 14B retrieval module even surpasses it. Furthermore, it generalizes well across both base and instruction-tuned models of various parameter sizes and is compatible with a wide range of RL algorithms.

Recent work on open domain question answering (QA) assumes strong supervision of the supporting evidence and/or assumes a blackbox information retrieval (IR) system to retrieve evidence candidates. We argue that both are suboptimal, since gold evidence is not always available, and QA is fundamentally different from IR. We show for the first time that it is possible to jointly learn the retriever and reader from question-answer string pairs and without any IR system. In this setting, evidence retrieval from all of Wikipedia is treated as a latent variable. Since this is impractical to learn from scratch, we pre-train the retriever with an Inverse Cloze Task. We evaluate on open versions of five QA datasets. On datasets where the questioner already knows the answer, a traditional IR system such as BM25 is sufficient. On datasets where a user is genuinely seeking an answer, we show that learned retrieval is crucial, outperforming BM25 by up to 19 points in exact match.

While large language models (LLMs) have exhibited impressive instruction-following capabilities, it is still unclear whether and to what extent they can respond to explicit constraints that might be entailed in various instructions. As a significant aspect of LLM alignment, it is thus important to formulate such a specialized set of instructions as well as investigate the resulting behavior of LLMs. To address this vacancy, we propose a new benchmark CoDI-Eval to systematically and comprehensively evaluate LLMs' responses to instructions with various constraints. We construct a large collection of constraints-attributed instructions as a test suite focused on both generalization and coverage. Specifically, we advocate an instruction diversification process to synthesize diverse forms of constraint expression and also deliberate the candidate task taxonomy with even finer-grained sub-categories. Finally, we automate the entire evaluation process to facilitate further developments. Different from existing studies on controllable text generation, CoDI-Eval extends the scope to the prevalent instruction-following paradigm for the first time. We provide extensive evaluations of representative LLMs (e.g., ChatGPT, Vicuna) on CoDI-Eval, revealing their limitations in following instructions with specific constraints and there is still a significant gap between open-source and commercial closed-source LLMs. We believe this benchmark will facilitate research into improving the controllability of LLMs' responses to instructions. Our data and code are available at https://github.com/Xt-cyh/CoDI-Eval.

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.

Reinforcement learning is emerging as a primary driver for improving language model reasoning capabilities. A fundamental question is whether current reinforcement learning algorithms -- such as Group Relative Policy Optimization (GRPO), the de facto standard algorithm used to improve language model reasoning -- merely sharpen the base model's distribution around problems it can already solve. We investigate this question in the context of formal theorem proving, which has access to a perfect verifier. We identify a degenerate rank bias in GRPO in which highly probable trajectories are reinforced and rare ones are neglected. This results in distribution sharpening: the model can solve some problems with fewer samples, but underperforms simply sampling more solutions from the original model. To overcome GRPO's rank bias we introduce unlikeliness reward, a simple method for explicitly up-weighting rare but correct solutions. We show that unlikeliness reward mitigates rank bias and improves pass@N across a large range of N in both synthetic and real theorem proving settings. We also uncover an unexpected link between rank bias and a seemingly mundane hyperparameter -- the number of updates per batch -- that leads to a second, complementary mitigation. We combine our insights into a revised GRPO training recipe for formal theorem proving, yielding an open pipeline that achieves competitive performance to DeepSeek-Prover-V1.5-RL on the miniF2F-test benchmark. We release our implementation at https://github.com/AndreHe02/rewarding-unlikely-release

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.

Instruction-tuning can be substantially optimized through enhanced diversity, resulting in models capable of handling a broader spectrum of tasks. However, existing data employed for such tuning often exhibit an inadequate coverage of individual domains, limiting the scope for nuanced comprehension and interactions within these areas. To address this deficiency, we propose Explore-Instruct, a novel approach to enhance the data coverage to be used in domain-specific instruction-tuning through active exploration via Large Language Models (LLMs). Built upon representative domain use cases, Explore-Instruct explores a multitude of variations or possibilities by implementing a search algorithm to obtain diversified and domain-focused instruction-tuning data. Our data-centric analysis validates the effectiveness of this proposed approach in improving domain-specific instruction coverage. Moreover, our model's performance demonstrates considerable advancements over multiple baselines, including those utilizing domain-specific data enhancement. Our findings offer a promising opportunity to improve instruction coverage, especially in domain-specific contexts, thereby advancing the development of adaptable language models. Our code, model weights, and data are public at https://github.com/fanqiwan/Explore-Instruct.

We present two different methods for estimating the cost of solving SAT problems. The methods focus on the online behaviour of the backtracking solver, as well as the structure of the problem. Modern SAT solvers present several challenges to estimate search cost including coping with nonchronological backtracking, learning and restarts. Our first method adapt an existing algorithm for estimating the size of a search tree to deal with these challenges. We then suggest a second method that uses a linear model trained on data gathered online at the start of search. We compare the effectiveness of these two methods using random and structured problems. We also demonstrate that predictions made in early restarts can be used to improve later predictions. We conclude by showing that the cost of solving a set of problems can be reduced by selecting a solver from a portfolio based on such cost estimations.

A major technique in learning-augmented online algorithms is combining multiple algorithms or predictors. Since the performance of each predictor may vary over time, it is desirable to use not the single best predictor as a benchmark, but rather a dynamic combination which follows different predictors at different times. We design algorithms that combine predictions and are competitive against such dynamic combinations for a wide class of online problems, namely, metrical task systems. Against the best (in hindsight) unconstrained combination of ell predictors, we obtain a competitive ratio of O(ell^2), and show that this is best possible. However, for a benchmark with slightly constrained number of switches between different predictors, we can get a (1+epsilon)-competitive algorithm. Moreover, our algorithms can be adapted to access predictors in a bandit-like fashion, querying only one predictor at a time. An unexpected implication of one of our lower bounds is a new structural insight about covering formulations for the k-server problem.

Recent LLMs have shown remarkable success in following user instructions, yet handling instructions with multiple constraints remains a significant challenge. In this work, we introduce WildIFEval - a large-scale dataset of 12K real user instructions with diverse, multi-constraint conditions. Unlike prior datasets, our collection spans a broad lexical and topical spectrum of constraints, in natural user prompts. We categorize these constraints into eight high-level classes to capture their distribution and dynamics in real-world scenarios. Leveraging WildIFEval, we conduct extensive experiments to benchmark the instruction-following capabilities of leading LLMs. Our findings reveal that all evaluated models experience performance degradation with an increasing number of constraints. Thus, we show that all models have a large room for improvement on such tasks. Moreover, we observe that the specific type of constraint plays a critical role in model performance. We release our dataset to promote further research on instruction-following under complex, realistic conditions.

In this paper, we present DuReader_retrieval, a large-scale Chinese dataset for passage retrieval. DuReader_retrieval contains more than 90K queries and over 8M unique passages from a commercial search engine. To alleviate the shortcomings of other datasets and ensure the quality of our benchmark, we (1) reduce the false negatives in development and test sets by manually annotating results pooled from multiple retrievers, and (2) remove the training queries that are semantically similar to the development and testing queries. Additionally, we provide two out-of-domain testing sets for cross-domain evaluation, as well as a set of human translated queries for for cross-lingual retrieval evaluation. The experiments demonstrate that DuReader_retrieval is challenging and a number of problems remain unsolved, such as the salient phrase mismatch and the syntactic mismatch between queries and paragraphs. These experiments also show that dense retrievers do not generalize well across domains, and cross-lingual retrieval is essentially challenging. DuReader_retrieval is publicly available at https://github.com/baidu/DuReader/tree/master/DuReader-Retrieval.

There has been an increase of interest in code search using natural language. Assessing the performance of such code search models can be difficult without a readily available evaluation suite. In this paper, we present an evaluation dataset consisting of natural language query and code snippet pairs, with the hope that future work in this area can use this dataset as a common benchmark. We also provide the results of two code search models ([1] and [6]) from recent work. The evaluation dataset is available at https://github.com/facebookresearch/Neural-Code-Search-Evaluation-Dataset

Large Language Models (LLMs) exhibit strong generalization capabilities to novel tasks when prompted with language instructions and in-context demos. Since this ability sensitively depends on the quality of prompts, various methods have been explored to automate the instruction design. While these methods demonstrated promising results, they also restricted the searched prompt to one instruction. Such simplification significantly limits their capacity, as a single demo-free instruction might not be able to cover the entire complex problem space of the targeted task. To alleviate this issue, we adopt the Mixture-of-Expert paradigm and divide the problem space into a set of sub-regions; Each sub-region is governed by a specialized expert, equipped with both an instruction and a set of demos. A two-phase process is developed to construct the specialized expert for each region: (1) demo assignment: Inspired by the theoretical connection between in-context learning and kernel regression, we group demos into experts based on their semantic similarity; (2) instruction assignment: A region-based joint search of an instruction per expert complements the demos assigned to it, yielding a synergistic effect. The resulting method, codenamed Mixture-of-Prompts (MoP), achieves an average win rate of 81% against prior arts across several major benchmarks.

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.

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.

Code search aims to retrieve semantically relevant code snippets for a given natural language query. Recently, many approaches employing contrastive learning have shown promising results on code representation learning and greatly improved the performance of code search. However, there is still a lot of room for improvement in using contrastive learning for code search. In this paper, we propose CoCoSoDa to effectively utilize contrastive learning for code search via two key factors in contrastive learning: data augmentation and negative samples. Specifically, soft data augmentation is to dynamically masking or replacing some tokens with their types for input sequences to generate positive samples. Momentum mechanism is used to generate large and consistent representations of negative samples in a mini-batch through maintaining a queue and a momentum encoder. In addition, multimodal contrastive learning is used to pull together representations of code-query pairs and push apart the unpaired code snippets and queries. We conduct extensive experiments to evaluate the effectiveness of our approach on a large-scale dataset with six programming languages. Experimental results show that: (1) CoCoSoDa outperforms 14 baselines and especially exceeds CodeBERT, GraphCodeBERT, and UniXcoder by 13.3%, 10.5%, and 5.9% on average MRR scores, respectively. (2) The ablation studies show the effectiveness of each component of our approach. (3) We adapt our techniques to several different pre-trained models such as RoBERTa, CodeBERT, and GraphCodeBERT and observe a significant boost in their performance in code search. (4) Our model performs robustly under different hyper-parameters. Furthermore, we perform qualitative and quantitative analyses to explore reasons behind the good performance of our model.

Recent research suggests that tree search algorithms (e.g. Monte Carlo Tree Search) can dramatically boost LLM performance on complex mathematical reasoning tasks. However, they often require more than 10 times the computational resources of greedy decoding due to wasteful search strategies, making them difficult to be deployed in practical applications. This study introduces a novel guided tree search algorithm with dynamic node selection and node-level exploration budget (maximum number of children) calculation to tackle this issue. By considering the search progress towards the final answer (history) and the guidance from a value network (future) trained without any step-wise annotations, our algorithm iteratively selects the most promising tree node before expanding it within the boundaries of the allocated computational budget. Experiments conducted on the GSM8K and TabMWP datasets demonstrate that our approach not only offers competitive performance but also enjoys significantly lower computational costs compared to baseline methods.

Modern IR systems are increasingly tasked with answering complex, multi-faceted queries that require deep reasoning rather than simple keyword or semantic matching. While LLM-based IR has shown great promise, the prevailing retrieve-then-rerank paradigm inherits the limitations of embedding-based retrieval; parametric generative approaches are difficult to update with new information; and long-context methods that place the entire corpus in context are computationally infeasible for large document collections. To address these challenges, we introduce LATTICE, a hierarchical retrieval framework that enables an LLM to reason over and navigate large corpora with logarithmic search complexity by imposing a semantic tree structure on the corpus. Our approach consists of two stages: (1) an offline phase that organizes the corpus into a semantic hierarchy via either a bottom-up agglomerative strategy or a top-down divisive strategy using multi-level summaries and (2) an online traversal phase where a search LLM navigates this tree. A central challenge in such LLM-guided search is that the model's relevance judgments are noisy, context-dependent, and unaware of the hierarchy, making cross-branch and cross-level comparisons difficult. To overcome this, we propose a traversal algorithm that estimates calibrated latent relevance scores from local LLM outputs and aggregates them into a global path relevance metric. Our training-free framework achieves state-of-the-art zero-shot performance on the reasoning-intensive BRIGHT benchmark, demonstrating up to 9% improvement in Recall@100 and 5% in nDCG@10 over the next best zero-shot baseline. Furthermore, compared to the fine-tuned SOTA method DIVER-v2, LATTICE attains comparable results on BRIGHT subsets that use a static corpus for evaluation.

We endow Large Language Models (LLMs) with fine-grained self-evaluation to refine multi-step reasoning inference. We propose an effective prompting approach that integrates self-evaluation guidance through stochastic beam search. Our approach explores the reasoning search space using a well-calibrated automatic criterion. This enables an efficient search to produce higher-quality final predictions. With the self-evaluation guided stochastic beam search, we also balance the quality-diversity trade-off in the generation of reasoning chains. This allows our approach to adapt well with majority voting and surpass the corresponding Codex-backboned baselines by 6.34%, 9.56%, and 5.46% on the GSM8K, AQuA, and StrategyQA benchmarks, respectively, in few-shot accuracy. Analysis of our decompositional reasoning finds it pinpoints logic failures and leads to higher consistency and robustness. Our code is publicly available at https://github.com/YuxiXie/SelfEval-Guided-Decoding.

Large language models (LLMs) currently dominate the field of natural language processing (NLP), representing the state-of-the-art across a diverse array of tasks. Developing a model of this nature, from training to inference, requires making numerous decisions which define a combinatorial search problem. For example, selecting the optimal pre-trained LLM, prompt, or hyperparameters to attain the best performance for a task often requires evaluating multiple candidates on an entire test set. This exhaustive evaluation can be time-consuming and costly, as both inference and metric computation with LLMs are resource-intensive. In this paper, we address the challenge of identifying the best method within a limited budget for evaluating methods on test examples. By leveraging the well-studied multi-armed bandit framework, which sequentially selects the next method-example pair to evaluate, our approach, combining multi-armed bandit algorithms with low-rank factorization, significantly reduces the required resources. Experiments show that our algorithms can identify the top-performing method using only 5-15\% of the typically needed resources, resulting in an 85-95\% reduction in cost.

Following natural instructions is crucial for the effective application of Retrieval-Augmented Generation (RAG) systems. Despite recent advancements in Large Language Models (LLMs), research on assessing and improving instruction-following (IF) alignment within the RAG domain remains limited. To address this issue, we propose VIF-RAG, the first automated, scalable, and verifiable synthetic pipeline for instruction-following alignment in RAG systems. We start by manually crafting a minimal set of atomic instructions (<100) and developing combination rules to synthesize and verify complex instructions for a seed set. We then use supervised models for instruction rewriting while simultaneously generating code to automate the verification of instruction quality via a Python executor. Finally, we integrate these instructions with extensive RAG and general data samples, scaling up to a high-quality VIF-RAG-QA dataset (>100k) through automated processes. To further bridge the gap in instruction-following auto-evaluation for RAG systems, we introduce FollowRAG Benchmark, which includes approximately 3K test samples, covering 22 categories of general instruction constraints and four knowledge-intensive QA datasets. Due to its robust pipeline design, FollowRAG can seamlessly integrate with different RAG benchmarks. Using FollowRAG and eight widely-used IF and foundational abilities benchmarks for LLMs, we demonstrate that VIF-RAG markedly enhances LLM performance across a broad range of general instruction constraints while effectively leveraging its capabilities in RAG scenarios. Further analysis offers practical insights for achieving IF alignment in RAG systems. Our code and datasets are released at https://FollowRAG.github.io.

While scaling training compute has led to remarkable improvements in large language models (LLMs), scaling inference compute has not yet yielded analogous gains. We hypothesize that a core missing component is a lack of diverse LLM outputs, leading to inefficient search due to models repeatedly sampling highly similar, yet incorrect generations. We empirically demonstrate that this lack of diversity can be mitigated by searching over candidate plans for solving a problem in natural language. Based on this insight, we propose PLANSEARCH, a novel search algorithm which shows strong results across HumanEval+, MBPP+, and LiveCodeBench (a contamination-free benchmark for competitive coding). PLANSEARCH generates a diverse set of observations about the problem and then uses these observations to construct plans for solving the problem. By searching over plans in natural language rather than directly over code solutions, PLANSEARCH explores a significantly more diverse range of potential solutions compared to baseline search methods. Using PLANSEARCH on top of Claude 3.5 Sonnet achieves a state-of-the-art pass@200 of 77.0% on LiveCodeBench, outperforming both the best score achieved without search (pass@1 = 41.4%) and using standard repeated sampling (pass@200 = 60.6%). Finally, we show that, across all models, search algorithms, and benchmarks analyzed, we can accurately predict performance gains due to search as a direct function of the diversity over generated ideas.

Retrieval-augmented generation (RAG) is considered to be a promising approach to alleviate the hallucination issue of large language models (LLMs), and it has received widespread attention from researchers recently. Due to the limitation in the semantic understanding of retrieval models, the success of RAG heavily lies on the ability of LLMs to identify passages with utility. Recent efforts have explored the ability of LLMs to assess the relevance of passages in retrieval, but there has been limited work on evaluating the utility of passages in supporting question answering. In this work, we conduct a comprehensive study about the capabilities of LLMs in utility evaluation for open-domain QA. Specifically, we introduce a benchmarking procedure and collection of candidate passages with different characteristics, facilitating a series of experiments with five representative LLMs. Our experiments reveal that: (i) well-instructed LLMs can distinguish between relevance and utility, and that LLMs are highly receptive to newly generated counterfactual passages. Moreover, (ii) we scrutinize key factors that affect utility judgments in the instruction design. And finally, (iii) to verify the efficacy of utility judgments in practical retrieval augmentation applications, we delve into LLMs' QA capabilities using the evidence judged with utility and direct dense retrieval results. (iv) We propose a k-sampling, listwise approach to reduce the dependency of LLMs on the sequence of input passages, thereby facilitating subsequent answer generation. We believe that the way we formalize and study the problem along with our findings contributes to a critical assessment of retrieval-augmented LLMs. Our code and benchmark can be found at https://github.com/ict-bigdatalab/utility_judgments.

Query expansion is a widely used technique to improve the recall of search systems. In this paper, we propose an approach to query expansion that leverages the generative abilities of Large Language Models (LLMs). Unlike traditional query expansion approaches such as Pseudo-Relevance Feedback (PRF) that relies on retrieving a good set of pseudo-relevant documents to expand queries, we rely on the generative and creative abilities of an LLM and leverage the knowledge inherent in the model. We study a variety of different prompts, including zero-shot, few-shot and Chain-of-Thought (CoT). We find that CoT prompts are especially useful for query expansion as these prompts instruct the model to break queries down step-by-step and can provide a large number of terms related to the original query. Experimental results on MS-MARCO and BEIR demonstrate that query expansions generated by LLMs can be more powerful than traditional query expansion methods.

Recent advancements in Large Language Models(LLMs) have demonstrated their capabilities not only in reasoning but also in invoking external tools, particularly search engines. However, teaching models to discern when to invoke search and when to rely on their internal knowledge remains a significant challenge. Existing reinforcement learning approaches often lead to redundant search behaviors, resulting in inefficiencies and over-cost. In this paper, we propose SEM, a novel post-training reinforcement learning framework that explicitly trains LLMs to optimize search usage. By constructing a balanced dataset combining MuSiQue and MMLU, we create scenarios where the model must learn to distinguish between questions it can answer directly and those requiring external retrieval. We design a structured reasoning template and employ Group Relative Policy Optimization(GRPO) to post-train the model's search behaviors. Our reward function encourages accurate answering without unnecessary search while promoting effective retrieval when needed. Experimental results demonstrate that our method significantly reduces redundant search operations while maintaining or improving answer accuracy across multiple challenging benchmarks. This framework advances the model's reasoning efficiency and extends its capability to judiciously leverage external knowledge.

Neural networks -- especially those that use large, pre-trained language models -- have improved search engines in various ways. Most prominently, they can estimate the relevance of a passage or document to a user's query. In this work, we depart from this direction by exploring whether neural networks can effectively predict which of a document's passages are unlikely to be relevant to any query submitted to the search engine. We refer to this query-agnostic estimation of passage relevance as a passage's quality. We find that our novel methods for estimating passage quality allow passage corpora to be pruned considerably while maintaining statistically equivalent effectiveness; our best methods can consistently prune >25% of passages in a corpora, across various retrieval pipelines. Such substantial pruning reduces the operating costs of neural search engines in terms of computing resources, power usage, and carbon footprint -- both when processing queries (thanks to a smaller index size) and when indexing (lightweight models can prune low-quality passages prior to the costly dense or learned sparse encoding step). This work sets the stage for developing more advanced neural "learning-what-to-index" methods.

Given an unconditional diffusion model and a predictor for a target property of interest (e.g., a classifier), the goal of training-free guidance is to generate samples with desirable target properties without additional training. Existing methods, though effective in various individual applications, often lack theoretical grounding and rigorous testing on extensive benchmarks. As a result, they could even fail on simple tasks, and applying them to a new problem becomes unavoidably difficult. This paper introduces a novel algorithmic framework encompassing existing methods as special cases, unifying the study of training-free guidance into the analysis of an algorithm-agnostic design space. Via theoretical and empirical investigation, we propose an efficient and effective hyper-parameter searching strategy that can be readily applied to any downstream task. We systematically benchmark across 7 diffusion models on 16 tasks with 40 targets, and improve performance by 8.5% on average. Our framework and benchmark offer a solid foundation for conditional generation in a training-free manner.

We address whether neural models for Natural Language Inference (NLI) can learn the compositional interactions between lexical entailment and negation, using four methods: the behavioral evaluation methods of (1) challenge test sets and (2) systematic generalization tasks, and the structural evaluation methods of (3) probes and (4) interventions. To facilitate this holistic evaluation, we present Monotonicity NLI (MoNLI), a new naturalistic dataset focused on lexical entailment and negation. In our behavioral evaluations, we find that models trained on general-purpose NLI datasets fail systematically on MoNLI examples containing negation, but that MoNLI fine-tuning addresses this failure. In our structural evaluations, we look for evidence that our top-performing BERT-based model has learned to implement the monotonicity algorithm behind MoNLI. Probes yield evidence consistent with this conclusion, and our intervention experiments bolster this, showing that the causal dynamics of the model mirror the causal dynamics of this algorithm on subsets of MoNLI. This suggests that the BERT model at least partially embeds a theory of lexical entailment and negation at an algorithmic level.

LLM agents enhanced by tree search algorithms have yielded notable performances in code generation. However, current search algorithms in this domain suffer from low search quality due to several reasons: 1) Ineffective design of the search space for the high-reasoning demands of code generation tasks, 2) Inadequate integration of code feedback with the search algorithm, and 3) Poor handling of negative feedback during the search, leading to reduced search efficiency and quality. To address these challenges, we propose to search for the reasoning process of the code and use the detailed feedback of code execution to refine erroneous thoughts during the search. In this paper, we introduce RethinkMCTS, which employs the Monte Carlo Tree Search (MCTS) algorithm to conduct thought-level searches before generating code, thereby exploring a wider range of strategies. More importantly, we construct verbal feedback from fine-grained code execution feedback to refine erroneous thoughts during the search. This ensures that the search progresses along the correct reasoning paths, thus improving the overall search quality of the tree by leveraging execution feedback. Through extensive experiments, we demonstrate that RethinkMCTS outperforms previous search-based and feedback-based code generation baselines. On the HumanEval dataset, it improves the pass@1 of GPT-3.5-turbo from 70.12 to 89.02 and GPT-4o-mini from 87.20 to 94.51. It effectively conducts more thorough exploration through thought-level searches and enhances the search quality of the entire tree by incorporating rethink operation.

Enterprise search systems often struggle to retrieve accurate, domain-specific information due to semantic mismatches and overlapping terminologies. These issues can degrade the performance of downstream applications such as knowledge management, customer support, and retrieval-augmented generation agents. To address this challenge, we propose a scalable hard-negative mining framework tailored specifically for domain-specific enterprise data. Our approach dynamically selects semantically challenging but contextually irrelevant documents to enhance deployed re-ranking models. Our method integrates diverse embedding models, performs dimensionality reduction, and uniquely selects hard negatives, ensuring computational efficiency and semantic precision. Evaluation on our proprietary enterprise corpus (cloud services domain) demonstrates substantial improvements of 15\% in MRR@3 and 19\% in MRR@10 compared to state-of-the-art baselines and other negative sampling techniques. Further validation on public domain-specific datasets (FiQA, Climate Fever, TechQA) confirms our method's generalizability and readiness for real-world applications.

Counterfactual statements describe events that did not or cannot take place. We consider the problem of counterfactual detection (CFD) in product reviews. For this purpose, we annotate a multilingual CFD dataset from Amazon product reviews covering counterfactual statements written in English, German, and Japanese languages. The dataset is unique as it contains counterfactuals in multiple languages, covers a new application area of e-commerce reviews, and provides high quality professional annotations. We train CFD models using different text representation methods and classifiers. We find that these models are robust against the selectional biases introduced due to cue phrase-based sentence selection. Moreover, our CFD dataset is compatible with prior datasets and can be merged to learn accurate CFD models. Applying machine translation on English counterfactual examples to create multilingual data performs poorly, demonstrating the language-specificity of this problem, which has been ignored so far.

While fine-tuned language models perform well on many tasks, they were also shown to rely on superficial surface features such as lexical overlap. Excessive utilization of such heuristics can lead to failure on challenging inputs. We analyze the use of lexical overlap heuristics in natural language inference, paraphrase detection, and reading comprehension (using a novel contrastive dataset), and find that larger models are much less susceptible to adopting lexical overlap heuristics. We also find that longer training leads models to abandon lexical overlap heuristics. Finally, we provide evidence that the disparity between models size has its source in the pre-trained model

We study the problem of retrieval with instructions, where users of a retrieval system explicitly describe their intent along with their queries. We aim to develop a general-purpose task-aware retrieval system using multi-task instruction tuning, which can follow human-written instructions to find the best documents for a given query. We introduce the first large-scale collection of approximately 40 retrieval datasets with instructions, BERRI, and present TART, a multi-task retrieval system trained on BERRI with instructions. TART shows strong capabilities to adapt to a new retrieval task via instructions and advances the state of the art on two zero-shot retrieval benchmarks, BEIR and LOTTE, outperforming models up to three times larger. We further introduce a new evaluation setup, X^2-Retrieval to better reflect real-world scenarios, where diverse domains and tasks are pooled and a system needs to find documents aligning users' intents. In this setup, TART significantly outperforms competitive baselines, further demonstrating the effectiveness of guiding retrieval with instructions.

Today, users ask Large language models (LLMs) as assistants to answer queries that require external knowledge; they ask about the weather in a specific city, about stock prices, and even about where specific locations are within their neighborhood. These queries require the LLM to produce code that invokes external APIs to answer the user's question, yet LLMs rarely produce correct code on the first try, requiring iterative code refinement upon execution results. In addition, using LLM assistants to support high query volumes can be expensive. In this work, we contribute a framework, EcoAssistant, that enables LLMs to answer code-driven queries more affordably and accurately. EcoAssistant contains three components. First, it allows the LLM assistants to converse with an automatic code executor to iteratively refine code or to produce answers based on the execution results. Second, we use a hierarchy of LLM assistants, which attempts to answer the query with weaker, cheaper LLMs before backing off to stronger, expensive ones. Third, we retrieve solutions from past successful queries as in-context demonstrations to help subsequent queries. Empirically, we show that EcoAssistant offers distinct advantages for affordability and accuracy, surpassing GPT-4 by 10 points of success rate with less than 50% of GPT-4's cost.

Large language models (LLMs) have revolutionized numerous domains with their impressive performance but still face their challenges. A predominant issue is the propensity for these models to generate non-existent facts, a concern termed hallucination. Our research is motivated by the observation that previous instruction tuning methods force the model to complete a sentence no matter whether the model knows the knowledge or not. When the question is out of the parametric knowledge, it will try to make up something and fail to indicate when it lacks knowledge. In this paper, we present a new approach called Refusal-Aware Instruction Tuning (R-Tuning). This approach is formalized by first identifying the knowledge gap between parametric knowledge and the instruction tuning data. Then, we construct the refusal-aware data based on the knowledge intersection, to tune LLMs to refrain from responding to questions beyond its parametric knowledge. Experimental results demonstrate this new instruction tuning approach effectively improves a model's ability to answer known questions and refrain from answering unknown questions. Furthermore, when tested on out-of-domain datasets, the refusal ability was found to be a meta-skill that could be generalized to other tasks. Further analysis surprisingly finds that learning the uncertainty during training displays a better ability to estimate uncertainty than uncertainty-based testing. Our code will be released at https://github.com/shizhediao/R-Tuning.

Understanding and manipulating the causal generation mechanisms in language models is essential for controlling their behavior. Previous work has primarily relied on techniques such as representation surgery -- e.g., model ablations or manipulation of linear subspaces tied to specific concepts -- to intervene on these models. To understand the impact of interventions precisely, it is useful to examine counterfactuals -- e.g., how a given sentence would have appeared had it been generated by the model following a specific intervention. We highlight that counterfactual reasoning is conceptually distinct from interventions, as articulated in Pearl's causal hierarchy. Based on this observation, we propose a framework for generating true string counterfactuals by reformulating language models as Generalized Structural-equation. Models using the Gumbel-max trick. This allows us to model the joint distribution over original strings and their counterfactuals resulting from the same instantiation of the sampling noise. We develop an algorithm based on hindsight Gumbel sampling that allows us to infer the latent noise variables and generate counterfactuals of observed strings. Our experiments demonstrate that the approach produces meaningful counterfactuals while at the same time showing that commonly used intervention techniques have considerable undesired side effects.

Solving mathematical problems requires advanced reasoning abilities and presents notable challenges for large language models. Previous works usually synthesize data from proprietary models to augment existing datasets, followed by instruction tuning to achieve top-tier results. However, our analysis of these datasets reveals severe biases towards easy queries, with frequent failures to generate any correct response for the most challenging queries. Hypothesizing that difficult queries are crucial to learn complex reasoning, we propose Difficulty-Aware Rejection Tuning (DART), a method that allocates difficult queries more trials during the synthesis phase, enabling more extensive training on difficult samples. Utilizing DART, we have created new datasets for mathematical problem-solving that focus more on difficult queries and are substantially smaller than previous ones. Remarkably, our synthesis process solely relies on a 7B-sized open-weight model, without reliance on the commonly used proprietary GPT-4. We fine-tune various base models on our datasets ranging from 7B to 70B in size, resulting in a series of strong models called DART-MATH. In comprehensive in-domain and out-of-domain evaluation on 6 mathematical benchmarks, DART-MATH outperforms vanilla rejection tuning significantly, being superior or comparable to previous arts, despite using much smaller datasets and no proprietary models. Furthermore, our results position our synthetic datasets as the most effective and cost-efficient publicly available resources for advancing mathematical problem-solving.

We introduce DeepSeek-Prover-V2, an open-source large language model designed for formal theorem proving in Lean 4, with initialization data collected through a recursive theorem proving pipeline powered by DeepSeek-V3. The cold-start training procedure begins by prompting DeepSeek-V3 to decompose complex problems into a series of subgoals. The proofs of resolved subgoals are synthesized into a chain-of-thought process, combined with DeepSeek-V3's step-by-step reasoning, to create an initial cold start for reinforcement learning. This process enables us to integrate both informal and formal mathematical reasoning into a unified model. The resulting model, DeepSeek-Prover-V2-671B, achieves state-of-the-art performance in neural theorem proving, reaching 88.9% pass ratio on the MiniF2F-test and solving 49 out of 658 problems from PutnamBench. In addition to standard benchmarks, we introduce ProverBench, a collection of 325 formalized problems, to enrich our evaluation, including 15 selected problems from the recent AIME competitions (years 24-25). Further evaluation on these 15 AIME problems shows that the model successfully solves 6 of them. In comparison, DeepSeek-V3 solves 8 of these problems using majority voting, highlighting that the gap between formal and informal mathematical reasoning in large language models is substantially narrowing.

Recent progress in large language models (LLMs) highlights the power of scaling test-time compute to achieve strong performance on complex tasks, such as mathematical reasoning and code generation. This raises a critical question: how should model training be modified to optimize performance under a subsequent test-time compute strategy and budget? To explore this, we focus on pass@N, a simple test-time strategy that searches for a correct answer in N independent samples. We show, surprisingly, that training with cross-entropy (CE) loss can be {it misaligned} with pass@N in that pass@N accuracy {it decreases} with longer training. We explain the origins of this misalignment in terms of model overconfidence induced by CE, and experimentally verify our prediction of overconfidence as an impediment to scaling test-time compute via pass@N. Furthermore we suggest a principled, modified training loss that is better aligned to pass@N by limiting model confidence and rescuing pass@N test performance. Our algorithm demonstrates improved mathematical reasoning on MATH and MiniF2F benchmarks under several scenarios: (1) providing answers to math questions; and (2) proving theorems by searching over proof trees of varying shapes. Overall our work underscores the importance of co-designing two traditionally separate phases of LLM development: training-time protocols and test-time search and reasoning strategies.

Large language models (LLMs) have shown promising abilities of in-context learning (ICL), adapting swiftly to new tasks with only few-shot demonstrations. However, current few-shot methods heavily depend on high-quality, query-specific demos, which are often lacking. When faced with out-of-demonstration (OOD) queries, methods that rely on hand-crafted demos or external retrievers might fail. To bridge the gap between limited demos and OOD queries, we propose Self-Demos, a novel prompting method that elicits the inherent generalizability in LLMs by query-aware demo generation. The generated demos strategically interpolate between existing demos and the given query, transforming the query from OOD to ID. To evaluate the effectiveness of our approach, we manually constructed OOD-Toolset, a dataset in the tool-using scenario with over 300 real-world APIs and 1000 instances, each consisting of three tool-use cases as demos and an OOD query. Thorough experiments on our dataset and two public math benchmarks have shown that our method can outperform state-of-the-art baselines in the OOD setting. Moreover, we conduct a range of analyses to validate Self-Demos's generalization and provide more insights.

Widespread LLM adoption has introduced characteristic repetitive phraseology, termed "slop," which degrades output quality and makes AI-generated text immediately recognizable. We present Antislop, a comprehensive framework providing tools to both detect and eliminate these overused patterns. Our approach combines three innovations: (1) The Antislop Sampler, which uses backtracking to suppress unwanted strings at inference time without destroying vocabulary; (2) An automated pipeline that profiles model-specific slop against human baselines and generates training data; (3) Final Token Preference Optimization (FTPO), a novel fine-tuning method that operates on individual tokens, surgically adjusting logits wherever a banned pattern has appeared in an inference trace. We demonstrate that some slop patterns appear over 1,000x more frequently in LLM output than human text. The Antislop Sampler successfully suppresses 8,000+ patterns while maintaining quality, whereas token banning becomes unusable at just 2,000. Most importantly, FTPO achieves 90% slop reduction while maintaining or improving performance in cross-domain evals including GSM8K, MMLU, and creative writing tasks. In contrast, DPO suffers significant degradation in writing quality and lexical diversity despite achieving weaker suppression. We release all code and results under MIT license: https://github.com/sam-paech/auto-antislop.

Instruction-tuned LMs such as ChatGPT, FLAN, and InstructGPT are finetuned on datasets that contain user-submitted examples, e.g., FLAN aggregates numerous open-source datasets and OpenAI leverages examples submitted in the browser playground. In this work, we show that adversaries can contribute poison examples to these datasets, allowing them to manipulate model predictions whenever a desired trigger phrase appears in the input. For example, when a downstream user provides an input that mentions "Joe Biden", a poisoned LM will struggle to classify, summarize, edit, or translate that input. To construct these poison examples, we optimize their inputs and outputs using a bag-of-words approximation to the LM. We evaluate our method on open-source instruction-tuned LMs. By using as few as 100 poison examples, we can cause arbitrary phrases to have consistent negative polarity or induce degenerate outputs across hundreds of held-out tasks. Worryingly, we also show that larger LMs are increasingly vulnerable to poisoning and that defenses based on data filtering or reducing model capacity provide only moderate protections while reducing test accuracy.

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.

We present Adjacent Possible Exploration (APE), a simple yet effective method for adapting large language models to specific tasks using minimal computational resources. Unlike traditional fine-tuning that requires extensive compute, APE iteratively fine-tunes models on small, carefully selected data batches (200 examples), retaining only improvements. On news summarization, APE achieves 40 percent BLEU improvement using just a T4 GPU in 60 minutes, matching or exceeding more complex methods like LoRA while remaining conceptually simple. Our approach is particularly valuable for researchers and practitioners with limited computational resources. We provide open-source code and demonstrate APE's effectiveness through both automatic metrics and human evaluation. While inspired by evolutionary theory's "adjacent possible", APE's core insight has a very practical application: small, iterative data perturbations can efficiently guide LLMs toward task-specific performance without expensive retraining.

We propose ImitSAT, a branching policy for conflict-driven clause learning (CDCL) solvers based on imitation learning for the Boolean satisfiability problem (SAT). Unlike previous methods that predict instance-level signals to improve CDCL branching indirectly, or rely on reinforcement learning and insufficient CDCL information to enhance branching, ImitSAT learns from expert KeyTrace that collapses a full run into the sequence of surviving decisions. Replaying a KeyTrace on the same instance is nearly conflict-free, providing dense decision-level supervision and directly reducing propagations -- the dominant contributor to wall-clock time. This prefix-conditioned supervision enables ImitSAT to reproduce high-quality branches without exploration, yielding faster convergence, stable training, and seamless integration into CDCL. Extensive experiments demonstrate that ImitSAT reduces propagation counts and runtime, outperforming state-of-the-art learned approaches. We released the source code and trained model at https://github.com/zewei-Zhang/ImitSAT

Taking inspiration from Set Theory, we introduce SetCSE, an innovative information retrieval framework. SetCSE employs sets to represent complex semantics and incorporates well-defined operations for structured information querying under the provided context. Within this framework, we introduce an inter-set contrastive learning objective to enhance comprehension of sentence embedding models concerning the given semantics. Furthermore, we present a suite of operations, including SetCSE intersection, difference, and operation series, that leverage sentence embeddings of the enhanced model for complex sentence retrieval tasks. Throughout this paper, we demonstrate that SetCSE adheres to the conventions of human language expressions regarding compounded semantics, provides a significant enhancement in the discriminatory capability of underlying sentence embedding models, and enables numerous information retrieval tasks involving convoluted and intricate prompts which cannot be achieved using existing querying methods.

Many program synthesis tasks prove too challenging for even state-of-the-art language models to solve in single attempts. Search-based evolutionary methods offer a promising alternative by exploring solution spaces iteratively, but their effectiveness remain limited by the fixed capabilities of the underlying generative model. We propose SOAR, a method that learns program synthesis by integrating language models into a self-improving evolutionary loop. SOAR alternates between (1) an evolutionary search that uses an LLM to sample and refine candidate solutions, and (2) a hindsight learning phase that converts search attempts into valid problem-solution pairs used to fine-tune the LLM's sampling and refinement capabilities\, -- \,enabling increasingly effective search in subsequent iterations. On the challenging ARC-AGI benchmark, SOAR achieves significant performance gains across model scales and iterations, leveraging positive transfer between the sampling and refinement finetuning tasks. These improvements carry over to test-time adaptation, enabling SOAR to solve 52\% of the public test set. Our code is open-sourced at: https://github.com/flowersteam/SOAR

Legal Passage Retrieval (LPR) systems are crucial as they help practitioners save time when drafting legal arguments. However, it remains an underexplored avenue. One primary reason is the significant vocabulary mismatch between the query and the target passage. To address this, we propose a simple yet effective method, the Generative query REwriter (GuRE). We leverage the generative capabilities of Large Language Models (LLMs) by training the LLM for query rewriting. "Rewritten queries" help retrievers to retrieve target passages by mitigating vocabulary mismatch. Experimental results show that GuRE significantly improves performance in a retriever-agnostic manner, outperforming all baseline methods. Further analysis reveals that different training objectives lead to distinct retrieval behaviors, making GuRE more suitable than direct retriever fine-tuning for real-world applications. Codes are avaiable at github.com/daehuikim/GuRE.

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,

In the realm of Large Language Models, the balance between instruction data quality and quantity has become a focal point. Recognizing this, we introduce a self-guided methodology for LLMs to autonomously discern and select cherry samples from vast open-source datasets, effectively minimizing manual curation and potential cost for instruction tuning an LLM. Our key innovation, the Instruction-Following Difficulty (IFD) metric, emerges as a pivotal tool to identify discrepancies between a model's expected responses and its autonomous generation prowess. Through the adept application of IFD, cherry samples are pinpointed, leading to a marked uptick in model training efficiency. Empirical validations on renowned datasets like Alpaca and WizardLM underpin our findings; with a mere 10% of conventional data input, our strategy showcases improved results. This synthesis of self-guided cherry-picking and the IFD metric signifies a transformative leap in the optimization of LLMs, promising both efficiency and resource-conscious advancements. Codes, data, and models are available: https://github.com/MingLiiii/Cherry_LLM

Agentic search, as a more autonomous and adaptive paradigm of retrieval augmentation, is driving the evolution of intelligent search systems. However, existing evaluation frameworks fail to align well with the goals of agentic search. First, the complex queries commonly used in current benchmarks often deviate from realistic user search scenarios. Second, prior approaches tend to introduce noise when extracting ground truth for end-to-end evaluations, leading to distorted assessments at a fine-grained level. Third, most current frameworks focus solely on the quality of final answers, neglecting the evaluation of the iterative process inherent to agentic search. To address these limitations, we propose RAVine -- a Reality-Aligned eValuation framework for agentic LLMs with search. RAVine targets multi-point queries and long-form answers that better reflect user intents, and introduces an attributable ground truth construction strategy to enhance the accuracy of fine-grained evaluation. Moreover, RAVine examines model's interaction with search tools throughout the iterative process, and accounts for factors of efficiency. We benchmark a series of models using RAVine and derive several insights, which we hope will contribute to advancing the development of agentic search systems. The code and datasets are available at https://github.com/SwordFaith/RAVine.

Retrieval-augmented generation (RAG) systems have advanced large language models (LLMs) in complex deep search scenarios requiring multi-step reasoning and iterative information retrieval. However, existing approaches face critical limitations that lack high-quality training trajectories or suffer from the distributional mismatches in simulated environments and prohibitive computational costs for real-world deployment. This paper introduces SimpleDeepSearcher, a lightweight yet effective framework that bridges this gap through strategic data engineering rather than complex training paradigms. Our approach synthesizes high-quality training data by simulating realistic user interactions in live web search environments, coupled with a multi-criteria curation strategy that optimizes the diversity and quality of input and output side. Experiments on five benchmarks across diverse domains demonstrate that SFT on only 871 curated samples yields significant improvements over RL-based baselines. Our work establishes SFT as a viable pathway by systematically addressing the data-scarce bottleneck, offering practical insights for efficient deep search systems. Our code is available at https://github.com/RUCAIBox/SimpleDeepSearcher.

Improving the quality of search results can significantly enhance users experience and engagement with search engines. In spite of several recent advancements in the fields of machine learning and data mining, correctly classifying items for a particular user search query has been a long-standing challenge, which still has a large room for improvement. This paper introduces the "Shopping Queries Dataset", a large dataset of difficult Amazon search queries and results, publicly released with the aim of fostering research in improving the quality of search results. The dataset contains around 130 thousand unique queries and 2.6 million manually labeled (query,product) relevance judgements. The dataset is multilingual with queries in English, Japanese, and Spanish. The Shopping Queries Dataset is being used in one of the KDDCup'22 challenges. In this paper, we describe the dataset and present three evaluation tasks along with baseline results: (i) ranking the results list, (ii) classifying product results into relevance categories, and (iii) identifying substitute products for a given query. We anticipate that this data will become the gold standard for future research in the topic of product search.

A machine learning system can score well on a given test set by relying on heuristics that are effective for frequent example types but break down in more challenging cases. We study this issue within natural language inference (NLI), the task of determining whether one sentence entails another. We hypothesize that statistical NLI models may adopt three fallible syntactic heuristics: the lexical overlap heuristic, the subsequence heuristic, and the constituent heuristic. To determine whether models have adopted these heuristics, we introduce a controlled evaluation set called HANS (Heuristic Analysis for NLI Systems), which contains many examples where the heuristics fail. We find that models trained on MNLI, including BERT, a state-of-the-art model, perform very poorly on HANS, suggesting that they have indeed adopted these heuristics. We conclude that there is substantial room for improvement in NLI systems, and that the HANS dataset can motivate and measure progress in this area

Text embedding models have been popular for information retrieval applications such as semantic search and Question-Answering systems based on Retrieval-Augmented Generation (RAG). Those models are typically Transformer models that are fine-tuned with contrastive learning objectives. Many papers introduced new embedding model architectures and training approaches, however, one of the key ingredients, the process of mining negative passages, remains poorly explored or described. One of the challenging aspects of fine-tuning embedding models is the selection of high quality hard-negative passages for contrastive learning. In this paper we propose a family of positive-aware mining methods that leverage the positive relevance score for more effective false negatives removal. We also provide a comprehensive ablation study on hard-negative mining methods over their configurations, exploring different teacher and base models. We demonstrate the efficacy of our proposed methods by introducing the NV-Retriever-v1 model, which scores 60.9 on MTEB Retrieval (BEIR) benchmark and 0.65 points higher than previous methods. The model placed 1st when it was published to MTEB Retrieval on July 07, 2024.

Instance-specific algorithm configuration and algorithm portfolios have been shown to offer significant improvements over single algorithm approaches in a variety of application domains. In the SAT and CSP domains algorithm portfolios have consistently dominated the main competitions in these fields for the past five years. For a portfolio approach to be effective there are two crucial conditions that must be met. First, there needs to be a collection of complementary solvers with which to make a portfolio. Second, there must be a collection of problem features that can accurately identify structural differences between instances. This paper focuses on the latter issue: feature representation, because, unlike SAT, not every problem has well-studied features. We employ the well-known SATzilla feature set, but compute alternative sets on different SAT encodings of CSPs. We show that regardless of what encoding is used to convert the instances, adequate structural information is maintained to differentiate between problem instances, and that this can be exploited to make an effective portfolio-based CSP solver.

LLM test-time compute (or LLM inference) via search has emerged as a promising research area with rapid developments. However, current frameworks often adopt distinct perspectives on three key aspects (task definition, LLM profiling, and search procedures), making direct comparisons challenging. Moreover, the search algorithms employed often diverge from standard implementations, and their specific characteristics are not thoroughly specified. In this survey, we provide a comprehensive technical review that unifies task definitions and provides modular definitions of LLM profiling and search procedures. The definitions enable precise comparisons of various LLM inference frameworks while highlighting their departures from conventional search algorithms. We also discuss the applicability, performance, and efficiency of these methods. For further details and ongoing updates, please refer to our GitHub repository: https://github.com/xinzhel/LLM-Agent-Survey/blob/main/search.md

Search agents powered by Large Language Models (LLMs) have demonstrated significant potential in tackling knowledge-intensive tasks. Reinforcement learning (RL) has emerged as a powerful paradigm for training these agents to perform complex, multi-step reasoning. However, prior RL-based methods often rely on sparse or rule-based rewards, which can lead agents to commit to suboptimal or erroneous reasoning paths without the ability to recover. To address these limitations, we propose ReSeek, a novel self-correcting framework for training search agents. Our framework introduces a self-correction mechanism that empowers the agent to dynamically identify and recover from erroneous search paths during an episode. By invoking a special JUDGE action, the agent can judge the information and re-plan its search strategy. To guide this process, we design a dense, instructive process reward function, which decomposes into a correctness reward for retrieving factual information and a utility reward for finding information genuinely useful for the query. Furthermore, to mitigate the risk of data contamination in existing datasets, we introduce FictionalHot, a new and challenging benchmark with recently curated questions requiring complex reasoning. Being intuitively reasonable and practically simple, extensive experiments show that agents trained with ReSeek significantly outperform SOTA baselines in task success rate and path faithfulness.

Recent advancements in language models have led to significant improvements in mathematical reasoning across various benchmarks. However, most of these benchmarks rely on automatic evaluation methods that only compare final answers using heuristics, without verifying the underlying reasoning steps. This limitation results in false positive solutions, where models may produce correct final answers but with flawed deduction paths. In this paper, we systematically examine the prevalence of false positive solutions in mathematical problem solving for language models. We analyze the characteristics and extent of this issue across different open-source models, datasets of varying difficulty levels, and decoding strategies. Specifically, we explore how false positives influence the inference time scaling behavior of language models. Our experimental results reveal that: (1) false positive solutions persist across different models, datasets, and decoding methods, (2) sampling-based inference time scaling methods do not alleviate the problem, and (3) the pass@N evaluation metric is more susceptible to false positives, suggesting a significantly lower scaling ceiling than what automatic evaluations indicate. Additionally, we analyze specific instances of false positives and discuss potential limitations in self-improvement techniques and synthetic data generation under such conditions. Our data and code are publicly available at https://github.com/Wloner0809/False-Positives-in-Math.

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.

The dominant approach to generating from language models subject to some constraint is locally constrained decoding (LCD), incrementally sampling tokens at each time step such that the constraint is never violated. Typically, this is achieved through token masking: looping over the vocabulary and excluding non-conforming tokens. There are two important problems with this approach. (i) Evaluating the constraint on every token can be prohibitively expensive -- LM vocabularies often exceed 100,000 tokens. (ii) LCD can distort the global distribution over strings, sampling tokens based only on local information, even if they lead down dead-end paths. This work introduces a new algorithm that addresses both these problems. First, to avoid evaluating a constraint on the full vocabulary at each step of generation, we propose an adaptive rejection sampling algorithm that typically requires orders of magnitude fewer constraint evaluations. Second, we show how this algorithm can be extended to produce low-variance, unbiased estimates of importance weights at a very small additional cost -- estimates that can be soundly used within previously proposed sequential Monte Carlo algorithms to correct for the myopic behavior of local constraint enforcement. Through extensive empirical evaluation in text-to-SQL, molecular synthesis, goal inference, pattern matching, and JSON domains, we show that our approach is superior to state-of-the-art baselines, supporting a broader class of constraints and improving both runtime and performance. Additional theoretical and empirical analyses show that our method's runtime efficiency is driven by its dynamic use of computation, scaling with the divergence between the unconstrained and constrained LM, and as a consequence, runtime improvements are greater for better models.

Retrieval-augmented language models are being increasingly tasked with subjective, contentious, and conflicting queries such as "is aspartame linked to cancer". To resolve these ambiguous queries, one must search through a large range of websites and consider "which, if any, of this evidence do I find convincing?". In this work, we study how LLMs answer this question. In particular, we construct ConflictingQA, a dataset that pairs controversial queries with a series of real-world evidence documents that contain different facts (e.g., quantitative results), argument styles (e.g., appeals to authority), and answers (Yes or No). We use this dataset to perform sensitivity and counterfactual analyses to explore which text features most affect LLM predictions. Overall, we find that current models rely heavily on the relevance of a website to the query, while largely ignoring stylistic features that humans find important such as whether a text contains scientific references or is written with a neutral tone. Taken together, these results highlight the importance of RAG corpus quality (e.g., the need to filter misinformation), and possibly even a shift in how LLMs are trained to better align with human judgements.

In today's software world with its cornucopia of reusable software libraries, when a programmer is faced with a programming task that they suspect can be completed through the use of a library, they often look for code examples using a search engine and then manually adapt found examples to their specific context of use. We put forward a vision based on a new breed of developer tools that have the potential to largely automate this process. The key idea is to adapt code autocompletion tools such that they take into account not only the developer's already-written code but also the intent of the task the developer is trying to achieve next, formulated in plain natural language. We call this practice of enriching the code with natural language intent to facilitate its completion natural language-guided programming. To show that this idea is feasible we design, implement and benchmark a tool that solves this problem in the context of a specific domain (data science) and a specific programming language (Python). Central to the tool is the use of language models trained on a large corpus of documented code. Our initial experiments confirm the feasibility of the idea but also make it clear that we have only scratched the surface of what may become possible in the future. We end the paper with a comprehensive research agenda to stimulate additional research in the budding area of natural language-guided programming.

Existing Large Reasoning Models (LRMs) have shown the potential of reinforcement learning (RL) to enhance the complex reasoning capabilities of Large Language Models~(LLMs). While they achieve remarkable performance on challenging tasks such as mathematics and coding, they often rely on their internal knowledge to solve problems, which can be inadequate for time-sensitive or knowledge-intensive questions, leading to inaccuracies and hallucinations. To address this, we propose R1-Searcher, a novel two-stage outcome-based RL approach designed to enhance the search capabilities of LLMs. This method allows LLMs to autonomously invoke external search systems to access additional knowledge during the reasoning process. Our framework relies exclusively on RL, without requiring process rewards or distillation for a cold start. % effectively generalizing to out-of-domain datasets and supporting both Base and Instruct models. Our experiments demonstrate that our method significantly outperforms previous strong RAG methods, even when compared to the closed-source GPT-4o-mini.

Retrieval-augmented in-context learning has emerged as a powerful approach for addressing knowledge-intensive tasks using frozen language models (LM) and retrieval models (RM). Existing work has combined these in simple "retrieve-then-read" pipelines in which the RM retrieves passages that are inserted into the LM prompt. To begin to fully realize the potential of frozen LMs and RMs, we propose Demonstrate-Search-Predict (DSP), a framework that relies on passing natural language texts in sophisticated pipelines between an LM and an RM. DSP can express high-level programs that bootstrap pipeline-aware demonstrations, search for relevant passages, and generate grounded predictions, systematically breaking down problems into small transformations that the LM and RM can handle more reliably. We have written novel DSP programs for answering questions in open-domain, multi-hop, and conversational settings, establishing in early evaluations new state-of-the-art in-context learning results and delivering 37-120%, 8-39%, and 80-290% relative gains against the vanilla LM (GPT-3.5), a standard retrieve-then-read pipeline, and a contemporaneous self-ask pipeline, respectively. We release DSP at https://github.com/stanfordnlp/dsp

The advent of large language models (LLMs) has transformed information access and reasoning through open-ended natural language interaction. However, LLMs remain limited by static knowledge, factual hallucinations, and the inability to retrieve real-time or domain-specific information. Retrieval-Augmented Generation (RAG) mitigates these issues by grounding model outputs in external evidence, but traditional RAG pipelines are often single turn and heuristic, lacking adaptive control over retrieval and reasoning. Recent advances in agentic search address these limitations by enabling LLMs to plan, retrieve, and reflect through multi-step interaction with search environments. Within this paradigm, reinforcement learning (RL) offers a powerful mechanism for adaptive and self-improving search behavior. This survey provides the first comprehensive overview of RL-based agentic search, organizing the emerging field along three complementary dimensions: (i) What RL is for (functional roles), (ii) How RL is used (optimization strategies), and (iii) Where RL is applied (scope of optimization). We summarize representative methods, evaluation protocols, and applications, and discuss open challenges and future directions toward building reliable and scalable RL driven agentic search systems. We hope this survey will inspire future research on the integration of RL and agentic search. Our repository is available at https://github.com/ventr1c/Awesome-RL-based-Agentic-Search-Papers.

In this paper, we propose a simple and efficient method for value model training on long-context reasoning traces. Compared to existing process reward models (PRMs), our method does not require a fine-grained notion of "step," which is difficult to define for long-context reasoning models. By collecting a dataset of 2.5 million reasoning traces, we train a 1.5B token-level value model and apply it to DeepSeek models for improved performance with test-time compute scaling. We find that block-wise value-guided search (VGS) with a final weighted majority vote achieves better test-time scaling than standard methods such as majority voting or best-of-n. With an inference budget of 64 generations, VGS with DeepSeek-R1-Distill-1.5B achieves an average accuracy of 45.7% across four competition math benchmarks (AIME 2024 & 2025, HMMT Feb 2024 & 2025), reaching parity with o3-mini-medium. Moreover, VGS significantly reduces the inference FLOPs required to achieve the same performance of majority voting. Our dataset, model and codebase are open-sourced.

While dense retrieval has been shown effective and efficient across tasks and languages, it remains difficult to create effective fully zero-shot dense retrieval systems when no relevance label is available. In this paper, we recognize the difficulty of zero-shot learning and encoding relevance. Instead, we propose to pivot through Hypothetical Document Embeddings~(HyDE). Given a query, HyDE first zero-shot instructs an instruction-following language model (e.g. InstructGPT) to generate a hypothetical document. The document captures relevance patterns but is unreal and may contain false details. Then, an unsupervised contrastively learned encoder~(e.g. Contriever) encodes the document into an embedding vector. This vector identifies a neighborhood in the corpus embedding space, where similar real documents are retrieved based on vector similarity. This second step ground the generated document to the actual corpus, with the encoder's dense bottleneck filtering out the incorrect details. Our experiments show that HyDE significantly outperforms the state-of-the-art unsupervised dense retriever Contriever and shows strong performance comparable to fine-tuned retrievers, across various tasks (e.g. web search, QA, fact verification) and languages~(e.g. sw, ko, ja).

Information seeking users often pose questions with false presuppositions, especially when asking about unfamiliar topics. Most existing question answering (QA) datasets, in contrast, assume all questions have well defined answers. We introduce CREPE, a QA dataset containing a natural distribution of presupposition failures from online information-seeking forums. We find that 25% of questions contain false presuppositions, and provide annotations for these presuppositions and their corrections. Through extensive baseline experiments, we show that adaptations of existing open-domain QA models can find presuppositions moderately well, but struggle when predicting whether a presupposition is factually correct. This is in large part due to difficulty in retrieving relevant evidence passages from a large text corpus. CREPE provides a benchmark to study question answering in the wild, and our analyses provide avenues for future work in better modeling and further studying the task.

Dense retrieval systems have been widely used in various NLP applications. However, their vulnerabilities to potential attacks have been underexplored. This paper investigates a novel attack scenario where the attackers aim to mislead the retrieval system into retrieving the attacker-specified contents. Those contents, injected into the retrieval corpus by attackers, can include harmful text like hate speech or spam. Unlike prior methods that rely on model weights and generate conspicuous, unnatural outputs, we propose a covert backdoor attack triggered by grammar errors. Our approach ensures that the attacked models can function normally for standard queries while covertly triggering the retrieval of the attacker's contents in response to minor linguistic mistakes. Specifically, dense retrievers are trained with contrastive loss and hard negative sampling. Surprisingly, our findings demonstrate that contrastive loss is notably sensitive to grammatical errors, and hard negative sampling can exacerbate susceptibility to backdoor attacks. Our proposed method achieves a high attack success rate with a minimal corpus poisoning rate of only 0.048\%, while preserving normal retrieval performance. This indicates that the method has negligible impact on user experience for error-free queries. Furthermore, evaluations across three real-world defense strategies reveal that the malicious passages embedded within the corpus remain highly resistant to detection and filtering, underscoring the robustness and subtlety of the proposed attack Codes of this work are available at https://github.com/ruyue0001/Backdoor_DPR..

Data quality and diversity are key to the construction of effective instruction-tuning datasets. % With the increasing availability of open-source instruction-tuning datasets, it is advantageous to automatically select high-quality and diverse subsets from a vast amount of data. % Existing methods typically prioritize instance quality and use heuristic rules to maintain diversity. % However, this absence of a comprehensive view of the entire collection often leads to suboptimal results. % Moreover, heuristic rules generally focus on distance or clustering within the embedding space, which fails to accurately capture the intent of complex instructions in the semantic space. % To bridge this gap, we propose a unified method for quantifying the information content of datasets. This method models the semantic space by constructing a label graph and quantifies diversity based on the distribution of information within the graph. % Based on such a measurement, we further introduce an efficient sampling method that selects data samples iteratively to Maximize the Information Gain (MIG) in semantic space. % Experiments on various datasets and base models demonstrate that MIG consistently outperforms state-of-the-art methods. % Notably, the model fine-tuned with 5\% Tulu3 data sampled by MIG achieves comparable performance to the official SFT model trained on the full dataset, with improvements of +5.73\% on AlpacaEval and +6.89\% on Wildbench.

While the current state-of-the-art dense retrieval models exhibit strong out-of-domain generalization, they might fail to capture nuanced domain-specific knowledge. In principle, fine-tuning these models for specialized retrieval tasks should yield higher effectiveness than relying on a one-size-fits-all model, but in practice, results can disappoint. We show that standard fine-tuning methods using an InfoNCE loss can unexpectedly degrade effectiveness rather than improve it, even for domain-specific scenarios. This holds true even when applying widely adopted techniques such as hard-negative mining and negative de-noising. To address this, we explore a training strategy that uses listwise distillation from a teacher cross-encoder, leveraging rich relevance signals to fine-tune the retriever. We further explore synthetic query generation using large language models. Through listwise distillation and training with a diverse set of queries ranging from natural user searches and factual claims to keyword-based queries, we achieve consistent effectiveness gains across multiple datasets. Our results also reveal that synthetic queries can rival human-written queries in training utility. However, we also identify limitations, particularly in the effectiveness of cross-encoder teachers as a bottleneck. We release our code and scripts to encourage further research.

In recent years, large pre-trained language models (LLMs) have demonstrated the ability to follow instructions and perform novel tasks from a few examples. The possibility to parameterise an LLM through such in-context examples widens their capability at a much lower cost than finetuning. We extend this line of reasoning and present a method which further expands the capabilities of an LLM by embedding it within an algorithm or program. To demonstrate the benefits of this approach, we present an illustrative example of evidence-supported question-answering. We obtain a 6.4\% improvement over the chain of thought baseline through a more algorithmic approach without any finetuning. Furthermore, we highlight recent work from this perspective and discuss the advantages and disadvantages in comparison to the standard approaches.

Large Language Models' success on text generation has also made them better at code generation and coding tasks. While a lot of work has demonstrated their remarkable performance on tasks such as code completion and editing, it is still unclear as to why. We help bridge this gap by exploring to what degree auto-regressive models understand the logical constructs of the underlying programs. We propose Counterfactual Analysis for Programming Concept Predicates (CACP) as a counterfactual testing framework to evaluate whether Large Code Models understand programming concepts. With only black-box access to the model, we use CACP to evaluate ten popular Large Code Models for four different programming concepts. Our findings suggest that current models lack understanding of concepts such as data flow and control flow.

Counterfactual reasoning is widely recognized as one of the most challenging and intricate aspects of causality in artificial intelligence. In this paper, we evaluate the performance of large language models (LLMs) in counterfactual reasoning. In contrast to previous studies that primarily focus on commonsense causal reasoning, where LLMs often rely on prior knowledge for inference, we specifically assess their ability to perform counterfactual inference using a set of formal rules. To support this evaluation, we introduce a new benchmark dataset, CounterBench, comprising 1K counterfactual reasoning questions. The dataset is designed with varying levels of difficulty, diverse causal graph structures, distinct types of counterfactual questions, and multiple nonsensical name variants. Our experiments demonstrate that counterfactual reasoning poses a significant challenge for LLMs, with most models performing at levels comparable to random guessing. To enhance LLM's counterfactual reasoning ability, we propose a novel reasoning paradigm, CoIn, which guides LLMs through iterative reasoning and backtracking to systematically explore counterfactual solutions. Experimental results show that our method significantly improves LLM performance on counterfactual reasoning tasks and consistently enhances performance across different LLMs.Our dataset is available at https://huggingface.co/datasets/CounterBench/CounterBench.

Large Language Models (LLMs) have shown remarkable capabilities in reasoning, exemplified by the success of OpenAI-o1 and DeepSeek-R1. However, integrating reasoning with external search processes remains challenging, especially for complex multi-hop questions requiring multiple retrieval steps. We propose ReSearch, a novel framework that trains LLMs to Reason with Search via reinforcement learning without using any supervised data on reasoning steps. Our approach treats search operations as integral components of the reasoning chain, where when and how to perform searches is guided by text-based thinking, and search results subsequently influence further reasoning. We train ReSearch on Qwen2.5-7B(-Instruct) and Qwen2.5-32B(-Instruct) models and conduct extensive experiments. Despite being trained on only one dataset, our models demonstrate strong generalizability across various benchmarks. Analysis reveals that ReSearch naturally elicits advanced reasoning capabilities such as reflection and self-correction during the reinforcement learning process.

In this work, we focus on the problem of retrieving relevant arguments for a query claim covering diverse aspects. State-of-the-art methods rely on explicit mappings between claims and premises, and thus are unable to utilize large available collections of premises without laborious and costly manual annotation. Their diversity approach relies on removing duplicates via clustering which does not directly ensure that the selected premises cover all aspects. This work introduces a new multi-step approach for the argument retrieval problem. Rather than relying on ground-truth assignments, our approach employs a machine learning model to capture semantic relationships between arguments. Beyond that, it aims to cover diverse facets of the query, instead of trying to identify duplicates explicitly. Our empirical evaluation demonstrates that our approach leads to a significant improvement in the argument retrieval task even though it requires less data.

Hypothesis ranking is a crucial component of automated scientific discovery, particularly in natural sciences where wet-lab experiments are costly and throughput-limited. Existing approaches focus on pre-experiment ranking, relying solely on large language model's internal reasoning without incorporating empirical outcomes from experiments. We introduce the task of experiment-guided ranking, which aims to prioritize candidate hypotheses based on the results of previously tested ones. However, developing such strategies is challenging due to the impracticality of repeatedly conducting real experiments in natural science domains. To address this, we propose a simulator grounded in three domain-informed assumptions, modeling hypothesis performance as a function of similarity to a known ground truth hypothesis, perturbed by noise. We curate a dataset of 124 chemistry hypotheses with experimentally reported outcomes to validate the simulator. Building on this simulator, we develop a pseudo experiment-guided ranking method that clusters hypotheses by shared functional characteristics and prioritizes candidates based on insights derived from simulated experimental feedback. Experiments show that our method outperforms pre-experiment baselines and strong ablations.

We introduce SATBench, a benchmark for evaluating the logical reasoning capabilities of large language models (LLMs) through logical puzzles derived from Boolean satisfiability (SAT) problems. Unlike prior work that focuses on inference rule-based reasoning, which often involves deducing conclusions from a set of premises, our approach leverages the search-based nature of SAT problems, where the objective is to find a solution that fulfills a specified set of logical constraints. Each instance in SATBench is generated from a SAT formula, then translated into a story context and conditions using LLMs. The generation process is fully automated and allows for adjustable difficulty by varying the number of clauses. All 2100 puzzles are validated through both LLM-assisted and solver-based consistency checks, with human validation on a subset. Experimental results show that even the strongest model, o4-mini, achieves only 65.0% accuracy on hard UNSAT problems, close to the random baseline of 50%. SATBench exposes fundamental limitations in the search-based logical reasoning abilities of current LLMs and provides a scalable testbed for future research in logical reasoning.

The capability gap between open-source and closed-source large language models (LLMs) remains a challenge in text-to-SQL tasks. In this paper, we introduce a synthetic data approach that combines data produced by larger, more powerful models (strong models) with error information data generated by smaller, not well-aligned models (weak models). The method not only enhances the domain generalization of text-to-SQL models but also explores the potential of error data supervision through preference learning. Furthermore, we employ the synthetic data approach for instruction tuning on open-source LLMs, resulting SENSE, a specialized text-to-SQL model. The effectiveness of SENSE is demonstrated through state-of-the-art results on the SPIDER and BIRD benchmarks, bridging the performance gap between open-source models and methods prompted by closed-source models.

While in-context Learning (ICL) has proven to be an effective technique to improve the performance of Large Language Models (LLMs) in a variety of complex tasks, notably in translating natural language questions into Structured Query Language (NL2SQL), the question of how to select the most beneficial demonstration examples remains an open research problem. While prior works often adapted off-the-shelf encoders to retrieve examples dynamically, an inherent discrepancy exists in the representational capacities between the external retrievers and the LLMs. Further, optimizing the selection of examples is a non-trivial task, since there are no straightforward methods to assess the relative benefits of examples without performing pairwise inference. To address these shortcomings, we propose DeTriever, a novel demonstration retrieval framework that learns a weighted combination of LLM hidden states, where rich semantic information is encoded. To train the model, we propose a proxy score that estimates the relative benefits of examples based on the similarities between output queries. Experiments on two popular NL2SQL benchmarks demonstrate that our method significantly outperforms the state-of-the-art baselines on one-shot NL2SQL tasks.

The scarcity of high-quality, logically sound data is a critical bottleneck for advancing the mathematical reasoning of Large Language Models (LLMs). Our work confronts this challenge by turning decades of automated theorem proving research into a scalable data engine. Rather than relying on error-prone LLMs or complex proof-assistant syntax like Lean and Isabelle, our framework leverages E-prover's saturation capabilities on the vast TPTP axiom library to derive a massive, guaranteed-valid corpus of theorems. Our pipeline is principled and simple: saturate axioms, filter for "interesting" theorems, and generate tasks. With no LLMs in the loop, we eliminate factual errors by construction. This purely symbolic data is then transformed into three difficulty-controlled challenges: entailment verification, premise selection, and proof reconstruction. Our zero-shot experiments on frontier models reveal a clear weakness: performance collapses on tasks requiring deep, structural reasoning. Our framework provides both the diagnostic tool to measure this gap and a scalable source of symbolic training data to address it. We make the code and data publicly available. https://github.com/sileod/reasoning_core https://hf.co/datasets/reasoning-core/rc1

Large Language Models have excelled in remarkable reasoning capabilities with advanced prompting techniques, but they fall short on tasks that require exploration, strategic foresight, and sequential decision-making. Recent works propose to utilize external programs to define search logic, such that LLMs can perform passive tree search to solve more challenging reasoning tasks. Though impressive results have been achieved, there are several fundamental limitations of these approaches. First, passive tree searches are not efficient as they usually require multiple rounds of LLM API calls to solve one single problem. Moreover, passive search methods are not flexible since they need task-specific program designs. Then a natural question arises: can we maintain the tree-search capability of LLMs without the aid of external programs, and can still generate responses that clearly demonstrate the process of a tree-structure search? To this end, we propose a new concept called autonomous tree-search ability of LLM, which can automatically generate a response containing search trajectories for the correct answer. Concretely, we perform search trajectories using capable LLM API via a fixed system prompt, allowing them to perform autonomous tree-search (ATS) right out of the box. Experiments on 4 puzzle games demonstrate our method can achieve huge improvements. The ATS-BFS method outperforms the Chain of Thought approach by achieving an average accuracy improvement of 33%. Compared to Tree of Thoughts, it requires 65.6% or 47.7% less GPT-api cost to attain a comparable level of accuracy. Moreover, we have collected data using the ATS prompt method and fine-tuned LLaMA. This approach yield a greater improvement compared to the ones fine-tuned on CoT data. Specifically, it outperforms CoT-tuned LLaMAs by an average of 40.6% and 38.5% for LLaMA2-7B and LLaMA2-13B, respectively.

The ability to follow instructions is crucial for Large Language Models (LLMs) to handle various real-world applications. Existing benchmarks primarily focus on evaluating pure response quality, rather than assessing whether the response follows constraints stated in the instruction. To fill this research gap, in this paper, we propose FollowBench, a Multi-level Fine-grained Constraints Following Benchmark for LLMs. FollowBench comprehensively includes five different types (i.e., Content, Situation, Style, Format, and Example) of fine-grained constraints. To enable a precise constraint following estimation on diverse difficulties, we introduce a Multi-level mechanism that incrementally adds a single constraint to the initial instruction at each increased level. To assess whether LLMs' outputs have satisfied every individual constraint, we propose to prompt strong LLMs with constraint-evolution paths to handle challenging open-ended instructions. By evaluating ten closed-source and open-source popular LLMs on FollowBench, we highlight the weaknesses of LLMs in instruction following and point towards potential avenues for future work. The data and code are publicly available at https://github.com/YJiangcm/FollowBench.

We investigate whether in-context examples, widely used in decoder-only language models (LLMs), can improve embedding model performance in retrieval tasks. Unlike in LLMs, naively prepending in-context examples (query-document pairs) to the target query at inference time does not work out of the box. We introduce a simple approach to enable retrievers to use in-context examples. Our approach, RARe, finetunes a pre-trained model with in-context examples whose query is semantically similar to the target query. This can be applied to adapt various base architectures (i.e., decoder-only language models, retriever models) and consistently achieves performance gains of up to +2.72% nDCG across various open-domain retrieval datasets (BeIR, RAR-b). In particular, we find RARe exhibits stronger out-of-domain generalization compared to models using queries without in-context examples, similar to what is seen for in-context learning in LLMs. We further provide analysis on the design choices of in-context example augmentation and lay the foundation for future work in this space.

We introduce iterative retrieval, a novel framework that empowers retrievers to make iterative decisions through policy optimization. Finding an optimal portfolio of retrieved items is a combinatorial optimization problem, generally considered NP-hard. This approach provides a learned approximation to such a solution, meeting specific task requirements under a given family of large language models (LLMs). We propose a training procedure based on reinforcement learning, incorporating feedback from LLMs. We instantiate an iterative retriever for composing in-context learning (ICL) exemplars and apply it to various semantic parsing tasks that demand synthesized programs as outputs. By adding only 4M additional parameters for state encoding, we convert an off-the-shelf dense retriever into a stateful iterative retriever, outperforming previous methods in selecting ICL exemplars on semantic parsing datasets such as CalFlow, TreeDST, and MTOP. Additionally, the trained iterative retriever generalizes across different inference LLMs beyond the one used during training.

The remarkable success of pretrained language models has motivated the study of what kinds of knowledge these models learn during pretraining. Reformulating tasks as fill-in-the-blanks problems (e.g., cloze tests) is a natural approach for gauging such knowledge, however, its usage is limited by the manual effort and guesswork required to write suitable prompts. To address this, we develop AutoPrompt, an automated method to create prompts for a diverse set of tasks, based on a gradient-guided search. Using AutoPrompt, we show that masked language models (MLMs) have an inherent capability to perform sentiment analysis and natural language inference without additional parameters or finetuning, sometimes achieving performance on par with recent state-of-the-art supervised models. We also show that our prompts elicit more accurate factual knowledge from MLMs than the manually created prompts on the LAMA benchmark, and that MLMs can be used as relation extractors more effectively than supervised relation extraction models. These results demonstrate that automatically generated prompts are a viable parameter-free alternative to existing probing methods, and as pretrained LMs become more sophisticated and capable, potentially a replacement for finetuning.

A retrieval model should not only interpolate the training data but also extrapolate well to the queries that are different from the training data. While neural retrieval models have demonstrated impressive performance on ad-hoc search benchmarks, we still know little about how they perform in terms of interpolation and extrapolation. In this paper, we demonstrate the importance of separately evaluating the two capabilities of neural retrieval models. Firstly, we examine existing ad-hoc search benchmarks from the two perspectives. We investigate the distribution of training and test data and find a considerable overlap in query entities, query intent, and relevance labels. This finding implies that the evaluation on these test sets is biased toward interpolation and cannot accurately reflect the extrapolation capacity. Secondly, we propose a novel evaluation protocol to separately evaluate the interpolation and extrapolation performance on existing benchmark datasets. It resamples the training and test data based on query similarity and utilizes the resampled dataset for training and evaluation. Finally, we leverage the proposed evaluation protocol to comprehensively revisit a number of widely-adopted neural retrieval models. Results show models perform differently when moving from interpolation to extrapolation. For example, representation-based retrieval models perform almost as well as interaction-based retrieval models in terms of interpolation but not extrapolation. Therefore, it is necessary to separately evaluate both interpolation and extrapolation performance and the proposed resampling method serves as a simple yet effective evaluation tool for future IR studies.

Logical reading comprehension is a challenging task that entails grasping the underlying semantics of text and applying reasoning to deduce the correct answer. Prior researches have primarily focused on enhancing logical reasoning capabilities through Chain-of-Thought (CoT) or data augmentation. However, previous work constructing chain-of-thought rationales concentrates solely on analyzing correct options, neglecting the incorrect alternatives. Addtionally, earlier efforts on data augmentation by altering contexts rely on rule-based methods, which result in generated contexts that lack diversity and coherence. To address these issues, we propose a Premise-Oriented Data Augmentation (PODA) framework. This framework can generate CoT rationales including analyses for both correct and incorrect options, while constructing diverse and high-quality counterfactual contexts from incorrect candidate options. We integrate summarizing premises and identifying premises for each option into rationales. Subsequently, we employ multi-step prompts with identified premises to construct counterfactual context. To facilitate the model's capabilities to better differentiate the reasoning process associated with each option, we introduce a novel thought-path contrastive learning method that compares reasoning paths between the original and counterfactual samples. Experimental results on three representative LLMs demonstrate that our method can improve the baselines substantially across two challenging logical reasoning benchmarks (ReClor and LogiQA 2.0). The data and code are released at https://github.com/lalalamdbf/TPReasoner.

In this work we address the problem of argument search. The purpose of argument search is the distillation of pro and contra arguments for requested topics from large text corpora. In previous works, the usual approach is to use a standard search engine to extract text parts which are relevant to the given topic and subsequently use an argument recognition algorithm to select arguments from them. The main challenge in the argument recognition task, which is also known as argument mining, is that often sentences containing arguments are structurally similar to purely informative sentences without any stance about the topic. In fact, they only differ semantically. Most approaches use topic or search term information only for the first search step and therefore assume that arguments can be classified independently of a topic. We argue that topic information is crucial for argument mining, since the topic defines the semantic context of an argument. Precisely, we propose different models for the classification of arguments, which take information about a topic of an argument into account. Moreover, to enrich the context of a topic and to let models understand the context of the potential argument better, we integrate information from different external sources such as Knowledge Graphs or pre-trained NLP models. Our evaluation shows that considering topic information, especially in connection with external information, provides a significant performance boost for the argument mining task.

Large Language Models (LLMs) exhibit strong potential in mathematical reasoning, yet their effectiveness is often limited by a shortage of high-quality queries. This limitation necessitates scaling up computational responses through self-generated data, yet current methods struggle due to spurious correlated data caused by ineffective exploration across all reasoning stages. To address such challenge, we introduce MARGE: Improving Math Reasoning with Guided Exploration, a novel method to address this issue and enhance mathematical reasoning through hit-guided exploration. MARGE systematically explores intermediate reasoning states derived from self-generated solutions, enabling adequate exploration and improved credit assignment throughout the reasoning process. Through extensive experiments across multiple backbone models and benchmarks, we demonstrate that MARGE significantly improves reasoning capabilities without requiring external annotations or training additional value models. Notably, MARGE improves both single-shot accuracy and exploration diversity, mitigating a common trade-off in alignment methods. These results demonstrate MARGE's effectiveness in enhancing mathematical reasoning capabilities and unlocking the potential of scaling self-generated training data. Our code and models are available at https://github.com/georgao35/MARGE{this link}.

Efficient multi-hop reasoning requires Large Language Models (LLMs) based agents to acquire high-value external knowledge iteratively. Previous work has explored reinforcement learning (RL) to train LLMs to perform search-based document retrieval, achieving notable improvements in QA performance, but underperform on complex, multi-hop QA resulting from the sparse rewards from global signal only. To address this gap in existing research, we introduce StepSearch, a framework for search LLMs that trained with step-wise proximal policy optimization method. It consists of richer and more detailed intermediate search rewards and token-level process supervision based on information gain and redundancy penalties to better guide each search step. We constructed a fine-grained question-answering dataset containing sub-question-level search trajectories based on open source datasets through a set of data pipeline method. On standard multi-hop QA benchmarks, it significantly outperforms global-reward baselines, achieving 11.2% and 4.2% absolute improvements for 3B and 7B models over various search with RL baselines using only 19k training data, demonstrating the effectiveness of fine-grained, stepwise supervision in optimizing deep search LLMs. Our code will be released on https://github.com/Zillwang/StepSearch.

Retrieval augmentation enables large language models to take advantage of external knowledge, for example on tasks like question answering and data imputation. However, the performance of such retrieval-augmented models is limited by the data quality of their underlying retrieval corpus. In this paper, we propose an algorithm based on multilinear extension for evaluating the data importance of retrieved data points. There are exponentially many terms in the multilinear extension, and one key contribution of this paper is a polynomial time algorithm that computes exactly, given a retrieval-augmented model with an additive utility function and a validation set, the data importance of data points in the retrieval corpus using the multilinear extension of the model's utility function. We further proposed an even more efficient ({\epsilon}, {\delta})-approximation algorithm. Our experimental results illustrate that we can enhance the performance of large language models by only pruning or reweighting the retrieval corpus, without requiring further training. For some tasks, this even allows a small model (e.g., GPT-JT), augmented with a search engine API, to outperform GPT-3.5 (without retrieval augmentation). Moreover, we show that weights based on multilinear extension can be computed efficiently in practice (e.g., in less than ten minutes for a corpus with 100 million elements).

Retrieval models are often evaluated on partially-annotated datasets. Each query is mapped to a few relevant texts and the remaining corpus is assumed to be irrelevant. As a result, models that successfully retrieve false negatives are punished in evaluation. Unfortunately, completely annotating all texts for every query is not resource efficient. In this work, we show that using partially-annotated datasets in evaluation can paint a distorted picture. We curate D-MERIT, a passage retrieval evaluation set from Wikipedia, aspiring to contain all relevant passages for each query. Queries describe a group (e.g., ``journals about linguistics'') and relevant passages are evidence that entities belong to the group (e.g., a passage indicating that Language is a journal about linguistics). We show that evaluating on a dataset containing annotations for only a subset of the relevant passages might result in misleading ranking of the retrieval systems and that as more relevant texts are included in the evaluation set, the rankings converge. We propose our dataset as a resource for evaluation and our study as a recommendation for balance between resource-efficiency and reliable evaluation when annotating evaluation sets for text retrieval.

Dense embedding-based text retrievalx2013retrieval of relevant passages from corpora via deep learning encodingsx2013has emerged as a powerful method attaining state-of-the-art search results and popularizing the use of Retrieval Augmented Generation (RAG). Still, like other search methods, embedding-based retrieval may be susceptible to search-engine optimization (SEO) attacks, where adversaries promote malicious content by introducing adversarial passages to corpora. To faithfully assess and gain insights into the susceptibility of such systems to SEO, this work proposes the GASLITE attack, a mathematically principled gradient-based search method for generating adversarial passages without relying on the corpus content or modifying the model. Notably, GASLITE's passages (1) carry adversary-chosen information while (2) achieving high retrieval ranking for a selected query distribution when inserted to corpora. We use GASLITE to extensively evaluate retrievers' robustness, testing nine advanced models under varied threat models, while focusing on realistic adversaries targeting queries on a specific concept (e.g., a public figure). We found GASLITE consistently outperformed baselines by geq140% success rate, in all settings. Particularly, adversaries using GASLITE require minimal effort to manipulate search resultsx2013by injecting a negligible amount of adversarial passages (leq0.0001% of the corpus), they could make them visible in the top-10 results for 61-100% of unseen concept-specific queries against most evaluated models. Inspecting variance in retrievers' robustness, we identify key factors that may contribute to models' susceptibility to SEO, including specific properties in the embedding space's geometry.

We propose a novel prompt design paradigm that challenges conventional wisdom in large language model (LLM) prompting. While conventional wisdom prioritizes well-crafted instructions and demonstrations for in-context learning (ICL), we show that pruning random demonstrations into seemingly incoherent "gibberish" can remarkably improve performance across diverse tasks. Notably, the "gibberish" always matches or surpasses state-of-the-art automatic prompt optimization techniques, achieving substantial gains regardless of LLM alignment. Nevertheless, discovering an effective pruning strategy is non-trivial, as existing attribution methods and prompt compression algorithms fail to deliver robust results, let alone human intuition. In terms of this, we propose a self-discover prompt optimization framework, PromptQuine, an evolutionary search framework that automatically searches for the pruning strategy by itself using only low-data regimes. Much like the emergent complexity in nature--such as symbiosis and self-organization--arising in response to resource constraints, our framework evolves and refines unconventional yet highly effective prompts by leveraging only the tokens present within the context. We demonstrate its effectiveness across classification, multi-choice question answering, generation and math reasoning tasks across LLMs, while achieving decent runtime efficiency. We hope our findings can guide mechanistic studies on in-context learning, and provide a call to action, to pave the way for more open-ended search algorithms for more effective LLM prompting.

Math word problem (MWP) solving requires generating a reasoning path based on a given problem description that often contains irrelevant conditions. Existing chain-of-thought (CoT) prompting methods elicited multi-step reasoning abilities of large language models (LLMs) to solve MWPs. However, they were seriously confused by the irrelevant conditions, resulting in low accuracy. In this paper, we propose a novel approach named I^3C that instructs LLMs to identify and ignore irrelevant conditions. It identifies a set of irrelevant condition candidates that have a weak semantic relevance with the question. Then it prompts LLMs to verify the irrelevant conditions. Lastly it instructs the LLMs with the verification on relevant and irrelevant conditions to avoid confusion and improve reasoning paths. Moreover, we propose to select (problem, reasoning paths) pairs as demonstrations to enhance I^3C with few-shot reasoning. We develop I^3C-Select that selects the most confusing problems based on the semantic relevance measurement. We conduct extensive experiments on eight MWP datasets. I^3C can be combined with any CoT prompting methods to improve the performance of solving MWPs. Notably, with GPT-3.5-Turbo and I^3C-Select, we achieve an accuracy of 96.0 and 94.1 on GSM-IC2-1K and GSM-ICM-1K, respectively, significantly outperforming the state-of-the-art few-shot prompting method Complex-CoT by +11.7 and +11.1. Our implementation is made publicly available at https://wzy6642.github.io/I3C.github.io/.

Advanced reasoning capabilities in Large Language Models (LLMs) have caused higher hallucination prevalence; yet most mitigation work focuses on after-the-fact filtering rather than shaping the queries that trigger them. We introduce QueryBandits, a bandit framework that designs rewrite strategies to maximize a reward model, that encapsulates hallucination propensity based upon the sensitivities of 17 linguistic features of the input query-and therefore, proactively steer LLMs away from generating hallucinations. Across 13 diverse QA benchmarks and 1,050 lexically perturbed queries per dataset, our top contextual QueryBandit (Thompson Sampling) achieves an 87.5% win rate over a no-rewrite baseline and also outperforms zero-shot static prompting ("paraphrase" or "expand") by 42.6% and 60.3% respectively. Therefore, we empirically substantiate the effectiveness of QueryBandits in mitigating hallucination via the intervention that takes the form of a query rewrite. Interestingly, certain static prompting strategies, which constitute a considerable number of current query rewriting literature, have a higher cumulative regret than the no-rewrite baseline, signifying that static rewrites can worsen hallucination. Moreover, we discover that the converged per-arm regression feature weight vectors substantiate that there is no single rewrite strategy optimal for all queries. In this context, guided rewriting via exploiting semantic features with QueryBandits can induce significant shifts in output behavior through forward-pass mechanisms, bypassing the need for retraining or gradient-based adaptation.

Competitive programming benchmarks are widely used in scenarios such as programming contests and large language model assessments. However, the growing presence of duplicate or highly similar problems raises concerns not only about competition fairness, but also about the validity of competitive programming as a benchmark for model evaluation. In this paper, we propose a new problem -- similar question retrieval -- to address this issue. Due to the lack of both data and models, solving this problem is challenging. To this end, we introduce CPRet, a retrieval-oriented benchmark suite for competitive programming, covering four retrieval tasks: two code-centric (i.e., Text-to-Code and Code-to-Code) and two newly proposed problem-centric tasks (i.e., Problem-to-Duplicate and Simplified-to-Full), built from a combination of automatically crawled problem-solution data and manually curated annotations. Our contribution includes both high-quality training data and temporally separated test sets for reliable evaluation. In addition, we develop two task-specialized retrievers based on this dataset: CPRetriever-Code, trained with a novel Group-InfoNCE loss for problem-code alignment, and CPRetriever-Prob, fine-tuned for identifying problem-level similarity. Both models achieve strong results and are open-sourced for local use. Finally, we analyze LiveCodeBench and find that high-similarity problems inflate model pass rates and reduce differentiation, underscoring the need for similarity-aware evaluation in future benchmarks. Code and data are available at: https://github.com/coldchair/CPRet

Large Language Models (LLMs) demonstrate impressive reasoning capabilities in familiar contexts, but struggle when the context conflicts with their parametric knowledge. To investigate this phenomenon, we introduce CounterLogic, a dataset containing 1,800 examples across 9 logical schemas, explicitly designed to evaluate logical reasoning through counterfactual (hypothetical knowledge-conflicting) scenarios. Our systematic evaluation of 11 LLMs across 6 different datasets reveals a consistent performance degradation, with accuracies dropping by 27% on average when reasoning through counterfactual information. We propose Self-Segregate, a prompting method enabling metacognitive awareness (explicitly identifying knowledge conflicts) before reasoning. Our method dramatically narrows the average performance gaps from 27% to just 11%, while significantly increasing the overall accuracy (+7.5%). We discuss the implications of these findings and draw parallels to human cognitive processes, particularly on how humans disambiguate conflicting information during reasoning tasks. Our findings offer practical insights for understanding and enhancing LLMs reasoning capabilities in real-world applications, especially where models must logically reason independently of their factual knowledge.

Text-to-SQL aims to automate the process of generating SQL queries on a database from natural language text. In this work, we propose "SQLPrompt", tailored to improve the few-shot prompting capabilities of Text-to-SQL for Large Language Models (LLMs). Our methods include innovative prompt design, execution-based consistency decoding strategy which selects the SQL with the most consistent execution outcome among other SQL proposals, and a method that aims to improve performance by diversifying the SQL proposals during consistency selection with different prompt designs ("MixPrompt") and foundation models ("MixLLMs"). We show that SQLPrompt outperforms previous approaches for in-context learning with few labeled data by a large margin, closing the gap with finetuning state-of-the-art with thousands of labeled data.

Large language models (LLMs) have recently shown strong performance on mathematical benchmarks. At the same time, they are prone to hallucination and sycophancy, often providing convincing but flawed proofs for incorrect mathematical statements provided by users. This significantly limits the applicability of LLMs in theorem proving, as verification of these flawed proofs must be done manually by expert mathematicians. However, existing benchmarks that measure sycophancy in mathematics are limited: they focus solely on final-answer problems, rely on very simple and often contaminated datasets, and construct benchmark samples using synthetic modifications that create ill-posed questions rather than well-posed questions that are demonstrably false. To address these issues, we introduce BrokenMath, the first benchmark for evaluating sycophantic behavior in LLMs within the context of natural language theorem proving. BrokenMath is built from advanced 2025 competition problems, which are perturbed with an LLM to produce false statements and subsequently refined through expert review. Using an LLM-as-a-judge framework, we evaluate state-of-the-art LLMs and agentic systems and find that sycophancy is widespread, with the best model, GPT-5, producing sycophantic answers 29% of the time. We further investigate several mitigation strategies, including test-time interventions and supervised fine-tuning on curated sycophantic examples. These approaches substantially reduce, but do not eliminate, sycophantic behavior.

Search agents connect LLMs to the Internet, enabling access to broader and more up-to-date information. However, unreliable search results may also pose safety threats to end users, establishing a new threat surface. In this work, we conduct two in-the-wild experiments to demonstrate both the prevalence of low-quality search results and their potential to misguide agent behaviors. To counter this threat, we introduce an automated red-teaming framework that is systematic, scalable, and cost-efficient, enabling lightweight and harmless safety assessments of search agents. Building on this framework, we construct the SafeSearch benchmark, which includes 300 test cases covering five categories of risks (e.g., misinformation and indirect prompt injection). Using this benchmark, we evaluate three representative search agent scaffolds, covering search workflow, tool-calling, and deep research, across 7 proprietary and 8 open-source backend LLMs. Our results reveal substantial vulnerabilities of LLM-based search agents: when exposed to unreliable websites, the highest ASR reached 90.5% for GPT-4.1-mini under a search workflow setting. Moreover, our analysis highlights the limited effectiveness of common defense practices, such as reminder prompting. This emphasizes the value of our framework in promoting transparency for safer agent development. Our codebase and test cases are publicly available: https://github.com/jianshuod/SafeSearch.

Augmenting large language models (LLMs) with external retrieval has become a standard method to address their inherent knowledge cutoff limitations. However, traditional retrieval-augmented generation methods employ static, pre-inference retrieval strategies, making them inadequate for complex tasks involving ambiguous, multi-step, or evolving information needs. Recent advances in test-time scaling techniques have demonstrated significant potential in enabling LLMs to dynamically interact with external tools, motivating the shift toward adaptive inference-time retrieval. Inspired by Information Foraging Theory (IFT), we propose InForage, a reinforcement learning framework that formalizes retrieval-augmented reasoning as a dynamic information-seeking process. Unlike existing approaches, InForage explicitly rewards intermediate retrieval quality, encouraging LLMs to iteratively gather and integrate information through adaptive search behaviors. To facilitate training, we construct a human-guided dataset capturing iterative search and reasoning trajectories for complex, real-world web tasks. Extensive evaluations across general question answering, multi-hop reasoning tasks, and a newly developed real-time web QA dataset demonstrate InForage's superior performance over baseline methods. These results highlight InForage's effectiveness in building robust, adaptive, and efficient reasoning agents.

Formal proofs are challenging to write even for experienced experts. Recent progress in Neural Theorem Proving (NTP) shows promise in expediting this process. However, the formal corpora available on the Internet are limited compared to the general text, posing a significant data scarcity challenge for NTP. To address this issue, this work proposes Alchemy, a general framework for data synthesis that constructs formal theorems through symbolic mutation. Specifically, for each candidate theorem in Mathlib, we identify all invocable theorems that can be used to rewrite or apply to it. Subsequently, we mutate the candidate theorem by replacing the corresponding term in the statement with its equivalent form or antecedent. As a result, our method increases the number of theorems in Mathlib by an order of magnitude, from 110k to 6M. Furthermore, we perform continual pretraining and supervised finetuning on this augmented corpus for large language models. Experimental results demonstrate the effectiveness of our approach, achieving a 5% absolute performance improvement on Leandojo benchmark. Additionally, our synthetic data achieve a 2.5% absolute performance gain on the out-of-distribution miniF2F benchmark. To provide further insights, we conduct a comprehensive analysis of synthetic data composition and the training paradigm, offering valuable guidance for developing a strong theorem prover.

Advanced applied mathematics problems are underrepresented in existing Large Language Model (LLM) benchmark datasets. To address this, we introduce HARDMath, a dataset inspired by a graduate course on asymptotic methods, featuring challenging applied mathematics problems that require analytical approximation techniques. These problems demand a combination of mathematical reasoning, computational tools, and subjective judgment, making them difficult for LLMs. Our framework auto-generates a large number of problems with solutions validated against numerical ground truths. We evaluate both open- and closed-source LLMs on HARDMath-mini, a sub-sampled test set of 366 problems, as well as on 40 word problems formulated in applied science contexts. Even leading closed-source models like GPT-4 achieve only 43.8% overall accuracy with few-shot Chain-of-Thought prompting, and all models demonstrate significantly lower performance compared to results on existing mathematics benchmark datasets. We additionally conduct a detailed error analysis to gain insights into the failure cases of LLMs. These results demonstrate limitations of current LLM performance on advanced graduate-level applied math problems and underscore the importance of datasets like HARDMath to advance mathematical abilities of LLMs.

Program synthesis with language models (LMs) has unlocked a large set of reasoning abilities; code-tuned LMs have proven adept at generating programs that solve a wide variety of algorithmic symbolic manipulation tasks (e.g. word concatenation). However, not all reasoning tasks are easily expressible as code, e.g. tasks involving commonsense reasoning, moral decision-making, and sarcasm understanding. Our goal is to extend an LM's program synthesis skills to such tasks and evaluate the results via pseudo-programs, namely Python programs where some leaf function calls are left undefined. To that end, we propose, Code Generation and Emulated EXecution (CoGEX). CoGEX works by (1) training LMs to generate their own pseudo-programs, (2) teaching them to emulate their generated program's execution, including those leaf functions, allowing the LM's knowledge to fill in the execution gaps; and (3) using them to search over many programs to find an optimal one. To adapt the CoGEX model to a new task, we introduce a method for performing program search to find a single program whose pseudo-execution yields optimal performance when applied to all the instances of a given dataset. We show that our approach yields large improvements compared to standard in-context learning approaches on a battery of tasks, both algorithmic and soft reasoning. This result thus demonstrates that code synthesis can be applied to a much broader class of problems than previously considered. Our released dataset, fine-tuned models, and implementation can be found at https://github.com/nweir127/CoGEX.

In this work, we dive into the fundamental challenges of evaluating Text2SQL solutions and highlight potential failure causes and the potential risks of relying on aggregate metrics in existing benchmarks. We identify two largely unaddressed limitations in current open benchmarks: (1) data quality issues in the evaluation data, mainly attributed to the lack of capturing the probabilistic nature of translating a natural language description into a structured query (e.g., NL ambiguity), and (2) the bias introduced by using different match functions as approximations for SQL equivalence. To put both limitations into context, we propose a unified taxonomy of all Text2SQL limitations that can lead to both prediction and evaluation errors. We then motivate the taxonomy by providing a survey of Text2SQL limitations using state-of-the-art Text2SQL solutions and benchmarks. We describe the causes of limitations with real-world examples and propose potential mitigation solutions for each category in the taxonomy. We conclude by highlighting the open challenges encountered when deploying such mitigation strategies or attempting to automatically apply the taxonomy.

Recent Meta-learning for Black-Box Optimization (MetaBBO) methods harness neural networks to meta-learn configurations of traditional black-box optimizers. Despite their success, they are inevitably restricted by the limitations of predefined hand-crafted optimizers. In this paper, we present Symbol, a novel framework that promotes the automated discovery of black-box optimizers through symbolic equation learning. Specifically, we propose a Symbolic Equation Generator (SEG) that allows closed-form optimization rules to be dynamically generated for specific tasks and optimization steps. Within Symbol, we then develop three distinct strategies based on reinforcement learning, so as to meta-learn the SEG efficiently. Extensive experiments reveal that the optimizers generated by Symbol not only surpass the state-of-the-art BBO and MetaBBO baselines, but also exhibit exceptional zero-shot generalization abilities across entirely unseen tasks with different problem dimensions, population sizes, and optimization horizons. Furthermore, we conduct in-depth analyses of our Symbol framework and the optimization rules that it generates, underscoring its desirable flexibility and interpretability.

In this work, we aim to develop an MLLM that understands and solves questions by learning to create each intermediate step of the reasoning involved till the final answer. To this end, we propose Collective Monte Carlo Tree Search (CoMCTS), a new learning-to-reason method for MLLMs, which introduces the concept of collective learning into ``tree search'' for effective and efficient reasoning-path searching and learning. The core idea of CoMCTS is to leverage collective knowledge from multiple models to collaboratively conjecture, search and identify effective reasoning paths toward correct answers via four iterative operations including Expansion, Simulation and Error Positioning, Backpropagation, and Selection. Using CoMCTS, we construct Mulberry-260k, a multimodal dataset with a tree of rich, explicit and well-defined reasoning nodes for each question. With Mulberry-260k, we perform collective SFT to train our model, Mulberry, a series of MLLMs with o1-like step-by-step Reasoning and Reflection capabilities. Extensive experiments demonstrate the superiority of our proposed methods on various benchmarks. Code will be available at https://github.com/HJYao00/Mulberry

This paper addresses the limitations of traditional keyword-based search in understanding user intent and introduces a novel hybrid search approach that leverages the strengths of non-semantic search engines, Large Language Models (LLMs), and embedding models. The proposed system integrates keyword matching, semantic vector embeddings, and LLM-generated structured queries to deliver highly relevant and contextually appropriate search results. By combining these complementary methods, the hybrid approach effectively captures both explicit and implicit user intent.The paper further explores techniques to optimize query execution for faster response times and demonstrates the effectiveness of this hybrid search model in producing comprehensive and accurate search outcomes.

Neural Information Retrieval (NIR) has significantly improved upon heuristic-based IR systems. Yet, failures remain frequent, the models used often being unable to retrieve documents relevant to the user's query. We address this challenge by proposing a lightweight abstention mechanism tailored for real-world constraints, with particular emphasis placed on the reranking phase. We introduce a protocol for evaluating abstention strategies in a black-box scenario, demonstrating their efficacy, and propose a simple yet effective data-driven mechanism. We provide open-source code for experiment replication and abstention implementation, fostering wider adoption and application in diverse contexts.

We introduce IFIR, the first comprehensive benchmark designed to evaluate instruction-following information retrieval (IR) in expert domains. IFIR includes 2,426 high-quality examples and covers eight subsets across four specialized domains: finance, law, healthcare, and science literature. Each subset addresses one or more domain-specific retrieval tasks, replicating real-world scenarios where customized instructions are critical. IFIR enables a detailed analysis of instruction-following retrieval capabilities by incorporating instructions at different levels of complexity. We also propose a novel LLM-based evaluation method to provide a more precise and reliable assessment of model performance in following instructions. Through extensive experiments on 15 frontier retrieval models, including those based on LLMs, our results reveal that current models face significant challenges in effectively following complex, domain-specific instructions. We further provide in-depth analyses to highlight these limitations, offering valuable insights to guide future advancements in retriever development.