Daily Papers

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

Automata learning is a popular technique used to automatically construct an automaton model from queries. Much research went into devising ad hoc adaptations of algorithms for different types of automata. The CALF project seeks to unify these using category theory in order to ease correctness proofs and guide the design of new algorithms. In this paper, we extend CALF to cover learning of algebraic structures that may not have a coalgebraic presentation. Furthermore, we provide a detailed algorithmic account of an abstract version of the popular L* algorithm, which was missing from CALF. We instantiate the abstract theory to a large class of Set functors, by which we recover for the first time practical tree automata learning algorithms from an abstract framework and at the same time obtain new algorithms to learn algebras of quotiented polynomial functors.

Attention, specifically scaled dot-product attention, has proven effective for natural language, but it does not have a mechanism for handling hierarchical patterns of arbitrary nesting depth, which limits its ability to recognize certain syntactic structures. To address this shortcoming, we propose stack attention: an attention operator that incorporates stacks, inspired by their theoretical connections to context-free languages (CFLs). We show that stack attention is analogous to standard attention, but with a latent model of syntax that requires no syntactic supervision. We propose two variants: one related to deterministic pushdown automata (PDAs) and one based on nondeterministic PDAs, which allows transformers to recognize arbitrary CFLs. We show that transformers with stack attention are very effective at learning CFLs that standard transformers struggle on, achieving strong results on a CFL with theoretically maximal parsing difficulty. We also show that stack attention is more effective at natural language modeling under a constrained parameter budget, and we include results on machine translation.

We show that transformer-based large language models are computationally universal when augmented with an external memory. Any deterministic language model that conditions on strings of bounded length is equivalent to a finite automaton, hence computationally limited. However, augmenting such models with a read-write memory creates the possibility of processing arbitrarily large inputs and, potentially, simulating any algorithm. We establish that an existing large language model, Flan-U-PaLM 540B, can be combined with an associative read-write memory to exactly simulate the execution of a universal Turing machine, U_{15,2}. A key aspect of the finding is that it does not require any modification of the language model weights. Instead, the construction relies solely on designing a form of stored instruction computer that can subsequently be programmed with a specific set of prompts.

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

Selective state-space models (SSMs) are an emerging alternative to the Transformer, offering the unique advantage of parallel training and sequential inference. Although these models have shown promising performance on a variety of tasks, their formal expressiveness and length generalization properties remain underexplored. In this work, we provide insight into the workings of selective SSMs by analyzing their expressiveness and length generalization performance on regular language tasks, i.e., finite-state automaton (FSA) emulation. We address certain limitations of modern SSM-based architectures by introducing the Selective Dense State-Space Model (SD-SSM), the first selective SSM that exhibits perfect length generalization on a set of various regular language tasks using a single layer. It utilizes a dictionary of dense transition matrices, a softmax selection mechanism that creates a convex combination of dictionary matrices at each time step, and a readout consisting of layer normalization followed by a linear map. We then proceed to evaluate variants of diagonal selective SSMs by considering their empirical performance on commutative and non-commutative automata. We explain the experimental results with theoretical considerations. Our code is available at https://github.com/IBM/selective-dense-state-space-model.

We show that autoregressive decoding of a transformer-based language model can realize universal computation, without external intervention or modification of the model's weights. Establishing this result requires understanding how a language model can process arbitrarily long inputs using a bounded context. For this purpose, we consider a generalization of autoregressive decoding where, given a long input, emitted tokens are appended to the end of the sequence as the context window advances. We first show that the resulting system corresponds to a classical model of computation, a Lag system, that has long been known to be computationally universal. By leveraging a new proof, we show that a universal Turing machine can be simulated by a Lag system with 2027 production rules. We then investigate whether an existing large language model can simulate the behaviour of such a universal Lag system. We give an affirmative answer by showing that a single system-prompt can be developed for gemini-1.5-pro-001 that drives the model, under deterministic (greedy) decoding, to correctly apply each of the 2027 production rules. We conclude that, by the Church-Turing thesis, prompted gemini-1.5-pro-001 with extended autoregressive (greedy) decoding is a general purpose computer.

LLMs are widely used in complex AI applications. These applications underscore the need for LLM outputs to adhere to a specific format, for their integration with other components in the systems. Typically the format rules e.g., for data serialization formats such as JSON, YAML, or Code in Programming Language are expressed as context-free grammar (CFG). Due to the hallucinations and unreliability of LLMs, instructing LLMs to adhere to specified syntax becomes an increasingly important challenge. We present SynCode, a novel framework for efficient and general syntactical decoding with LLMs, to address this challenge. SynCode leverages the CFG of a formal language, utilizing an offline-constructed efficient lookup table called DFA mask store based on the discrete finite automaton (DFA) of the language grammar terminals. We demonstrate SynCode's soundness and completeness given the CFG of the formal language, presenting its ability to retain syntactically valid tokens while rejecting invalid ones. SynCode seamlessly integrates with any language defined by CFG, as evidenced by experiments focusing on generating JSON, Python, and Go outputs. Our experiments evaluating the effectiveness of SynCode for JSON generation demonstrate that SynCode eliminates all syntax errors and significantly outperforms state-of-the-art baselines. Furthermore, our results underscore how SynCode significantly reduces 96.07% of syntax errors in generated Python and Go code, showcasing its substantial impact on enhancing syntactical precision in LLM generation. Our code is available at https://github.com/uiuc-focal-lab/syncode

We design controlled experiments to study HOW generative language models, like GPT, learn context-free grammars (CFGs) -- diverse language systems with a tree-like structure capturing many aspects of natural languages, programs, and logics. CFGs are as hard as pushdown automata, and can be ambiguous so that verifying if a string satisfies the rules requires dynamic programming. We construct synthetic data and demonstrate that even for difficult (long and ambiguous) CFGs, pre-trained transformers can learn to generate sentences with near-perfect accuracy and impressive diversity. More importantly, we delve into the physical principles behind how transformers learns CFGs. We discover that the hidden states within the transformer implicitly and precisely encode the CFG structure (such as putting tree node information exactly on the subtree boundary), and learn to form "boundary to boundary" attentions resembling dynamic programming. We also cover some extension of CFGs as well as the robustness aspect of transformers against grammar mistakes. Overall, our research provides a comprehensive and empirical understanding of how transformers learn CFGs, and reveals the physical mechanisms utilized by transformers to capture the structure and rules of languages.

We contribute to the study of formal languages that can be recognized by transformer encoders. We focus on two self-attention mechanisms: (1) UHAT (Unique Hard Attention Transformers) and (2) AHAT (Average Hard Attention Transformers). UHAT encoders are known to recognize only languages inside the circuit complexity class {sf AC}^0, i.e., accepted by a family of poly-sized and depth-bounded boolean circuits with unbounded fan-ins. On the other hand, AHAT encoders can recognize languages outside {sf AC}^0), but their expressive power still lies within the bigger circuit complexity class {sf TC}^0, i.e., {sf AC}^0-circuits extended by majority gates. We first show a negative result that there is an {sf AC}^0-language that cannot be recognized by an UHAT encoder. On the positive side, we show that UHAT encoders can recognize a rich fragment of {sf AC}^0-languages, namely, all languages definable in first-order logic with arbitrary unary numerical predicates. This logic, includes, for example, all regular languages from {sf AC}^0. We then show that AHAT encoders can recognize all languages of our logic even when we enrich it with counting terms. We apply these results to derive new results on the expressive power of UHAT and AHAT up to permutation of letters (a.k.a. Parikh images).

Formal verification can provably guarantee the correctness of critical system software, but the high proof burden has long hindered its wide adoption. Recently, Large Language Models (LLMs) have shown success in code analysis and synthesis. In this paper, we present a combination of LLMs and static analysis to synthesize invariants, assertions, and other proof structures for a Rust-based formal verification framework called Verus. In a few-shot setting, LLMs demonstrate impressive logical ability in generating postconditions and loop invariants, especially when analyzing short code snippets. However, LLMs lack the ability to retain and propagate context information, a strength of traditional static analysis. Based on these observations, we developed a prototype based on OpenAI's GPT-4 model. Our prototype decomposes the verification task into multiple smaller ones, iteratively queries GPT-4, and combines its output with lightweight static analysis. We evaluated the prototype with a developer in the automation loop on 20 vector-manipulating programs. The results demonstrate that it significantly reduces human effort in writing entry-level proof code.

Communicating state machines provide a formal foundation for distributed computation. Unfortunately, they are Turing-complete and, thus, challenging to analyse. In this paper, we classify restrictions on channels which have been proposed to work around the undecidability of verification questions. We compare half-duplex communication, existential B-boundedness, and k-synchronisability. These restrictions do not prevent the communication channels from growing arbitrarily large but still restrict the power of the model. Each restriction gives rise to a set of languages so, for every pair of restrictions, we check whether one subsumes the other or if they are incomparable. We investigate their relationship in two different contexts: first, the one of communicating state machines, and, second, the one of communication protocol specifications using high-level message sequence charts. Surprisingly, these two contexts yield different conclusions. In addition, we integrate multiparty session types, another approach to specify communication protocols, into our classification. We show that multiparty session type languages are half-duplex, existentially 1-bounded, and 1-synchronisable. To~show this result, we provide the first formal embedding of multiparty session types into high-level message sequence charts.

We present our position on the elusive quest for a general-purpose framework for specifying and studying deep learning architectures. Our opinion is that the key attempts made so far lack a coherent bridge between specifying constraints which models must satisfy and specifying their implementations. Focusing on building a such a bridge, we propose to apply category theory -- precisely, the universal algebra of monads valued in a 2-category of parametric maps -- as a single theory elegantly subsuming both of these flavours of neural network design. To defend our position, we show how this theory recovers constraints induced by geometric deep learning, as well as implementations of many architectures drawn from the diverse landscape of neural networks, such as RNNs. We also illustrate how the theory naturally encodes many standard constructs in computer science and automata theory.

Byte-Pair Encoding (BPE) is a popular algorithm used for tokenizing data in NLP, despite being devised initially as a compression method. BPE appears to be a greedy algorithm at face value, but the underlying optimization problem that BPE seeks to solve has not yet been laid down. We formalize BPE as a combinatorial optimization problem. Via submodular functions, we prove that the iterative greedy version is a 1{{sigma(mu^star)}}(1-e^{-{sigma(mu^star)}})-approximation of an optimal merge sequence, where {sigma(mu^star)} is the total backward curvature with respect to the optimal merge sequence mu^star. Empirically the lower bound of the approximation is approx 0.37. We provide a faster implementation of BPE which improves the runtime complexity from Oleft(N Mright) to Oleft(N log Mright), where N is the sequence length and M is the merge count. Finally, we optimize the brute-force algorithm for optimal BPE using memoization.

Tokenization is the first - and often underappreciated - layer of computation in language models. While Chain-of-Thought (CoT) prompting enables transformer models to approximate recurrent computation by externalizing intermediate steps, we show that the success of such reasoning is fundamentally bounded by the structure of tokenized inputs. This work presents a theoretical and empirical investigation into how tokenization schemes, particularly subword-based methods like byte-pair encoding (BPE), impede symbolic computation by merging or obscuring atomic reasoning units. We introduce the notion of Token Awareness to formalize how poor token granularity disrupts logical alignment and prevents models from generalizing symbolic procedures. Through systematic evaluation on arithmetic and symbolic tasks, we demonstrate that token structure dramatically affect reasoning performance, causing failure even with CoT, while atomically-aligned formats unlock strong generalization, allowing small models (e.g., GPT-4o-mini) to outperform larger systems (e.g., o1) in structured reasoning. Our findings reveal that symbolic reasoning ability in LLMs is not purely architectural, but deeply conditioned on token-level representations.

The objective of pre-trained language models is to learn contextual representations of textual data. Pre-trained language models have become mainstream in natural language processing and code modeling. Using probes, a technique to study the linguistic properties of hidden vector spaces, previous works have shown that these pre-trained language models encode simple linguistic properties in their hidden representations. However, none of the previous work assessed whether these models encode the whole grammatical structure of a programming language. In this paper, we prove the existence of a syntactic subspace, lying in the hidden representations of pre-trained language models, which contain the syntactic information of the programming language. We show that this subspace can be extracted from the models' representations and define a novel probing method, the AST-Probe, that enables recovering the whole abstract syntax tree (AST) of an input code snippet. In our experimentations, we show that this syntactic subspace exists in five state-of-the-art pre-trained language models. In addition, we highlight that the middle layers of the models are the ones that encode most of the AST information. Finally, we estimate the optimal size of this syntactic subspace and show that its dimension is substantially lower than those of the models' representation spaces. This suggests that pre-trained language models use a small part of their representation spaces to encode syntactic information of the programming languages.

Many graph algorithms can be viewed as sets of rules that are iteratively applied, with the number of iterations dependent on the size and complexity of the input graph. Existing machine learning architectures often struggle to represent these algorithmic decisions as discrete state transitions. Therefore, we propose a novel framework: GraphFSA (Graph Finite State Automaton). GraphFSA is designed to learn a finite state automaton that runs on each node of a given graph. We test GraphFSA on cellular automata problems, showcasing its abilities in a straightforward algorithmic setting. For a comprehensive empirical evaluation of our framework, we create a diverse range of synthetic problems. As our main application, we then focus on learning more elaborate graph algorithms. Our findings suggest that GraphFSA exhibits strong generalization and extrapolation abilities, presenting an alternative approach to represent these algorithms.

Several recent advances in AI systems (e.g., Tree-of-Thoughts and Program-Aided Language Models) solve problems by providing a "scaffolding" program that structures multiple calls to language models to generate better outputs. A scaffolding program is written in a programming language such as Python. In this work, we use a language-model-infused scaffolding program to improve itself. We start with a seed "improver" that improves an input program according to a given utility function by querying a language model several times and returning the best solution. We then run this seed improver to improve itself. Across a small set of downstream tasks, the resulting improved improver generates programs with significantly better performance than its seed improver. Afterward, we analyze the variety of self-improvement strategies proposed by the language model, including beam search, genetic algorithms, and simulated annealing. Since the language models themselves are not altered, this is not full recursive self-improvement. Nonetheless, it demonstrates that a modern language model, GPT-4 in our proof-of-concept experiments, is capable of writing code that can call itself to improve itself. We critically consider concerns around the development of self-improving technologies and evaluate the frequency with which the generated code bypasses a sandbox.

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

Large Language Models (LLMs) have revolutionized natural language processing by unifying tasks into text generation, yet their large parameter sizes and autoregressive nature limit inference speed. SAM-Decoding addresses this by introducing a novel retrieval-based speculative decoding method that uses a suffix automaton for efficient and accurate draft generation. Unlike n-gram matching used by the existing method, SAM-Decoding finds the longest suffix match in generating text and text corpuss, achieving an average time complexity of O(1) per generation step. SAM-Decoding constructs static and dynamic suffix automatons for the text corpus and input prompts, respectively, enabling fast and precise draft generation. Meanwhile, it is designed as an approach that can be combined with existing methods, allowing SAM-Decoding to adaptively select a draft generation strategy based on the matching length, thus increasing the inference speed of the LLM. When combined with Token Recycling, evaluations show SAM-Decoding outperforms existing model-free methods, achieving a speedup of 2.27times over autoregressive decoding on Spec-Bench. When combined with EAGLE2, it reaches a speedup of 2.49times, surpassing all current approaches. Our code is available at https://github.com/hyx1999/SAM-Decoding.

Recent advancements in large language models (LLMs) have catalyzed significant interest in the automatic generation of Register-Transfer Level (RTL) code, particularly Verilog, from natural language instructions. While commercial LLMs like ChatGPT have dominated this domain, open-source alternatives have lagged considerably in performance, limiting the flexibility and data privacy of this emerging technology. This study introduces a novel approach utilizing reinforcement learning with golden code feedback to enhance the performance of pre-trained models. Leveraging open-source data and base models, we have achieved state-of-the-art (SOTA) results with a substantial margin. Notably, our 6.7B parameter model demonstrates superior performance compared to current best-in-class 13B and 16B models. Furthermore, through a comprehensive analysis of the limitations in direct fine-tuning and the training dynamics of reinforcement learning, we posit that the development of comprehensive supervisory signals, which are align with the inherent parallel semantics of Verilog code, is critical to effective generation. The code and data associated with this research are publicly available at https://github.com/CatIIIIIIII/veriseek. The model weights can be accessed at https://huggingface.co/WANGNingroci/VeriSeek.

The formalization of existing mathematical proofs is a notoriously difficult process. Despite decades of research on automation and proof assistants, writing formal proofs remains arduous and only accessible to a few experts. While previous studies to automate formalization focused on powerful search algorithms, no attempts were made to take advantage of available informal proofs. In this work, we introduce Draft, Sketch, and Prove (DSP), a method that maps informal proofs to formal proof sketches, and uses the sketches to guide an automated prover by directing its search to easier sub-problems. We investigate two relevant setups where informal proofs are either written by humans or generated by a language model. Our experiments and ablation studies show that large language models are able to produce well-structured formal sketches that follow the same reasoning steps as the informal proofs. Guiding an automated prover with these sketches enhances its performance from 20.9% to 39.3% on a collection of mathematical competition problems.

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

The integration of knowledge extracted from diverse models, whether described by domain experts or generated by machine learning algorithms, has historically been challenged by the absence of a suitable framework for specifying and integrating structures, learning processes, data transformations, and data models or rules. In this work, we extend algebraic specification methods to address these challenges within such a framework. In our work, we tackle the challenging task of developing a comprehensive framework for defining and analyzing deep learning architectures. We believe that previous efforts have fallen short by failing to establish a clear connection between the constraints a model must adhere to and its actual implementation. Our methodology employs graphical structures that resemble Ehresmann's sketches, interpreted within a universe of fuzzy sets. This approach offers a unified theory that elegantly encompasses both deterministic and non-deterministic neural network designs. Furthermore, we highlight how this theory naturally incorporates fundamental concepts from computer science and automata theory. Our extended algebraic specification framework, grounded in graphical structures akin to Ehresmann's sketches, offers a promising solution for integrating knowledge across disparate models and domains. By bridging the gap between domain-specific expertise and machine-generated insights, we pave the way for more comprehensive, collaborative, and effective approaches to knowledge integration and modeling.

Rapid advancements in large language models (LLMs) have the potential to assist in scientific progress. A critical capability toward this endeavor is the ability to reproduce existing work. To evaluate the ability of AI agents to reproduce results in an active research area, we introduce the Automated LLM Speedrunning Benchmark, leveraging the research community contributions on the NanoGPT speedrun, a competition to train a GPT-2 model in the shortest time. Each of the 19 speedrun tasks provides the agent with the previous records training script, optionally paired with one of three hint formats, ranging from pseudocode to paper-like descriptions of the new records improvements. Records execute quickly by design and speedrun improvements encompass diverse code-level changes, ranging from high-level algorithmic advancements to hardware-aware optimizations. These features make the benchmark both accessible and realistic for the frontier problem of improving LLM training. We find that recent reasoning LLMs combined with SoTA scaffolds struggle to reimplement already-known innovations in our benchmark, even when given detailed hints. Our benchmark thus provides a simple, non-saturated measure of an LLMs ability to automate scientific reproduction, a necessary (but not sufficient) skill for an autonomous research agent.

Although large language models (LLMs) are typically aligned, they remain vulnerable to jailbreaking through either carefully crafted prompts in natural language or, interestingly, gibberish adversarial suffixes. However, gibberish tokens have received relatively less attention despite their success in attacking aligned LLMs. Recent work, AmpleGCG~liao2024amplegcg, demonstrates that a generative model can quickly produce numerous customizable gibberish adversarial suffixes for any harmful query, exposing a range of alignment gaps in out-of-distribution (OOD) language spaces. To bring more attention to this area, we introduce AmpleGCG-Plus, an enhanced version that achieves better performance in fewer attempts. Through a series of exploratory experiments, we identify several training strategies to improve the learning of gibberish suffixes. Our results, verified under a strict evaluation setting, show that it outperforms AmpleGCG on both open-weight and closed-source models, achieving increases in attack success rate (ASR) of up to 17\% in the white-box setting against Llama-2-7B-chat, and more than tripling ASR in the black-box setting against GPT-4. Notably, AmpleGCG-Plus jailbreaks the newer GPT-4o series of models at similar rates to GPT-4, and, uncovers vulnerabilities against the recently proposed circuit breakers defense. We publicly release AmpleGCG-Plus along with our collected training datasets.

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

Despite the remarkable strides made by autoregressive language models, their potential is often hampered by the slow inference speeds inherent in sequential token generation. Blockwise parallel decoding (BPD) was proposed by Stern et al. (2018) as a way to improve inference speed of language models. In this paper, we make two contributions to understanding and improving BPD drafts. We first offer an analysis of the token distributions produced by the BPD prediction heads. Secondly, we use this analysis to inform algorithms to improve BPD inference speed by refining the BPD drafts using small n-gram or neural language models. We empirically show that these refined BPD drafts yield a higher average verified prefix length across tasks.

Large language models (LLMs) are vulnerable to adversarial attacks that add malicious tokens to an input prompt to bypass the safety guardrails of an LLM and cause it to produce harmful content. In this work, we introduce erase-and-check, the first framework for defending against adversarial prompts with certifiable safety guarantees. Given a prompt, our procedure erases tokens individually and inspects the resulting subsequences using a safety filter. Our safety certificate guarantees that harmful prompts are not mislabeled as safe due to an adversarial attack up to a certain size. We implement the safety filter in two ways, using Llama 2 and DistilBERT, and compare the performance of erase-and-check for the two cases. We defend against three attack modes: i) adversarial suffix, where an adversarial sequence is appended at the end of a harmful prompt; ii) adversarial insertion, where the adversarial sequence is inserted anywhere in the middle of the prompt; and iii) adversarial infusion, where adversarial tokens are inserted at arbitrary positions in the prompt, not necessarily as a contiguous block. Our experimental results demonstrate that this procedure can obtain strong certified safety guarantees on harmful prompts while maintaining good empirical performance on safe prompts. Additionally, we propose three efficient empirical defenses: i) RandEC, a randomized subsampling version of erase-and-check; ii) GreedyEC, which greedily erases tokens that maximize the softmax score of the harmful class; and iii) GradEC, which uses gradient information to optimize tokens to erase. We demonstrate their effectiveness against adversarial prompts generated by the Greedy Coordinate Gradient (GCG) attack algorithm. The code for our experiments is available at https://github.com/aounon/certified-llm-safety.

As large language models (LLMs) become increasingly prevalent and integrated into autonomous systems, ensuring their safety is imperative. Despite significant strides toward safety alignment, recent work GCG~zou2023universal proposes a discrete token optimization algorithm and selects the single suffix with the lowest loss to successfully jailbreak aligned LLMs. In this work, we first discuss the drawbacks of solely picking the suffix with the lowest loss during GCG optimization for jailbreaking and uncover the missed successful suffixes during the intermediate steps. Moreover, we utilize those successful suffixes as training data to learn a generative model, named AmpleGCG, which captures the distribution of adversarial suffixes given a harmful query and enables the rapid generation of hundreds of suffixes for any harmful queries in seconds. AmpleGCG achieves near 100\% attack success rate (ASR) on two aligned LLMs (Llama-2-7B-chat and Vicuna-7B), surpassing two strongest attack baselines. More interestingly, AmpleGCG also transfers seamlessly to attack different models, including closed-source LLMs, achieving a 99\% ASR on the latest GPT-3.5. To summarize, our work amplifies the impact of GCG by training a generative model of adversarial suffixes that is universal to any harmful queries and transferable from attacking open-source LLMs to closed-source LLMs. In addition, it can generate 200 adversarial suffixes for one harmful query in only 4 seconds, rendering it more challenging to defend.

Formal theorem proving (FTP) has emerged as a critical foundation for evaluating the reasoning capabilities of large language models, enabling automated verification of mathematical proofs at scale. However, progress has been constrained by limited datasets due to the high cost of manual curation and the scarcity of challenging problems with verified formal-informal correspondences. We propose leveraging theoretical computer science (TCS) as a scalable source of rigorous proof problems, where algorithmic definitions enable automated generation of arbitrarily many challenging theorem-proof pairs. We demonstrate this approach on two TCS domains: Busy Beaver problems, which involve proving bounds on Turing machine halting behavior, and Mixed Boolean Arithmetic problems, which combine logical and arithmetic reasoning. Our framework automatically synthesizes problems with parallel formal (Lean4) and informal (Markdown) specifications, creating a scalable pipeline for generating verified proof challenges. Evaluation on frontier models reveals substantial gaps in automated theorem proving: while DeepSeekProver-V2-671B achieves 57.5\% success on Busy Beaver problems, it manages only 12\% on Mixed Boolean Arithmetic problems. These results highlight the difficulty of long-form proof generation even for problems that are computationally easy to verify, demonstrating the value of TCS domains for advancing automated reasoning research.

In arbitrary-order language models, it is an open question how to sample tokens in parallel from the correct joint distribution. With discrete diffusion models, the more tokens they generate in parallel, the less their predicted distributions adhere to the originally learned data distribution, as they rely on a conditional independence assumption that only works with infinitesimally small timesteps. We find that a different class of models, any-subset autoregressive models (AS-ARMs), holds the solution. As implied by the name, AS-ARMs can generate tokens in any order, and in parallel. Moreover, AS-ARMs support parallelized joint probability density estimation, allowing them to correct their own parallel-generated token distributions, via our Any-Subset Speculative Decoding (ASSD) algorithm. ASSD provably enables generation of tokens from the correct joint distribution, with the number of neural network calls upper bounded by the number of tokens predicted. We empirically verify that ASSD speeds up language generation, without sacrificing quality. Furthermore, we provide a mathematically justified scheme for training AS-ARMs for generation, and show that AS-ARMs achieve state-of-the-art performance among sub-200M parameter models on infilling benchmark tasks, and nearly match the performance of models 50X larger on code generation. Our theoretical and empirical results indicate that the once-forgotten AS-ARMs are a promising direction of language modeling.

We study the code generation behavior of instruction-tuned models built on top of code pre-trained language models when they could access an auxiliary function to implement a function. We design several ways to provide auxiliary functions to the models by adding them to the query or providing a response prefix to incorporate the ability to utilize auxiliary functions with the instruction-following capability. Our experimental results show the effectiveness of combining the base models' auxiliary function utilization ability with the instruction following ability. In particular, the performance of adopting our approaches with the open-sourced language models surpasses that of the recent powerful proprietary language models, i.e., gpt-4o.

Large Language Models (LLMs) exhibit strong but shallow alignment: they directly refuse harmful queries when a refusal is expected at the very start of an assistant turn, yet this protection collapses once a harmful continuation is underway (either through the adversarial attacks or via harmful assistant-prefill attacks). This raises a fundamental question: Can the innate shallow alignment in LLMs be unlocked to ensure safety at arbitrary generation depths? To achieve this goal, we propose Any-Depth Alignment (ADA), an effective inference-time defense with negligible overhead. ADA is built based on our observation that alignment is concentrated in the assistant header tokens through repeated use in shallow-refusal training, and these tokens possess the model's strong alignment priors. By reintroducing these tokens mid-stream, ADA induces the model to reassess harmfulness and recover refusals at any point in generation. Across diverse open-source model families (Llama, Gemma, Mistral, Qwen, DeepSeek, and gpt-oss), ADA achieves robust safety performance without requiring any changes to the base model's parameters. It secures a near-100% refusal rate against challenging adversarial prefill attacks ranging from dozens to thousands of tokens. Furthermore, ADA reduces the average success rate of prominent adversarial prompt attacks (such as GCG, AutoDAN, PAIR, and TAP) to below 3%. This is all accomplished while preserving utility on benign tasks with minimal over-refusal. ADA maintains this resilience even after the base model undergoes subsequent instruction tuning (benign or adversarial).

The Game of Life (Life), a well known algorithm within the broader class of cellular automata (CA), exhibits complex emergent dynamics, with extreme sensitivity to initial conditions. Modeling and predicting such intricate behavior without explicit knowledge of the system's underlying topology presents a significant challenge, motivating the development of algorithms that can generalize across various grid configurations and boundary conditions. We develop a decoder-only generative pretrained transformer model to solve this problem, showing that our model can simulate Life on a toroidal grid with no prior knowledge on the size of the grid, or its periodic boundary conditions (LifeGPT). LifeGPT is topology-agnostic with respect to its training data and our results show that a GPT model is capable of capturing the deterministic rules of a Turing-complete system with near-perfect accuracy, given sufficiently diverse training data. We also introduce the idea of an `autoregressive autoregressor' to recursively implement Life using LifeGPT. Our results pave the path towards true universal computation within a large language model (LLM) framework, synthesizing of mathematical analysis with natural language processing, and probing AI systems for situational awareness about the evolution of such algorithms without ever having to compute them. Similar GPTs could potentially solve inverse problems in multicellular self-assembly by extracting CA-compatible rulesets from real-world biological systems to create new predictive models, which would have significant consequences for the fields of bioinspired materials, tissue engineering, and architected materials design.

Recent research has shown that Large Language Models (LLMs) are vulnerable to automated jailbreak attacks, where adversarial suffixes crafted by algorithms appended to harmful queries bypass safety alignment and trigger unintended responses. Current methods for generating these suffixes are computationally expensive and have low Attack Success Rates (ASR), especially against well-aligned models like Llama2 and Llama3. To overcome these limitations, we introduce ADV-LLM, an iterative self-tuning process that crafts adversarial LLMs with enhanced jailbreak ability. Our framework significantly reduces the computational cost of generating adversarial suffixes while achieving nearly 100\% ASR on various open-source LLMs. Moreover, it exhibits strong attack transferability to closed-source models, achieving 99\% ASR on GPT-3.5 and 49\% ASR on GPT-4, despite being optimized solely on Llama3. Beyond improving jailbreak ability, ADV-LLM provides valuable insights for future safety alignment research through its ability to generate large datasets for studying LLM safety.

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

The application of large-language models (LLMs) to digital hardware code generation is an emerging field. Most LLMs are primarily trained on natural language and software code. Hardware code, such as Verilog, represents only a small portion of the training data and few hardware benchmarks exist. To address this gap, the open-source VerilogEval benchmark was released in 2023, providing a consistent evaluation framework for LLMs on code completion tasks. It was tested on state-of-the-art models at the time including GPT-4. However, VerilogEval and other Verilog generation benchmarks lack failure analysis and, in present form, are not conducive to exploring prompting techniques. Also, since VerilogEval's release, both commercial and open-source models have seen continued development. In this work, we evaluate new commercial and open-source models of varying sizes against an improved VerilogEval benchmark suite. We enhance VerilogEval's infrastructure and dataset by automatically classifying failures, introduce new prompts for supporting in-context learning (ICL) examples, and extend the supported tasks to specification-to-RTL translation. We find a measurable improvement in commercial state-of-the-art models, with GPT-4 Turbo achieving a 59% pass rate on spec-to-RTL tasks. We also study the performance of open-source and domain-specific models that have emerged, and demonstrate that models can benefit substantially from ICL. We find that recently-released Llama 3.1 405B achieves a pass rate of 58%, effectively matching that of GPT-4 Turbo, and that the much smaller domain-specific RTL-Coder 6.7B models achieve an impressive 37% pass rate. However, prompt engineering is key to achieving good pass rates, and varies widely with model and task. A benchmark infrastructure that allows for prompt engineering and failure analysis is key to continued model development and deployment.

Autoregressive models (ARMs), which predict subsequent tokens one-by-one ``from left to right,'' have achieved significant success across a wide range of sequence generation tasks. However, they struggle to accurately represent sequences that require satisfying sophisticated constraints or whose sequential dependencies are better addressed by out-of-order generation. Masked Diffusion Models (MDMs) address some of these limitations, but the process of unmasking multiple tokens simultaneously in MDMs can introduce incoherences, and MDMs cannot handle arbitrary infilling constraints when the number of tokens to be filled in is not known in advance. In this work, we introduce Insertion Language Models (ILMs), which learn to insert tokens at arbitrary positions in a sequence -- that is, they select jointly both the position and the vocabulary element to be inserted. By inserting tokens one at a time, ILMs can represent strong dependencies between tokens, and their ability to generate sequences in arbitrary order allows them to accurately model sequences where token dependencies do not follow a left-to-right sequential structure. To train ILMs, we propose a tailored network parameterization and use a simple denoising objective. Our empirical evaluation demonstrates that ILMs outperform both ARMs and MDMs on common planning tasks. Furthermore, we show that ILMs outperform MDMs and perform on par with ARMs in an unconditional text generation task while offering greater flexibility than MDMs in arbitrary-length text infilling.

We present Prover Agent, a novel AI agent for automated theorem proving that integrates large language models (LLMs) with a formal proof assistant, Lean. Prover Agent coordinates an informal reasoning LLM, a formal prover model, and feedback from Lean while also generating auxiliary lemmas. These auxiliary lemmas are not limited to subgoals in the formal proof but can also include special cases or potentially useful facts derived from the assumptions, which help in discovering a viable proof strategy. It achieves an 88.1% success rate on the MiniF2F benchmark, establishing a new state-of-the-art among methods using small language models (SLMs) with a much lower sample budget than previous approaches. We also present theoretical analyses and case studies that illustrate how these generated lemmas contribute to solving challenging problems. Our code is publicly available at: https://github.com/kAIto47802/Prover-Agent.

We explore the application of transformer-based language models to automated theorem proving. This work is motivated by the possibility that a major limitation of automated theorem provers compared to humans -- the generation of original mathematical terms -- might be addressable via generation from language models. We present an automated prover and proof assistant, GPT-f, for the Metamath formalization language, and analyze its performance. GPT-f found new short proofs that were accepted into the main Metamath library, which is to our knowledge, the first time a deep-learning based system has contributed proofs that were adopted by a formal mathematics community.

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

Recent large-scale neural autoregressive sequence models have shown impressive performances on a variety of natural language generation tasks. However, their generated sequences often exhibit degenerate properties such as non-termination, undesirable repetition, and premature termination, when generated with decoding algorithms such as greedy search, beam search, top-k sampling, and nucleus sampling. In this paper, we focus on the problem of non-terminating sequences resulting from an incomplete decoding algorithm. We first define an incomplete probable decoding algorithm which includes greedy search, top-k sampling, and nucleus sampling, beyond the incomplete decoding algorithm originally put forward by Welleck et al. (2020). We then propose a non-monotonic self-terminating language model, which significantly relaxes the constraint of monotonically increasing termination probability in the originally proposed self-terminating language model by Welleck et al. (2020), to address the issue of non-terminating sequences when using incomplete probable decoding algorithms. We prove that our proposed model prevents non-terminating sequences when using not only incomplete probable decoding algorithms but also beam search. We empirically validate our model on sequence completion tasks with various architectures.

We study suffix-based jailbreaksx2013a powerful family of attacks against large language models (LLMs) that optimize adversarial suffixes to circumvent safety alignment. Focusing on the widely used foundational GCG attack (Zou et al., 2023), we observe that suffixes vary in efficacy: some markedly more universalx2013generalizing to many unseen harmful instructionsx2013than others. We first show that GCG's effectiveness is driven by a shallow, critical mechanism, built on the information flow from the adversarial suffix to the final chat template tokens before generation. Quantifying the dominance of this mechanism during generation, we find GCG irregularly and aggressively hijacks the contextualization process. Crucially, we tie hijacking to the universality phenomenon, with more universal suffixes being stronger hijackers. Subsequently, we show that these insights have practical implications: GCG universality can be efficiently enhanced (up to times5 in some cases) at no additional computational cost, and can also be surgically mitigated, at least halving attack success with minimal utility loss. We release our code and data at http://github.com/matanbt/interp-jailbreak.

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

Byte Pair Encoding (BPE) tokenizers, widely used in Large Language Models, face challenges in multilingual settings, including penalization of non-Western scripts and the creation of tokens with partial UTF-8 sequences. Pretokenization, often reliant on complex regular expressions, can also introduce fragility and unexpected edge cases. We propose SCRIPT (Script Category Representation in PreTokenization), a novel encoding scheme that bypasses UTF-8 byte conversion by using initial tokens based on Unicode script and category properties. This approach enables a simple, rule-based pretokenization strategy that respects script boundaries, offering a robust alternative to pretokenization strategies based on regular expressions. We also introduce and validate a constrained BPE merging strategy that enforces character integrity, applicable to both SCRIPT-BPE and byte-based BPE. Our experiments demonstrate that SCRIPT-BPE achieves competitive compression while eliminating encoding-based penalties for non-Latin-script languages.

Auxiliary function is a helpful component to improve language model's code generation ability. However, a systematic exploration of how they affect has yet to be done. In this work, we comprehensively evaluate the ability to utilize auxiliary functions encoded in recent code-pretrained language models. First, we construct a human-crafted evaluation set, called HumanExtension, which contains examples of two functions where one function assists the other. With HumanExtension, we design several experiments to examine their ability in a multifaceted way. Our evaluation processes enable a comprehensive understanding of including auxiliary functions in the prompt in terms of effectiveness and robustness. An additional implementation style analysis captures the models' various implementation patterns when they access the auxiliary function. Through this analysis, we discover the models' promising ability to utilize auxiliary functions including their self-improving behavior by implementing the two functions step-by-step. However, our analysis also reveals the model's underutilized behavior to call the auxiliary function, suggesting the future direction to enhance their implementation by eliciting the auxiliary function call ability encoded in the models. We release our code and dataset to facilitate this research direction.

Because "out-of-the-box" large language models are capable of generating a great deal of objectionable content, recent work has focused on aligning these models in an attempt to prevent undesirable generation. While there has been some success at circumventing these measures -- so-called "jailbreaks" against LLMs -- these attacks have required significant human ingenuity and are brittle in practice. In this paper, we propose a simple and effective attack method that causes aligned language models to generate objectionable behaviors. Specifically, our approach finds a suffix that, when attached to a wide range of queries for an LLM to produce objectionable content, aims to maximize the probability that the model produces an affirmative response (rather than refusing to answer). However, instead of relying on manual engineering, our approach automatically produces these adversarial suffixes by a combination of greedy and gradient-based search techniques, and also improves over past automatic prompt generation methods. Surprisingly, we find that the adversarial prompts generated by our approach are quite transferable, including to black-box, publicly released LLMs. Specifically, we train an adversarial attack suffix on multiple prompts (i.e., queries asking for many different types of objectionable content), as well as multiple models (in our case, Vicuna-7B and 13B). When doing so, the resulting attack suffix is able to induce objectionable content in the public interfaces to ChatGPT, Bard, and Claude, as well as open source LLMs such as LLaMA-2-Chat, Pythia, Falcon, and others. In total, this work significantly advances the state-of-the-art in adversarial attacks against aligned language models, raising important questions about how such systems can be prevented from producing objectionable information. Code is available at github.com/llm-attacks/llm-attacks.

We report a peculiar observation that LLMs can assign hidden meanings to sequences that seem visually incomprehensible to humans: for example, a nonsensical phrase consisting of Byzantine musical symbols is recognized by gpt-4o as "say abracadabra". Moreover, some models can communicate using these sequences. Some of these meanings are hypothesized to partly originate in the massive spurious correlations due to BPE tokenization. We systematically evaluate the presence of such abilities in a wide range of models: Claude-3.5 Haiku, Claude-3.5 Sonnet (New and Old), Claude-3.7 Sonnet, gpt-4o mini, gpt-4o, o1-mini, Llama-3.3 70B, DeepSeek-R1-Distill-Lllama 70B, Qwen2.5 1.5B, Qwen2.5 32B, Phi-3.5 mini, GigaChat-Max, Vikhr-Llama-3.2 1B. We argue that this observation might have far-reaching consequences for both safety and security of the modern and future LLMs and systems that employ them. As an illustration, we show that applying this method in combination with simple templates is sufficient to jailbreak previous generation models, with ASR = 0.4 on gpt-4o mini. Our code and data artifacts are available at https://github.com/L3G5/llm-hidden-meanings

The Automunge open source python library platform for tabular data pre-processing automates feature engineering data transformations of numerical encoding and missing data infill to received tidy data on bases fit to properties of columns in a designated train set for consistent and efficient application to subsequent data pipelines such as for inference, where transformations may be applied to distinct columns in "family tree" sets with generations and branches of derivations. Included in the library of transformations are methods to extract structure from bounded categorical string sets by way of automated string parsing, in which comparisons between entries in the set of unique values are parsed to identify character subset overlaps which may be encoded by appended columns of boolean overlap detection activations or by replacing string entries with identified overlap partitions. Further string parsing options, which may also be applied to unbounded categoric sets, include extraction of numeric substring partitions from entries or search functions to identify presence of specified substring partitions. The aggregation of these methods into "family tree" sets of transformations are demonstrated for use to automatically extract structure from categoric string compositions in relation to the set of entries in a column, such as may be applied to prepare categoric string set encodings for machine learning without human intervention.

We present MIPS, a novel method for program synthesis based on automated mechanistic interpretability of neural networks trained to perform the desired task, auto-distilling the learned algorithm into Python code. We test MIPS on a benchmark of 62 algorithmic tasks that can be learned by an RNN and find it highly complementary to GPT-4: MIPS solves 32 of them, including 13 that are not solved by GPT-4 (which also solves 30). MIPS uses an integer autoencoder to convert the RNN into a finite state machine, then applies Boolean or integer symbolic regression to capture the learned algorithm. As opposed to large language models, this program synthesis technique makes no use of (and is therefore not limited by) human training data such as algorithms and code from GitHub. We discuss opportunities and challenges for scaling up this approach to make machine-learned models more interpretable and trustworthy.

The most fundamental capability of modern AI methods such as Large Language Models (LLMs) is the ability to predict the next token in a long sequence of tokens, known as ``sequence modeling." Although the Transformers model is the current dominant approach to sequence modeling, its quadratic computational cost with respect to sequence length is a significant drawback. State-space models (SSMs) offer a promising alternative due to their linear decoding efficiency and high parallelizability during training. However, existing SSMs often rely on seemingly ad hoc linear recurrence designs. In this work, we explore SSM design through the lens of online learning, conceptualizing SSMs as meta-modules for specific online learning problems. This approach links SSM design to formulating precise online learning objectives, with state transition rules derived from optimizing these objectives. Based on this insight, we introduce a novel deep SSM architecture based on the implicit update for optimizing an online regression objective. Our experimental results show that our models outperform state-of-the-art SSMs, including the Mamba model, on standard sequence modeling benchmarks and language modeling tasks.

Code benchmarks such as HumanEval are widely adopted to evaluate the capabilities of Large Language Models (LLMs), providing insights into their strengths and weaknesses. However, current benchmarks primarily exercise LLMs' capability on common coding tasks (e.g., bubble sort, greatest common divisor), leaving domain-specific coding tasks (e.g., computation, system, cryptography) unexplored. To fill this gap, we propose a multi-domain code benchmark, DOMAINEVAL, designed to evaluate LLMs' coding capabilities thoroughly. Our pipeline works in a fully automated manner, enabling a push-bottom construction from code repositories into formatted subjects under study. Interesting findings are observed by evaluating 12 representative LLMs against DOMAINEVAL. We notice that LLMs are generally good at computation tasks while falling short on cryptography and system coding tasks. The performance gap can be as much as 68.94% (80.94% - 12.0%) in some LLMs. We also observe that generating more samples can increase the overall performance of LLMs, while the domain bias may even increase. The contributions of this study include a code generation benchmark dataset DOMAINEVAL, encompassing six popular domains, a fully automated pipeline for constructing code benchmarks, and an identification of the limitations of LLMs in code generation tasks based on their performance on DOMAINEVAL, providing directions for future research improvements. The leaderboard is available at https://domaineval.github.io/.

Length generalization refers to the ability to extrapolate from short training sequences to long test sequences and is a challenge for current large language models. While prior work has proposed some architecture or data format changes to achieve length generalization, these proposals typically apply to a limited set of tasks. Building on prior scratchpad and Chain-of-Thought (CoT) techniques, we propose Turing Programs, a novel CoT strategy that decomposes an algorithmic task into steps mimicking the computation of a Turing Machine. This framework is both universal, as it can accommodate any algorithmic task, and simple, requiring only copying text from the context with small modifications. We show that by using Turing Programs, we obtain robust length generalization on a range of algorithmic tasks: addition, multiplication and in-context SGD. We then demonstrate that transformers achieve length generalization on random Turing Programs, suggesting that length generalization is possible for any algorithmic task. Finally, we theoretically prove that transformers can implement Turing Programs, constructing a simple RASP (Weiss et al.) program that simulates an arbitrary Turing machine.

Automated Theorem Proving (ATP) in formal languages is a foundational challenge for AI. While Large Language Models (LLMs) have driven remarkable progress, a significant gap remains between their powerful informal reasoning capabilities and their weak formal proving performance. Recent studies show that the informal accuracy exceeds 80% while formal success remains below 8% on benchmarks like PutnamBench. We argue this gap persists because current state-of-the-art provers, by tightly coupling reasoning and proving, are trained with paradigms that inadvertently punish deep reasoning in favor of shallow, tactic-based strategies. To bridge this fundamental gap, we propose a novel framework that decouples high-level reasoning from low-level proof generation. Our approach utilizes two distinct, specialized models: a powerful, general-purpose Reasoner to generate diverse, strategic subgoal lemmas, and an efficient Prover to rigorously verify them. This modular design liberates the model's full reasoning potential and bypasses the pitfalls of end-to-end training. We evaluate our method on a challenging set of post-2000 IMO problems, a problem set on which no prior open-source prover has reported success. Our decoupled framework successfully solves 5 of these problems, demonstrating a significant step towards automated reasoning on exceptionally difficult mathematical challenges. To foster future research, we release our full dataset of generated and verified lemmas for a wide range of IMO problems, available at https://tencent-imo.github.io/ .

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

We continue the study of the virtual large cardinal hierarchy by analysing virtual versions of superstrong, Woodin, and Berkeley cardinals. Gitman and Schindler showed that virtualizations of strong and supercompact cardinals yield the same large cardinal notion. We provide various equivalent characterizations of virtually Woodin cardinals, including showing that On is virtually Woodin if and only if for every class A, there is a proper class of virtually A-extendible cardinals. We introduce the virtual Vopenka principle for finite languages and show that it is not equivalent to the virtual Vopenka principle (although the two principles are equiconsistent), but is equivalent to the assertion that On is virtually pre-Woodin, a weakening of virtually Woodin, which is equivalent to having for every class A, a weakly virtually A-extendible cardinal. We show that if there are no virtually Berkeley cardinals, then On is virtually Woodin if and only if On is virtually pre-Woodin (if and only if the virtual Vopenka principle for finite languages holds). In particular, if the virtual Vopenka principle holds and On is not Mahlo, then On is not virtually Woodin, and hence there is a virtually Berkeley cardinal.

The rapid advancement of large language models (LLMs) has revolutionized code generation tasks across various programming languages. However, the unique characteristics of programming languages, particularly those like Verilog with specific syntax and lower representation in training datasets, pose significant challenges for conventional tokenization and decoding approaches. In this paper, we introduce a novel application of speculative decoding for Verilog code generation, showing that it can improve both inference speed and output quality, effectively achieving speed and quality all in one. Unlike standard LLM tokenization schemes, which often fragment meaningful code structures, our approach aligns decoding stops with syntactically significant tokens, making it easier for models to learn the token distribution. This refinement addresses inherent tokenization issues and enhances the model's ability to capture Verilog's logical constructs more effectively. Our experimental results show that our method achieves up to a 5.05x speedup in Verilog code generation and increases pass@10 functional accuracy on RTLLM by up to 17.19% compared to conventional training strategies. These findings highlight speculative decoding as a promising approach to bridge the quality gap in code generation for specialized programming languages.

The performance of large language models (LLMs) in program synthesis and mathematical reasoning is fundamentally limited by the quality of their pre-training corpora. We introduce two openly licensed datasets, released under the Llama 3.3 Community License, that significantly enhance LLM performance by systematically rewriting public data. SwallowCode (approximately 16.1 billion tokens) refines Python snippets from The-Stack-v2 through a novel four-stage pipeline: syntax validation, pylint-based style filtering, and a two-stage LLM rewriting process that enforces style conformity and transforms snippets into self-contained, algorithmically efficient examples. Unlike prior methods that rely on exclusionary filtering or limited transformations, our transform-and-retain approach upgrades low-quality code, maximizing data utility. SwallowMath (approximately 2.3 billion tokens) enhances Finemath-4+ by removing boilerplate, restoring context, and reformatting solutions into concise, step-by-step explanations. Within a fixed 50 billion token training budget, continual pre-training of Llama-3.1-8B with SwallowCode boosts pass@1 by +17.0 on HumanEval and +17.7 on HumanEval+ compared to Stack-Edu, surpassing the baseline model's code generation capabilities. Similarly, substituting SwallowMath yields +12.4 accuracy on GSM8K and +7.6 on MATH. Ablation studies confirm that each pipeline stage contributes incrementally, with rewriting delivering the largest gains. All datasets, prompts, and checkpoints are publicly available, enabling reproducible research and advancing LLM pre-training for specialized domains.

Large Language Models (LLM) based agents have shown promise in autonomously completing tasks across various domains, e.g., robotics, games, and web navigation. However, these agents typically require elaborate design and expert prompts to solve tasks in specific domains, which limits their adaptability. We introduce AutoManual, a framework enabling LLM agents to autonomously build their understanding through interaction and adapt to new environments. AutoManual categorizes environmental knowledge into diverse rules and optimizes them in an online fashion by two agents: 1) The Planner codes actionable plans based on current rules for interacting with the environment. 2) The Builder updates the rules through a well-structured rule system that facilitates online rule management and essential detail retention. To mitigate hallucinations in managing rules, we introduce a *case-conditioned prompting* strategy for the Builder. Finally, the Formulator agent compiles these rules into a comprehensive manual. The self-generated manual can not only improve the adaptability but also guide the planning of smaller LLMs while being human-readable. Given only one simple demonstration, AutoManual significantly improves task success rates, achieving 97.4\% with GPT-4-turbo and 86.2\% with GPT-3.5-turbo on ALFWorld benchmark tasks. The code is available at https://github.com/minghchen/automanual.

The popularity of the Rust language continues to explode; yet, many critical codebases remain authored in C, and cannot be realistically rewritten by hand. Automatically translating C to Rust is thus an appealing course of action. Several works have gone down this path, handling an ever-increasing subset of C through a variety of Rust features, such as unsafe. While the prospect of automation is appealing, producing code that relies on unsafe negates the memory safety guarantees offered by Rust, and therefore the main advantages of porting existing codebases to memory-safe languages. We instead explore a different path, and explore what it would take to translate C to safe Rust; that is, to produce code that is trivially memory safe, because it abides by Rust's type system without caveats. Our work sports several original contributions: a type-directed translation from (a subset of) C to safe Rust; a novel static analysis based on "split trees" that allows expressing C's pointer arithmetic using Rust's slices and splitting operations; an analysis that infers exactly which borrows need to be mutable; and a compilation strategy for C's struct types that is compatible with Rust's distinction between non-owned and owned allocations. We apply our methodology to existing formally verified C codebases: the HACL* cryptographic library, and binary parsers and serializers from EverParse, and show that the subset of C we support is sufficient to translate both applications to safe Rust. Our evaluation shows that for the few places that do violate Rust's aliasing discipline, automated, surgical rewrites suffice; and that the few strategic copies we insert have a negligible performance impact. Of particular note, the application of our approach to HACL* results in a 80,000 line verified cryptographic library, written in pure Rust, that implements all modern algorithms - the first of its kind.

Recent work has developed optimization procedures to find token sequences, called adversarial triggers, which can elicit unsafe responses from aligned language models. These triggers are believed to be universally transferable, i.e., a trigger optimized on one model can jailbreak other models. In this paper, we concretely show that such adversarial triggers are not universal. We extensively investigate trigger transfer amongst 13 open models and observe inconsistent transfer. Our experiments further reveal a significant difference in robustness to adversarial triggers between models Aligned by Preference Optimization (APO) and models Aligned by Fine-Tuning (AFT). We find that APO models are extremely hard to jailbreak even when the trigger is optimized directly on the model. On the other hand, while AFT models may appear safe on the surface, exhibiting refusals to a range of unsafe instructions, we show that they are highly susceptible to adversarial triggers. Lastly, we observe that most triggers optimized on AFT models also generalize to new unsafe instructions from five diverse domains, further emphasizing their vulnerability. Overall, our work highlights the need for more comprehensive safety evaluations for aligned language models.

Language agents powered by large language models (LLMs) have seen exploding development. Their capability of using language as a vehicle for thought and communication lends an incredible level of flexibility and versatility. People have quickly capitalized on this capability to connect LLMs to a wide range of external components and environments: databases, tools, the Internet, robotic embodiment, etc. Many believe an unprecedentedly powerful automation technology is emerging. However, new automation technologies come with new safety risks, especially for intricate systems like language agents. There is a surprisingly large gap between the speed and scale of their development and deployment and our understanding of their safety risks. Are we building a house of cards? In this position paper, we present the first systematic effort in mapping adversarial attacks against language agents. We first present a unified conceptual framework for agents with three major components: Perception, Brain, and Action. Under this framework, we present a comprehensive discussion and propose 12 potential attack scenarios against different components of an agent, covering different attack strategies (e.g., input manipulation, adversarial demonstrations, jailbreaking, backdoors). We also draw connections to successful attack strategies previously applied to LLMs. We emphasize the urgency to gain a thorough understanding of language agent risks before their widespread deployment.

Conversational large language models are fine-tuned for both instruction-following and safety, resulting in models that obey benign requests but refuse harmful ones. While this refusal behavior is widespread across chat models, its underlying mechanisms remain poorly understood. In this work, we show that refusal is mediated by a one-dimensional subspace, across 13 popular open-source chat models up to 72B parameters in size. Specifically, for each model, we find a single direction such that erasing this direction from the model's residual stream activations prevents it from refusing harmful instructions, while adding this direction elicits refusal on even harmless instructions. Leveraging this insight, we propose a novel white-box jailbreak method that surgically disables refusal with minimal effect on other capabilities. Finally, we mechanistically analyze how adversarial suffixes suppress propagation of the refusal-mediating direction. Our findings underscore the brittleness of current safety fine-tuning methods. More broadly, our work showcases how an understanding of model internals can be leveraged to develop practical methods for controlling model behavior.

The increasing complexity and high costs associated with modern processor design have led to a surge in demand for processor design automation. Instruction-tuned large language models (LLMs) have demonstrated remarkable performance in automatically generating code for general-purpose programming languages like Python. However, these methods fail on hardware description languages (HDLs) like Verilog due to the scarcity of high-quality instruction tuning data, as even advanced LLMs like GPT-3.5 exhibit limited performance on Verilog generation. Regarding this issue, we observe that (1) Verilog code collected from the real world has higher quality than those generated by LLMs. (2) LLMs like GPT-3.5 excel in summarizing Verilog code rather than generating it. Based on these observations, this paper introduces CodeV, a series of open-source instruction-tuned Verilog generation LLMs. Instead of generating descriptions first and then getting the corresponding code from advanced LLMs, we prompt the LLM with Verilog code and let the LLM generate the corresponding natural language description by multi-level summarization. Experimental results show that CodeV relatively surpasses the previous open-source SOTA by 14.4% (BetterV in VerilogEval) and 11.3% (RTLCoder in RTLLM) respectively, and also relatively outperforms previous commercial SOTA GPT-4 by 22.1% in VerilogEval.

Speculative decoding is a technique to leverage hardware concurrency to improve the efficiency of large-scale autoregressive (AR) Transformer models by enabling multiple steps of token generation in a single forward pass. State-space models (SSMs) are already more efficient than AR Transformers, since their state summarizes all past data with no need to cache or re-process tokens in the sliding window context. However, their state can also comprise thousands of tokens; so, speculative decoding has recently been extended to SSMs. Existing approaches, however, do not leverage the tree-based verification methods, since current SSMs lack the means to compute a token tree efficiently. We propose the first scalable algorithm to perform tree-based speculative decoding in state-space models (SSMs) and hybrid architectures of SSMs and Transformer layers. We exploit the structure of accumulated state transition matrices to facilitate tree-based speculative decoding with minimal overhead to current SSM state update implementations. With the algorithm, we describe a hardware-aware implementation that improves naive application of AR Transformer tree-based speculative decoding methods to SSMs. Furthermore, we outperform vanilla speculative decoding with SSMs even with a baseline drafting model and tree structure on three different benchmarks, opening up opportunities for further speed up with SSM and hybrid model inference. Code will be released upon paper acceptance.

Recent progress in large-scale language models has enabled breakthroughs in previously intractable computer programming tasks. Prior work in meta-learning and neural architecture search has led to substantial successes across various task domains, spawning myriad approaches for algorithmically optimizing the design and learning dynamics of deep learning models. At the intersection of these research areas, we implement a code-generating language model with the ability to modify its own source code. Self-programming AI algorithms have been of interest since the dawn of AI itself. Although various theoretical formulations of generalized self-programming AI have been posed, no such system has been successfully implemented to date under real-world computational constraints. Applying AI-based code generation to AI itself, we develop and experimentally validate the first practical implementation of a self-programming AI system. We empirically show that a self-programming AI implemented using a code generation model can successfully modify its own source code to improve performance and program sub-models to perform auxiliary tasks. Our model can self-modify various properties including model architecture, computational capacity, and learning dynamics.

During Automated Program Repair (APR), it can be challenging to synthesize correct patches for real-world systems in general-purpose programming languages. Recent Large Language Models (LLMs) have been shown to be helpful "copilots" in assisting developers with various coding tasks, and have also been directly applied for patch synthesis. However, most LLMs treat programs as sequences of tokens, meaning that they are ignorant of the underlying semantics constraints of the target programming language. This results in plenty of statically invalid generated patches, impeding the practicality of the technique. Therefore, we propose Repilot, a framework to further copilot the AI "copilots" (i.e., LLMs) by synthesizing more valid patches during the repair process. Our key insight is that many LLMs produce outputs autoregressively (i.e., token by token), resembling human writing programs, which can be significantly boosted and guided through a Completion Engine. Repilot synergistically synthesizes a candidate patch through the interaction between an LLM and a Completion Engine, which 1) prunes away infeasible tokens suggested by the LLM and 2) proactively completes the token based on the suggestions provided by the Completion Engine. Our evaluation on a subset of the widely-used Defects4j 1.2 and 2.0 datasets shows that Repilot fixes 66 and 50 bugs, respectively, surpassing the best-performing baseline by 14 and 16 bugs fixed. More importantly, Repilot is capable of producing more valid and correct patches than the base LLM when given the same generation budget.

Following the advancement of large language models (LLMs), the development of LLM-based autonomous agents has become increasingly prevalent. As a result, the need to understand the security vulnerabilities of these agents has become a critical task. We examine how ReAct agents can be exploited using a straightforward yet effective method we refer to as the foot-in-the-door attack. Our experiments show that indirect prompt injection attacks, prompted by harmless and unrelated requests (such as basic calculations) can significantly increase the likelihood of the agent performing subsequent malicious actions. Our results show that once a ReAct agents thought includes a specific tool or action, the likelihood of executing this tool in the subsequent steps increases significantly, as the agent seldom re-evaluates its actions. Consequently, even random, harmless requests can establish a foot-in-the-door, allowing an attacker to embed malicious instructions into the agents thought process, making it more susceptible to harmful directives. To mitigate this vulnerability, we propose implementing a simple reflection mechanism that prompts the agent to reassess the safety of its actions during execution, which can help reduce the success of such attacks.

Language agents have achieved considerable performance on various complex tasks. Despite the incessant exploration in this field, existing language agent systems still struggle with costly, non-reproducible data reliance and face the challenge of compelling a single model for multiple functions. To this end, we introduce AutoAct, an automatic agent learning framework that does not rely on large-scale annotated data and synthetic trajectories from closed-source models (e.g., GPT-4). Given limited data with a tool library, AutoAct first automatically synthesizes planning trajectories without any assistance from humans or strong closed-source models. Then, AutoAct leverages a division-of-labor strategy to automatically differentiate based on the target task information and synthesized trajectories, producing a sub-agent group to complete the task. We conduct comprehensive experiments with different LLMs, which demonstrates that AutoAct yields better or parallel performance compared to various strong baselines. We even notice that AutoAct, when using the Llama-2-13b model, can achieve performance comparable to that of the GPT-3.5-Turbo agent. Code will be available at https://github.com/zjunlp/AutoAct.

Recently, there has been a growing interest in leveraging Large Language Models for Verilog code generation. However, the current quality of the generated Verilog code remains suboptimal. This is largely due to the absence of well-defined, well-organized datasets with high-quality samples, as well as a lack of innovative fine-tuning methods and models specifically trained on Verilog. In this paper, we introduce a novel open-source dataset and a corresponding fine-tuning technique, which utilizes a multi-layered structure that we refer to as PyraNet. Our experiments demonstrate that employing the proposed dataset and fine-tuning approach leads to a more accurate fine-tuned model, producing syntactically and functionally correct Verilog code. The evaluation results show improvements by up-to 32.6% in comparison to the CodeLlama-7B baseline model and up-to 16.7% in comparison to the state-of-the-art models using VerilogEval evaluation platform.

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

With recent dramatic increases in AI system capabilities, there has been growing interest in utilizing machine learning for reasoning-heavy, quantitative tasks, particularly mathematics. While there are many resources capturing mathematics at the high-school, undergraduate, and graduate level, there are far fewer resources available that align with the level of difficulty and open endedness encountered by professional mathematicians working on open problems. To address this, we introduce a new collection of datasets, the Algebraic Combinatorics Dataset Repository (ACD Repo), representing either foundational results or open problems in algebraic combinatorics, a subfield of mathematics that studies discrete structures arising from abstract algebra. Further differentiating our dataset collection is the fact that it aims at the conjecturing process. Each dataset includes an open-ended research-level question and a large collection of examples (up to 10M in some cases) from which conjectures should be generated. We describe all nine datasets, the different ways machine learning models can be applied to them (e.g., training with narrow models followed by interpretability analysis or program synthesis with LLMs), and discuss some of the challenges involved in designing datasets like these.

Since the success of GPT, large language models (LLMs) have been revolutionizing machine learning and have initiated the so-called LLM prompting paradigm. In the era of LLMs, people train a single general-purpose LLM and provide the LLM with different prompts to perform different tasks. However, such empirical success largely lacks theoretical understanding. Here, we present the first theoretical study on the LLM prompting paradigm to the best of our knowledge. In this work, we show that prompting is in fact Turing-complete: there exists a finite-size Transformer such that for any computable function, there exists a corresponding prompt following which the Transformer computes the function. Furthermore, we show that even though we use only a single finite-size Transformer, it can still achieve nearly the same complexity bounds as that of the class of all unbounded-size Transformers. Overall, our result reveals that prompting can enable a single finite-size Transformer to be efficiently universal, which establishes a theoretical underpinning for prompt engineering in practice.

Automated Verilog code synthesis poses significant challenges and typically demands expert oversight. Traditional high-level synthesis (HLS) methods often fail to scale for real-world designs. While large language models (LLMs) have enhanced scalability, they often introduce syntactical and logical errors requiring extensive post-generation verification. Here, we introduce a novel conjunctive normal form (CNF)-guided synthesis methodology. The idea is to have an LLM generate CNF clauses, a format widely used for formal verification and synthesis validation in hardware design, but here it is used to formally describe the desired circuit functionality. These CNF specifications are then deterministically converted into Verilog, ensuring correctness by construction. Our approach fine-tunes an open-source and lightweight LLM, namely the CPU-deployable LLama-3.2-3B-Instruct model (parameters < 4B), on a dataset of standard RTL components. Experimental results demonstrate that our approach reliably produces functionally correct Verilog code on the first attempt, compared to other lightweight open-source SoTA works such as Verigen (2B parameters) and RTLCoder (4-bit quantized with around 7B parameters). We will release our method and data in full post peer-review.

Researchers are investing substantial effort in developing powerful general-purpose agents, wherein Foundation Models are used as modules within agentic systems (e.g. Chain-of-Thought, Self-Reflection, Toolformer). However, the history of machine learning teaches us that hand-designed solutions are eventually replaced by learned solutions. We formulate a new research area, Automated Design of Agentic Systems (ADAS), which aims to automatically create powerful agentic system designs, including inventing novel building blocks and/or combining them in new ways. We further demonstrate that there is an unexplored yet promising approach within ADAS where agents can be defined in code and new agents can be automatically discovered by a meta agent programming ever better ones in code. Given that programming languages are Turing Complete, this approach theoretically enables the learning of any possible agentic system: including novel prompts, tool use, control flows, and combinations thereof. We present a simple yet effective algorithm named Meta Agent Search to demonstrate this idea, where a meta agent iteratively programs interesting new agents based on an ever-growing archive of previous discoveries. Through extensive experiments across multiple domains including coding, science, and math, we show that our algorithm can progressively invent agents with novel designs that greatly outperform state-of-the-art hand-designed agents. Importantly, we consistently observe the surprising result that agents invented by Meta Agent Search maintain superior performance even when transferred across domains and models, demonstrating their robustness and generality. Provided we develop it safely, our work illustrates the potential of an exciting new research direction toward automatically designing ever-more powerful agentic systems to benefit humanity.

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.

Large Language Models (LLMs) have demonstrated remarkable capabilities across various domains, with code generation emerging as a key area of focus. While numerous benchmarks have been proposed to evaluate their code generation abilities, these benchmarks face several critical limitations. First, they often rely on manual annotations, which are time-consuming and difficult to scale across different programming languages and problem complexities. Second, most existing benchmarks focus primarily on Python, while the few multilingual benchmarks suffer from limited difficulty and uneven language distribution. To address these challenges, we propose AutoCodeGen, an automated method for generating high-difficulty multilingual code generation datasets without manual annotations. AutoCodeGen ensures the correctness and completeness of test cases by generating test inputs with LLMs and obtaining test outputs through a multilingual sandbox, while achieving high data quality through reverse-order problem generation and multiple filtering steps. Using this novel method, we introduce AutoCodeBench, a large-scale code generation benchmark comprising 3,920 problems evenly distributed across 20 programming languages. It is specifically designed to evaluate LLMs on challenging, diverse, and practical multilingual tasks. We evaluate over 30 leading open-source and proprietary LLMs on AutoCodeBench and its simplified version AutoCodeBench-Lite. The results show that even the most advanced LLMs struggle with the complexity, diversity, and multilingual nature of these tasks. Besides, we introduce AutoCodeBench-Complete, specifically designed for base models to assess their few-shot code generation capabilities. We hope the AutoCodeBench series will serve as a valuable resource and inspire the community to focus on more challenging and practical multilingual code generation scenarios.

The objective is the design of a Cellular Automata rule that can form patterns with 'touching' loops. A loop is defined as a closed path of 1-cells in a 2D grid on a zero background and with a zero border. A path cell is connected with two of its adjacent neighbors. In touching loops a path cell is also allowed to touch another on a diagonal. A CA rule was designed that can evolve stable touching loop patterns. The rule tries to cover the 2D space by overlapping tiles. The rule uses so-called templates, 5 x 5 matching patterns which are systematically derived from the given set of 3 x 3 tiles. The rule checks the pattern being evolved against a list of templates. If the outer neighbors of a template match, then the cell's state is set to the template's center value. Noise is injected if there is no matching template, or the tiles are not properly assembled. Thereby the evolution is driven to the desired loop patterns.

To fully understand the behavior of a large language model (LLM) requires our understanding of its input space. If this input space differs from our assumption, our understanding of and conclusions about the LLM is likely flawed, regardless of its architecture. Here, we elucidate the structure of the token embeddings, the input domain for LLMs, both empirically and theoretically. We present a generalized and statistically testable model where the neighborhood of each token splits into well-defined signal and noise dimensions. This model is based on a generalization of a manifold called a fiber bundle, so we denote our hypothesis test as the ``fiber bundle null.'' Failing to reject the null is uninformative, but rejecting it at a specific token indicates that token has a statistically significant local structure, and so is of interest to us. By running our test over several open-source LLMs, each with unique token embeddings, we find that the null is frequently rejected, and so the token subspace is provably not a fiber bundle and hence also not a manifold. As a consequence of our findings, when an LLM is presented with two semantically equivalent prompts, and if one prompt contains a token implicated by our test, that prompt will likely exhibit more output variability proportional to the local signal dimension of the token.

Recent progress in large language models (LLMs) like GPT-4 and PaLM-2 has brought significant advancements in addressing math reasoning problems. In particular, OpenAI's latest version of GPT-4, known as GPT-4 Code Interpreter, shows remarkable performance on challenging math datasets. In this paper, we explore the effect of code on enhancing LLMs' reasoning capability by introducing different constraints on the Code Usage Frequency of GPT-4 Code Interpreter. We found that its success can be largely attributed to its powerful skills in generating and executing code, evaluating the output of code execution, and rectifying its solution when receiving unreasonable outputs. Based on this insight, we propose a novel and effective prompting method, explicit code-based self-verification~(CSV), to further boost the mathematical reasoning potential of GPT-4 Code Interpreter. This method employs a zero-shot prompt on GPT-4 Code Interpreter to encourage it to use code to self-verify its answers. In instances where the verification state registers as ``False'', the model shall automatically amend its solution, analogous to our approach of rectifying errors during a mathematics examination. Furthermore, we recognize that the states of the verification result indicate the confidence of a solution, which can improve the effectiveness of majority voting. With GPT-4 Code Interpreter and CSV, we achieve an impressive zero-shot accuracy on MATH dataset (53.9\% to 84.3\%).

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.

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

We introduce and study the problem of adversarial arithmetic, which provides a simple yet challenging testbed for language model alignment. This problem is comprised of arithmetic questions posed in natural language, with an arbitrary adversarial string inserted before the question is complete. Even in the simple setting of 1-digit addition problems, it is easy to find adversarial prompts that make all tested models (including PaLM2, GPT4, Claude2) misbehave, and even to steer models to a particular wrong answer. We additionally provide a simple algorithm for finding successful attacks by querying those same models, which we name "prompt inversion rejection sampling" (PIRS). We finally show that models can be partially hardened against these attacks via reinforcement learning and via agentic constitutional loops. However, we were not able to make a language model fully robust against adversarial arithmetic attacks.

This paper investigates the ability of transformer-based models to learn structural recursion from examples. Recursion is a universal concept in both natural and formal languages. Structural recursion is central to the programming language and formal mathematics tasks where symbolic tools currently excel beyond neural models, such as inferring semantic relations between datatypes and emulating program behavior. We introduce a general framework that nicely connects the abstract concepts of structural recursion in the programming language domain to concrete sequence modeling problems and learned models' behavior. The framework includes a representation that captures the general syntax of structural recursion, coupled with two different frameworks for understanding their semantics -- one that is more natural from a programming languages perspective and one that helps bridge that perspective with a mechanistic understanding of the underlying transformer architecture. With our framework as a powerful conceptual tool, we identify different issues under various set-ups. The models trained to emulate recursive computations cannot fully capture the recursion yet instead fit short-cut algorithms and thus cannot solve certain edge cases that are under-represented in the training distribution. In addition, it is difficult for state-of-the-art large language models (LLMs) to mine recursive rules from in-context demonstrations. Meanwhile, these LLMs fail in interesting ways when emulating reduction (step-wise computation) of the recursive function.

In recent studies, linear recurrent neural networks (LRNNs) have achieved Transformer-level performance in natural language and long-range modeling, while offering rapid parallel training and constant inference cost. With the resurgence of interest in LRNNs, we study whether they can learn the hidden rules in training sequences, such as the grammatical structures of regular language. We theoretically analyze some existing LRNNs and discover their limitations in modeling regular language. Motivated by this analysis, we propose a new LRNN equipped with a block-diagonal and input-dependent transition matrix. Experiments suggest that the proposed model is the only LRNN capable of performing length extrapolation on regular language tasks such as Sum, Even Pair, and Modular Arithmetic. The code is released at https://github.com/tinghanf/RegluarLRNN.

In this article we prove that the general transformer neural model undergirding modern large language models (LLMs) is Turing complete under reasonable assumptions. This is the first work to directly address the Turing completeness of the underlying technology employed in GPT-x as past work has focused on the more expressive, full auto-encoder transformer architecture. From this theoretical analysis, we show that the sparsity/compressibility of the word embedding is an important consideration for Turing completeness to hold. We also show that Transformers are are a variant of B machines studied by Hao Wang.

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

This paper presents a concrete and a symbolic rewriting logic semantics for parametric time Petri nets with inhibitor arcs (PITPNs), a flexible model of timed systems where parameters are allowed in firing bounds. We prove that our semantics is bisimilar to the "standard" semantics of PITPNs. This allows us to use the rewriting logic tool Maude, combined with SMT solving, to provide sound and complete formal analyses for PITPNs. We develop and implement a new general folding approach for symbolic reachability, so that Maude-with-SMT reachability analysis terminates whenever the parametric state-class graph of the PITPN is finite. Our work opens up the possibility of using the many formal analysis capabilities of Maude -- including full LTL model checking, analysis with user-defined analysis strategies, and even statistical model checking -- for such nets. We illustrate this by explaining how almost all formal analysis and parameter synthesis methods supported by the state-of-the-art PITPN tool Romeo can be performed using Maude with SMT. In addition, we also support analysis and parameter synthesis from parametric initial markings, as well as full LTL model checking and analysis with user-defined execution strategies. Experiments show that our methods outperform Romeo in many cases.

Large Language Models (LLMs) have shown remarkable abilities in structured reasoning and symbolic tasks, with coding emerging as a particular area of strength. This success has sparked growing interest in applying LLMs to mathematics, both in informal problem-solving and formal theorem proving. However, progress in formal mathematics has proven to be significantly more difficult, despite surface-level similarities between programming and proof construction. This discrepancy raises important questions about how LLMs ``reason'', how they are supervised, and whether they internally track a notion of computational or deductive state. In this article, we address the state-of-the-art of the discipline, focusing on recent models and benchmarks, and explore three central issues at the intersection of machine learning and mathematical cognition: (i) the trade-offs between formal and informal mathematics as training domains; (ii) the deeper reasons why proof generation remains more brittle than code synthesis; (iii) and the question of whether LLMs represent, or merely mimic, a notion of evolving logical state. Our goal is not to draw hard boundaries, but to identify where the current limits lie, and how they might be extended.

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

Researchers have made significant progress in automating the software development process in the past decades. Recent progress in Large Language Models (LLMs) has significantly impacted the development process, where developers can use LLM-based programming assistants to achieve automated coding. Nevertheless, software engineering involves the process of program improvement apart from coding, specifically to enable software maintenance (e.g. bug fixing) and software evolution (e.g. feature additions). In this paper, we propose an automated approach for solving GitHub issues to autonomously achieve program improvement. In our approach called AutoCodeRover, LLMs are combined with sophisticated code search capabilities, ultimately leading to a program modification or patch. In contrast to recent LLM agent approaches from AI researchers and practitioners, our outlook is more software engineering oriented. We work on a program representation (abstract syntax tree) as opposed to viewing a software project as a mere collection of files. Our code search exploits the program structure in the form of classes/methods to enhance LLM's understanding of the issue's root cause, and effectively retrieve a context via iterative search. The use of spectrum-based fault localization using tests, further sharpens the context, as long as a test-suite is available. Experiments on SWE-bench-lite (300 real-life GitHub issues) show increased efficacy in solving GitHub issues (19% on SWE-bench-lite), which is higher than the efficacy of the recently reported SWE-agent. In addition, AutoCodeRover achieved this efficacy with significantly lower cost (on average, $0.43 USD), compared to other baselines. We posit that our workflow enables autonomous software engineering, where, in future, auto-generated code from LLMs can be autonomously improved.

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

Prompt engineering is crucial for deploying LLMs but is poorly understood mathematically. We formalize LLM systems as a class of discrete stochastic dynamical systems to explore prompt engineering through the lens of control theory. We investigate the reachable set of output token sequences R_y(mathbf x_0) for which there exists a control input sequence mathbf u for each mathbf y in R_y(mathbf x_0) that steers the LLM to output mathbf y from initial state sequence mathbf x_0. We offer analytic analysis on the limitations on the controllability of self-attention in terms of reachable set, where we prove an upper bound on the reachable set of outputs R_y(mathbf x_0) as a function of the singular values of the parameter matrices. We present complementary empirical analysis on the controllability of a panel of LLMs, including Falcon-7b, Llama-7b, and Falcon-40b. Our results demonstrate a lower bound on the reachable set of outputs R_y(mathbf x_0) w.r.t. initial state sequences mathbf x_0 sampled from the Wikitext dataset. We find that the correct next Wikitext token following sequence mathbf x_0 is reachable over 97% of the time with prompts of kleq 10 tokens. We also establish that the top 75 most likely next tokens, as estimated by the LLM itself, are reachable at least 85% of the time with prompts of kleq 10 tokens. Intriguingly, short prompt sequences can dramatically alter the likelihood of specific outputs, even making the least likely tokens become the most likely ones. This control-centric analysis of LLMs demonstrates the significant and poorly understood role of input sequences in steering output probabilities, offering a foundational perspective for enhancing language model system capabilities.

This paper introduces Adaptive Computation Time (ACT), an algorithm that allows recurrent neural networks to learn how many computational steps to take between receiving an input and emitting an output. ACT requires minimal changes to the network architecture, is deterministic and differentiable, and does not add any noise to the parameter gradients. Experimental results are provided for four synthetic problems: determining the parity of binary vectors, applying binary logic operations, adding integers, and sorting real numbers. Overall, performance is dramatically improved by the use of ACT, which successfully adapts the number of computational steps to the requirements of the problem. We also present character-level language modelling results on the Hutter prize Wikipedia dataset. In this case ACT does not yield large gains in performance; however it does provide intriguing insight into the structure of the data, with more computation allocated to harder-to-predict transitions, such as spaces between words and ends of sentences. This suggests that ACT or other adaptive computation methods could provide a generic method for inferring segment boundaries in sequence data.

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.

The widespread adoption of Large Language Models (LLMs) for code generation, exemplified by GitHub CopilotA coding extension powered by a Code-LLM to assist in code completion tasks surpassing a million users, highlights the transformative potential of these tools in improving developer productivity. However, this rapid growth also underscores critical concerns regarding the quality, safety, and reliability of the code they generate. As Code-LLMs evolve, they face significant challenges, including the diminishing returns of model scaling and the scarcity of new, high-quality training data. To address these issues, this paper introduces Adversarial Knowledge Distillation (AKD), a novel approach that leverages adversarially generated synthetic datasets to distill the capabilities of larger models into smaller, more efficient ones. By systematically stress-testing and refining the reasoning capabilities of Code-LLMs, AKD provides a framework for enhancing model robustness, reliability, and security while improving their parameter-efficiency. We believe this work represents a critical step toward ensuring dependable automated code generation within the constraints of existing data and the cost-efficiency of model execution.

This work introduces a general code generation framework that incorporates infilling operations into auto-regressive decoding. Our approach capitalizes on the observation that recent code language models with infilling capabilities can perform self-infilling: whereas infilling operations aim to fill in the middle based on a predefined prefix and suffix, self-infilling sequentially generates both such surrounding context and the infilled content. We utilize this feature to develop an infilling-augmented decoding process that facilitates non-monotonic generation. This approach allows for postponing the generation of uncertain code snippets until a definitive suffix is established, leading to improved control over the generation sequence. In addition, it facilitates a looping mechanism, which can iteratively update and synchronize each piece of generation in a cyclic manner. Extensive experiments are conducted to demonstrate that our proposed decoding process is effective in enhancing regularity and quality across several code generation benchmarks.

This research aims to accelerate the inference speed of large language models (LLMs) with billions of parameters. We propose Smart Parallel Auto-Correct dEcoding (SPACE), an innovative approach designed for achieving lossless acceleration of LLMs. By integrating semi-autoregressive inference and speculative decoding capabilities, SPACE uniquely enables autoregressive LLMs to parallelize token generation and verification. This is realized through a specialized semi-autoregressive supervised fine-tuning process that equips existing LLMs with the ability to simultaneously predict multiple tokens. Additionally, an auto-correct decoding algorithm facilitates the simultaneous generation and verification of token sequences within a single model invocation. Through extensive experiments on a range of LLMs, SPACE has demonstrated inference speedup ranging from 2.7x-4.0x on HumanEval-X while maintaining output quality.

Autoregressive language models demonstrate excellent performance in various scenarios. However, the inference efficiency is limited by its one-step-one-word generation mode, which has become a pressing problem recently as the models become increasingly larger. Speculative decoding employs a "draft and then verify" mechanism to allow multiple tokens to be generated in one step, realizing lossless acceleration. Existing methods mainly adopt fixed heuristic draft structures, which fail to adapt to different situations to maximize the acceptance length during verification. To alleviate this dilemma, we proposed OPT-Tree, an algorithm to construct adaptive and scalable draft trees. It searches the optimal tree structure that maximizes the mathematical expectation of the acceptance length in each decoding step. Experimental results reveal that OPT-Tree outperforms the existing draft structures and achieves a speed-up ratio of up to 3.2 compared with autoregressive decoding. If the draft model is powerful enough and the node budget is sufficient, it can generate more than ten tokens in a single step. Our code is available at https://github.com/Jikai0Wang/OPT-Tree.

Retrieval-based language models (R-LM) model the probability of natural language text by combining a standard language model (LM) with examples retrieved from an external datastore at test time. While effective, a major bottleneck of using these models in practice is the computationally costly datastore search, which can be performed as frequently as every time step. In this paper, we present RetoMaton - retrieval automaton - which approximates the datastore search, based on (1) saving pointers between consecutive datastore entries, and (2) clustering of entries into "states". This effectively results in a weighted finite automaton built on top of the datastore, instead of representing the datastore as a flat list. The creation of the automaton is unsupervised, and a RetoMaton can be constructed from any text collection: either the original training corpus or from another domain. Traversing this automaton at inference time, in parallel to the LM inference, reduces its perplexity by up to 1.85, or alternatively saves up to 83% of the nearest neighbor searches over kNN-LM (Khandelwal et al., 2020) without hurting perplexity. Our code and trained models are available at https://github.com/neulab/retomaton .

Large language models display remarkable capabilities in logical and mathematical reasoning, allowing them to solve complex tasks. Interestingly, these abilities emerge in networks trained on the simple task of next-token prediction. In this work, we present a theoretical framework for studying auto-regressive next-token predictors. We demonstrate that even simple models such as linear next-token predictors, trained on Chain-of-Thought (CoT) data, can approximate any function efficiently computed by a Turing machine. We introduce a new complexity measure -- length complexity -- which measures the number of intermediate tokens in a CoT sequence required to approximate some target function, and analyze the interplay between length complexity and other notions of complexity. Finally, we show experimentally that simple next-token predictors, such as linear networks and shallow Multi-Layer Perceptrons (MLPs), display non-trivial performance on text generation and arithmetic tasks. Our results demonstrate that the power of language models can be attributed, to a great extent, to the auto-regressive next-token training scheme, and not necessarily to a particular choice of architecture.

The ability of Large Language Models (LLMs) to generate structured outputs, such as JSON, is crucial for their use in Compound AI Systems. However, evaluating and improving this capability remains challenging. In this work, we introduce StructuredRAG, a benchmark of six tasks designed to assess LLMs' proficiency in following response format instructions. We evaluate two state-of-the-art LLMs, Gemini 1.5 Pro and Llama 3 8B-instruct with 4-bit quantization using two distinct prompting strategies. We introduce these prompting strategies as f-String and Follow the Format (FF) prompting. Across 24 experiments, we find an average success rate of 82.55%. We further find a high variance in performance across tasks, models, and prompting strategies with success rates ranging from 0 to 100%. We find that Llama 3 8B-instruct often performs competitively with Gemini 1.5 Pro. We observe that task complexity significantly influences performance, with tasks involving lists or composite object outputs proving more challenging. Our findings highlight the need for further research into improving the reliability and consistency of structured output generation in LLMs. We have open-sourced our experimental code and results at github.com/weaviate/structured-rag.

Chain-of-Thought (CoT) prompting has become the de facto method to elicit reasoning capabilities from large language models (LLMs). However, to mitigate hallucinations in CoT that are notoriously difficult to detect, current methods such as process reward models (PRMs) or self-consistency operate as opaque boxes and do not provide checkable evidence for their judgments, possibly limiting their effectiveness. To address this issue, we draw inspiration from the idea that "the gold standard for supporting a mathematical claim is to provide a proof". We propose a retrospective, step-aware formal verification framework Safe. Rather than assigning arbitrary scores, we strive to articulate mathematical claims in formal mathematical language Lean 4 at each reasoning step and provide formal proofs to identify hallucinations. We evaluate our framework Safe across multiple language models and various mathematical datasets, demonstrating a significant performance improvement while offering interpretable and verifiable evidence. We also propose FormalStep as a benchmark for step correctness theorem proving with 30,809 formal statements. To the best of our knowledge, our work represents the first endeavor to utilize formal mathematical language Lean 4 for verifying natural language content generated by LLMs, aligning with the reason why formal mathematical languages were created in the first place: to provide a robust foundation for hallucination-prone human-written proofs.

As text generation has become a core capability of modern Large Language Models (LLMs), it underpins a wide range of downstream applications. However, most existing LLMs rely on autoregressive (AR) generation, producing one token at a time based on previously generated context-resulting in limited generation speed due to the inherently sequential nature of the process. To address this challenge, an increasing number of researchers have begun exploring parallel text generation-a broad class of techniques aimed at breaking the token-by-token generation bottleneck and improving inference efficiency. Despite growing interest, there remains a lack of comprehensive analysis on what specific techniques constitute parallel text generation and how they improve inference performance. To bridge this gap, we present a systematic survey of parallel text generation methods. We categorize existing approaches into AR-based and Non-AR-based paradigms, and provide a detailed examination of the core techniques within each category. Following this taxonomy, we assess their theoretical trade-offs in terms of speed, quality, and efficiency, and examine their potential for combination and comparison with alternative acceleration strategies. Finally, based on our findings, we highlight recent advancements, identify open challenges, and outline promising directions for future research in parallel text generation. We have also created a GitHub repository for indexing relevant papers and open resources available at https://github.com/zhanglingzhe0820/Awesome-Parallel-Text-Generation.

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.

Diffusion-based Large Language Models (dLLMs) parallelize text generation by framing decoding as a denoising process, but suffer from high computational overhead since they predict all future suffix tokens at each step while retaining only a small fraction. We propose Diffusion Scratchpad (DPad), a training-free method that restricts attention to a small set of nearby suffix tokens, preserving fidelity while eliminating redundancy. DPad integrates two strategies: (i) a sliding window, which maintains a fixed-length suffix window, and (ii) distance-decay dropout, which deterministically removes distant suffix tokens before attention computation. This simple design is compatible with existing optimizations such as prefix caching and can be implemented with only a few lines of code. Comprehensive evaluations across multiple benchmarks on LLaDA-1.5 and Dream models demonstrate that DPad delivers up to 61.4times speedup over vanilla dLLMs while maintaining comparable accuracy, highlighting its potential for efficient and scalable long-sequence inference. Our code is available at https://github.com/Crys-Chen/DPad.

Originally proposed for handling time series data, Auto-regressive Decision Trees (ARDTs) have not yet been explored for language modeling. This paper delves into both the theoretical and practical applications of ARDTs in this new context. We theoretically demonstrate that ARDTs can compute complex functions, such as simulating automata, Turing machines, and sparse circuits, by leveraging "chain-of-thought" computations. Our analysis provides bounds on the size, depth, and computational efficiency of ARDTs, highlighting their surprising computational power. Empirically, we train ARDTs on simple language generation tasks, showing that they can learn to generate coherent and grammatically correct text on par with a smaller Transformer model. Additionally, we show that ARDTs can be used on top of transformer representations to solve complex reasoning tasks. This research reveals the unique computational abilities of ARDTs, aiming to broaden the architectural diversity in language model development.

Instruction following evaluates large language models (LLMs) on their ability to generate outputs that adhere to user-defined constraints. However, existing benchmarks often rely on templated constraint prompts, which lack the diversity of real-world usage and limit fine-grained performance assessment. To fill this gap, we propose a multi-dimensional constraint framework encompassing three constraint patterns, four constraint categories, and four difficulty levels. Building on this framework, we develop an automated instruction generation pipeline that performs constraint expansion, conflict detection, and instruction rewriting, yielding 1,200 code-verifiable instruction-following test samples. We evaluate 19 LLMs across seven model families and uncover substantial variation in performance across constraint forms. For instance, average performance drops from 77.67% at Level I to 32.96% at Level IV. Furthermore, we demonstrate the utility of our approach by using it to generate data for reinforcement learning, achieving substantial gains in instruction following without degrading general performance. In-depth analysis indicates that these gains stem primarily from modifications in the model's attention modules parameters, which enhance constraint recognition and adherence. Code and data are available in https://github.com/Junjie-Ye/MulDimIF.

We introduce Psi-Turing Machines (Psi-TM): classical Turing machines equipped with a constant-depth introspection interface iota and an explicit per-step information budget B(d,n)=c,dlog_2 n . With the interface frozen, we develop an information-theoretic lower-bound toolkit: Budget counting, Psi -Fooling, and Psi -Fano, with worked examples L_k and L_k^{phase} . We prove an oracle-relative separation P^{Psi} neq NP^{Psi} and a strict depth hierarchy, reinforced by an Anti-Simulation Hook that rules out polynomial emulation of iota_k using many calls to iota_{k-1} under the budget regime. We also present two independent platforms (Psi-decision trees and interface-constrained circuits IC-AC^{0}/IC-NC^{1}) and bridges that transfer bounds among machine, tree, and circuit with explicit poly/log losses. The model preserves classical computational power outside iota yet enables precise oracle-aware statements about barriers (relativization; partial/conditional progress on natural proofs and proof complexity). The aim is a standardized minimal introspection interface with clearly accounted information budgets.

Linear Recurrence has proven to be a powerful tool for modeling long sequences efficiently. In this work, we show that existing models fail to take full advantage of its potential. Motivated by this finding, we develop GateLoop, a foundational sequence model that generalizes linear recurrent models such as S4, S5, LRU and RetNet, by employing data-controlled state transitions. Utilizing this theoretical advance, GateLoop empirically outperforms existing models for auto-regressive language modeling. Our method comes with a low-cost O(l) recurrent mode and an efficient O(l log_{2} l) parallel mode making use of highly optimized associative scan implementations. Furthermore, we derive an O(l^2) surrogate attention mode, revealing remarkable implications for Transformer and recently proposed architectures. Specifically, we prove that our approach can be interpreted as providing data-controlled relative-positional information to Attention. While many existing models solely rely on data-controlled cumulative sums for context aggregation, our findings suggest that incorporating data-controlled complex cumulative products may be a crucial step towards more powerful sequence models.

In this paper, we investigate the length-extension of state-space models (SSMs) in language modeling. Length extension involves training models on short sequences and testing them on longer ones. We show that state-space models trained with zero hidden states initialization have difficulty doing length extension. We explain this difficulty by pointing out the length extension is equivalent to polynomial extrapolation. Based on the theory, we propose a simple yet effective method - changing the hidden states initialization scheme - to improve the length extension. Moreover, our method shows that using long training sequence length is beneficial but not necessary to length extension. Changing the hidden state initialization enables the efficient training of long-memory model with a smaller training context length.

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

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.

Large Language Models (LLMs) have demonstrated exceptional proficiency in instruction-following, becoming increasingly crucial across various applications. However, this capability brings with it the risk of prompt injection attacks, where attackers inject instructions into LLMs' input to elicit undesirable actions or content. Understanding the robustness of LLMs against such attacks is vital for their safe implementation. In this work, we establish a benchmark to evaluate the robustness of instruction-following LLMs against prompt injection attacks. Our objective is to determine the extent to which LLMs can be influenced by injected instructions and their ability to differentiate between these injected and original target instructions. Through extensive experiments with leading instruction-following LLMs, we uncover significant vulnerabilities in their robustness to such attacks. Our results indicate that some models are overly tuned to follow any embedded instructions in the prompt, overly focusing on the latter parts of the prompt without fully grasping the entire context. By contrast, models with a better grasp of the context and instruction-following capabilities will potentially be more susceptible to compromise by injected instructions. This underscores the need to shift the focus from merely enhancing LLMs' instruction-following capabilities to improving their overall comprehension of prompts and discernment of instructions that are appropriate to follow. We hope our in-depth analysis offers insights into the underlying causes of these vulnerabilities, aiding in the development of future solutions. Code and data are available at https://github.com/Leezekun/instruction-following-robustness-eval

Recent advances in language model (LM) agents and function calling have enabled autonomous, feedback-driven systems to solve problems across various digital domains. To better understand the unique limitations of LM agents, we introduce RefactorBench, a benchmark consisting of 100 large handcrafted multi-file refactoring tasks in popular open-source repositories. Solving tasks within RefactorBench requires thorough exploration of dependencies across multiple files and strong adherence to relevant instructions. Every task is defined by 3 natural language instructions of varying specificity and is mutually exclusive, allowing for the creation of longer combined tasks on the same repository. Baselines on RefactorBench reveal that current LM agents struggle with simple compositional tasks, solving only 22% of tasks with base instructions, in contrast to a human developer with short time constraints solving 87%. Through trajectory analysis, we identify various unique failure modes of LM agents, and further explore the failure mode of tracking past actions. By adapting a baseline agent to condition on representations of state, we achieve a 43.9% improvement in solving RefactorBench tasks. We further extend our state-aware approach to encompass entire digital environments and outline potential directions for future research. RefactorBench aims to support the study of LM agents by providing a set of real-world, multi-hop tasks within the realm of code.

Many applications today provide users with multiple auto-complete drafts as they type, including GitHub's code completion, Gmail's smart compose, and Apple's messaging auto-suggestions. Under the hood, language models support this by running an autoregressive inference pass to provide a draft. Consequently, providing k drafts to the user requires running an expensive language model k times. To alleviate the computation cost of running k inference passes, we propose Superposed Decoding, a new decoding algorithm that generates k drafts at the computation cost of one autoregressive inference pass. We achieve this by feeding a superposition of the most recent token embeddings from the k drafts as input to the next decoding step of the language model. At every inference step we combine the k drafts with the top-k tokens to get k^2 new drafts and cache the k most likely options, using an n-gram interpolation with minimal compute overhead to filter out incoherent generations. Our experiments show that k drafts from Superposed Decoding are at least as coherent and factual as Nucleus Sampling and Greedy Decoding respectively, while being at least 2.44times faster for kge3. In a compute-normalized setting, user evaluations demonstrably favor text generated by Superposed Decoding over Nucleus Sampling. Code and more examples open-sourced at https://github.com/RAIVNLab/SuperposedDecoding.

Jailbreaking attacks on the vision modality typically rely on imperceptible adversarial perturbations, whereas attacks on the textual modality are generally assumed to require visible modifications (e.g., non-semantic suffixes). In this paper, we introduce imperceptible jailbreaks that exploit a class of Unicode characters called variation selectors. By appending invisible variation selectors to malicious questions, the jailbreak prompts appear visually identical to original malicious questions on screen, while their tokenization is "secretly" altered. We propose a chain-of-search pipeline to generate such adversarial suffixes to induce harmful responses. Our experiments show that our imperceptible jailbreaks achieve high attack success rates against four aligned LLMs and generalize to prompt injection attacks, all without producing any visible modifications in the written prompt. Our code is available at https://github.com/sail-sg/imperceptible-jailbreaks.

Large Language Models are powerful tools for program synthesis and advanced auto-completion, but come with no guarantee that their output code is syntactically correct. This paper contributes an incremental parser that allows early rejection of syntactically incorrect code, as well as efficient detection of complete programs for fill-in-the-middle (FIM) tasks. We extend the Earley parsing algorithm to allow for left and right quotients of context-free grammars, and develop methods to handle quotienting of several context-sensitive features present in the grammars of many common programming languages. The result of these contributions is an efficient, general, and well-grounded method for left and right quotient parsing. To validate our theoretical contributions -- and the effectiveness of certain design decisions -- we evaluate our method on the particularly difficult case of FIM completion for Python 3, with syntax-correctness constraints. Our results demonstrate that constrained generation can significantly reduce the incidence of syntax errors in recommended code.

Diffusion-based large language models (dLLMs) have recently emerged as a powerful alternative to autoregressive LLMs, offering faster inference and greater interactivity via parallel decoding and bidirectional modeling. However, despite strong performance in code generation and text infilling, we identify a fundamental safety concern: existing alignment mechanisms fail to safeguard dLLMs against context-aware, masked-input adversarial prompts, exposing novel vulnerabilities. To this end, we present DIJA, the first systematic study and jailbreak attack framework that exploits unique safety weaknesses of dLLMs. Specifically, our proposed DIJA constructs adversarial interleaved mask-text prompts that exploit the text generation mechanisms of dLLMs, i.e., bidirectional modeling and parallel decoding. Bidirectional modeling drives the model to produce contextually consistent outputs for masked spans, even when harmful, while parallel decoding limits model dynamic filtering and rejection sampling of unsafe content. This causes standard alignment mechanisms to fail, enabling harmful completions in alignment-tuned dLLMs, even when harmful behaviors or unsafe instructions are directly exposed in the prompt. Through comprehensive experiments, we demonstrate that DIJA significantly outperforms existing jailbreak methods, exposing a previously overlooked threat surface in dLLM architectures. Notably, our method achieves up to 100% keyword-based ASR on Dream-Instruct, surpassing the strongest prior baseline, ReNeLLM, by up to 78.5% in evaluator-based ASR on JailbreakBench and by 37.7 points in StrongREJECT score, while requiring no rewriting or hiding of harmful content in the jailbreak prompt. Our findings underscore the urgent need for rethinking safety alignment in this emerging class of language models. Code is available at https://github.com/ZichenWen1/DIJA.

Using AI to write formal proofs for mathematical problems is a challenging task that has seen some advancements in recent years. Automated systems such as Lean can verify the correctness of proofs written in formal language, yet writing the proofs in formal language can be challenging for humans and machines. The miniF2F benchmark has 20 IMO problems in its test set, yet formal proofs are available only for 6 of these problems (3 of which are only written by mathematicians). The model with best accuracy can only prove 2 of these 20 IMO problems, from 1950s and 60s, while its training set is a secret. In this work, we write complete, original formal proofs for the remaining IMO problems in Lean along with 3 extra problems from IMO 2022 and 2023. This effort expands the availability of proof currently in the public domain by creating 5,880 lines of Lean proof. The goal of the paper is to pave the way for developing AI models that can automatically write the formal proofs for all the IMO problems in miniF2F and beyond by providing an evaluation benchmark. In this pursuit, we devise a method to decompose the proofs of these problems into their building blocks, constructing a dataset of 1,329 lemmas with more than 40k lines of Lean code. These lemmas are not trivial, yet they are approachable, providing the opportunity to evaluate and diagnose the failures and successes of AI models. We evaluate the ability of the SOTA LLMs on our dataset and analyze their success and failure modes from different perspectives. Our dataset and code is available at: https://github.com/roozbeh-yz/IMO-Steps.

Efficient parallelization of Large Language Models (LLMs) with long sequences is essential but challenging due to their significant computational and memory demands, particularly stemming from communication bottlenecks in attention mechanisms. While sequence parallelism (SP) has been introduced as a potential solution, existing methods often suffer from limited scalability or inefficiency, rendering their effectiveness. Ring-Attention demonstrates the potential for scaling sequence processing but faces significant limitations due to its reliance on peer-to-peer (P2P) communication and inefficient utilization of network resources. As the degree of SP increases, the quadratic decrease in computation time per step contrasts sharply with the linear reduction in communication volume, exacerbating communication bottlenecks. To address these challenges, we propose TokenRing, a fine-grained parallel framework that leverages bidirectional P2P communication to effectively overlap computation and data transmission. By partitioning the attention block and concurrently transmitting Query and block outputs (i.e., block_out and block_lse) within a fully connected mesh topology, TokenRing achieves significant reductions in communication overhead and better load balancing. These innovations improve the scalability and efficiency of distributed Transformer models, particularly for long-context sequences. Experimental results demonstrate that TokenRing enhances throughput and reduces communication latency. Moreover, its design adapts seamlessly to various multi-GPU interconnect solutions, such as Huawei Ascend, ensuring broad compatibility and cost-effectiveness for distributed LLM inference and training. The code is available at: https://github.com/ACA-Lab-SJTU/token-ring.

As Large Language Models become more ubiquitous across domains, it becomes important to examine their inherent limitations critically. This work argues that hallucinations in language models are not just occasional errors but an inevitable feature of these systems. We demonstrate that hallucinations stem from the fundamental mathematical and logical structure of LLMs. It is, therefore, impossible to eliminate them through architectural improvements, dataset enhancements, or fact-checking mechanisms. Our analysis draws on computational theory and Godel's First Incompleteness Theorem, which references the undecidability of problems like the Halting, Emptiness, and Acceptance Problems. We demonstrate that every stage of the LLM process-from training data compilation to fact retrieval, intent classification, and text generation-will have a non-zero probability of producing hallucinations. This work introduces the concept of Structural Hallucination as an intrinsic nature of these systems. By establishing the mathematical certainty of hallucinations, we challenge the prevailing notion that they can be fully mitigated.

In this paper, we present JADE, a targeted linguistic fuzzing platform which strengthens the linguistic complexity of seed questions to simultaneously and consistently break a wide range of widely-used LLMs categorized in three groups: eight open-sourced Chinese, six commercial Chinese and four commercial English LLMs. JADE generates three safety benchmarks for the three groups of LLMs, which contain unsafe questions that are highly threatening: the questions simultaneously trigger harmful generation of multiple LLMs, with an average unsafe generation ratio of 70% (please see the table below), while are still natural questions, fluent and preserving the core unsafe semantics. We release the benchmark demos generated for commercial English LLMs and open-sourced English LLMs in the following link: https://github.com/whitzard-ai/jade-db. For readers who are interested in evaluating on more questions generated by JADE, please contact us. JADE is based on Noam Chomsky's seminal theory of transformational-generative grammar. Given a seed question with unsafe intention, JADE invokes a sequence of generative and transformational rules to increment the complexity of the syntactic structure of the original question, until the safety guardrail is broken. Our key insight is: Due to the complexity of human language, most of the current best LLMs can hardly recognize the invariant evil from the infinite number of different syntactic structures which form an unbound example space that can never be fully covered. Technically, the generative/transformative rules are constructed by native speakers of the languages, and, once developed, can be used to automatically grow and transform the parse tree of a given question, until the guardrail is broken. For more evaluation results and demo, please check our website: https://whitzard-ai.github.io/jade.html.

Recent advancements in large language models (LLMs) suggest great promises in code and proof generations. However, scaling automated formal verification to real-world projects requires resolving cross-module dependencies and global contexts, which are crucial challenges overlooked by existing LLM-based methods with a special focus on targeting isolated, function-level verification tasks. To systematically explore and address the significant challenges of verifying entire software repositories, we introduce RVBench, the first verification benchmark explicitly designed for repository-level evaluation, constructed from four diverse and complex open-source Verus projects. We further introduce RagVerus, an extensible framework that synergizes retrieval-augmented generation with context-aware prompting to automate proof synthesis for multi-module repositories. RagVerus triples proof pass rates on existing benchmarks under constrained model inference budgets, and achieves a 27% relative improvement on the more challenging RVBench benchmark, demonstrating a scalable and sample-efficient verification solution.

In recent years, there has been remarkable progress in leveraging Language Models (LMs), encompassing Pre-trained Language Models (PLMs) and Large-scale Language Models (LLMs), within the domain of mathematics. This paper conducts a comprehensive survey of mathematical LMs, systematically categorizing pivotal research endeavors from two distinct perspectives: tasks and methodologies. The landscape reveals a large number of proposed mathematical LLMs, which are further delineated into instruction learning, tool-based methods, fundamental CoT techniques, and advanced CoT methodologies. In addition, our survey entails the compilation of over 60 mathematical datasets, including training datasets, benchmark datasets, and augmented datasets. Addressing the primary challenges and delineating future trajectories within the field of mathematical LMs, this survey is positioned as a valuable resource, poised to facilitate and inspire future innovation among researchers invested in advancing this domain.

Autoregressive models, such as the GPT family, use a fixed order, usually left-to-right, to generate sequences. However, this is not a necessity. In this paper, we challenge this assumption and show that by simply adding a positional encoding for the output, this order can be modulated on-the-fly per-sample which offers key advantageous properties. It allows for the sampling of and conditioning on arbitrary subsets of tokens, and it also allows sampling in one shot multiple tokens dynamically according to a rejection strategy, leading to a sub-linear number of model evaluations. We evaluate our method across various domains, including language modeling, path-solving, and aircraft vertical rate prediction, decreasing the number of steps required for generation by an order of magnitude.

In this article, we introduce a new parameterized family of topological invariants, taking the form of candidate decompositions, for multi-parameter persistence modules. We prove that our candidate decompositions are controllable approximations: when restricting to modules that can be decomposed into interval summands, we establish theoretical results about the approximation error between our candidate decompositions and the true underlying module in terms of the standard interleaving and bottleneck distances. Moreover, even when the underlying module does not admit such a decomposition, our candidate decompositions are nonetheless stable invariants; small perturbations in the underlying module lead to small perturbations in the candidate decomposition. Then, we introduce MMA (Multipersistence Module Approximation): an algorithm for computing stable instances of such invariants, which is based on fibered barcodes and exact matchings, two constructions that stem from the theory of single-parameter persistence. By design, MMA can handle an arbitrary number of filtrations, and has bounded complexity and running time. Finally, we present empirical evidence validating the generalization capabilities and running time speed-ups of MMA on several data sets.

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.

Recently, remarkable progress has been made in automated task-solving through the use of multi-agent driven by large language models (LLMs). However, existing LLM-based multi-agent works primarily focus on solving simple dialogue tasks, and complex tasks are rarely studied, mainly due to the LLM hallucination problem. This type of hallucination becomes cascading when naively chaining multiple intelligent agents, resulting in a failure to effectively address complex problems. Therefore, we introduce MetaGPT, an innovative framework that incorporates efficient human workflows as a meta programming approach into LLM-based multi-agent collaboration. Specifically, MetaGPT encodes Standardized Operating Procedures (SOPs) into prompts to enhance structured coordination. Subsequently, it mandates modular outputs, empowering agents with domain expertise comparable to human professionals, to validate outputs and minimize compounded errors. In this way, MetaGPT leverages the assembly line paradigm to assign diverse roles to various agents, thereby establishing a framework that can effectively and cohesively deconstruct complex multi-agent collaborative problems. Our experiments on collaborative software engineering benchmarks demonstrate that MetaGPT generates more coherent and correct solutions compared to existing chat-based multi-agent systems. This highlights the potential of integrating human domain knowledge into multi-agent systems, thereby creating new opportunities to tackle complex real-world challenges. The GitHub repository of this project is publicly available on:https://github.com/geekan/MetaGPT.

Recently, large language models (LLMs) have demonstrated excellent performance in understanding human instructions and generating code, which has inspired researchers to explore the feasibility of generating RTL code with LLMs. However, the existing approaches to fine-tune LLMs on RTL codes typically are conducted on fixed datasets, which do not fully stimulate the capability of LLMs and require large amounts of reference data. To mitigate these issues , we introduce a simple yet effective iterative training paradigm named ITERTL. During each iteration, samples are drawn from the model trained in the previous cycle. Then these new samples are employed for training in this loop. Through this iterative approach, the distribution mismatch between the model and the training samples is reduced. Additionally, the model is thus enabled to explore a broader generative space and receive more comprehensive feedback. Theoretical analyses are conducted to investigate the mechanism of the effectiveness. Experimental results show the model trained through our proposed approach can compete with and even outperform the state-of-the-art (SOTA) open-source model with nearly 37\% reference samples, achieving remarkable 42.9\% and 62.2\% pass@1 rate on two VerilogEval evaluation datasets respectively. While using the same amount of reference samples, our method can achieved a relative improvement of 16.9\% and 12.5\% in pass@1 compared to the non-iterative method. This study facilitates the application of LLMs for generating RTL code in practical scenarios with limited data.

Large Language Models (LLMs) have demonstrated remarkable capabilities across a wide range of natural language processing and reasoning tasks. However, their performance in the foundational domain of arithmetic remains unsatisfactory. When dealing with arithmetic tasks, LLMs often memorize specific examples rather than learning the underlying computational logic, limiting their ability to generalize to new problems. In this paper, we propose a Composable Arithmetic Execution Framework (CAEF) that enables LLMs to learn to execute step-by-step computations by emulating Turing Machines, thereby gaining a genuine understanding of computational logic. Moreover, the proposed framework is highly scalable, allowing composing learned operators to significantly reduce the difficulty of learning complex operators. In our evaluation, CAEF achieves nearly 100% accuracy across seven common mathematical operations on the LLaMA 3.1-8B model, effectively supporting computations involving operands with up to 100 digits, a level where GPT-4o falls short noticeably in some settings.

Autoregressive language models (ARMs) deliver strong likelihoods, but are inherently serial: they generate one token per forward pass, which limits throughput and inflates latency for long sequences. Diffusion Language Models (DLMs) parallelize across positions and thus appear promising for language generation, yet standard discrete diffusion typically needs hundreds to thousands of model evaluations to reach high quality, trading serial depth for iterative breadth. We introduce FS-DFM, Few-Step Discrete Flow-Matching. A discrete flow-matching model designed for speed without sacrificing quality. The core idea is simple: make the number of sampling steps an explicit parameter and train the model to be consistent across step budgets, so one big move lands where many small moves would. We pair this with a reliable update rule that moves probability in the right direction without overshooting, and with strong teacher guidance distilled from long-run trajectories. Together, these choices make few-step sampling stable, accurate, and easy to control. On language modeling benchmarks, FS-DFM with 8 sampling steps achieves perplexity parity with a 1,024-step discrete-flow baseline for generating 1,024 tokens using a similar-size model, delivering up to 128 times faster sampling and corresponding latency/throughput gains.

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

State-space models (SSMs) and transformers dominate the language modeling landscape. However, they are constrained to a lower computational complexity than classical recurrent neural networks (RNNs), limiting their expressivity. In contrast, RNNs lack parallelization during training, raising fundamental questions about the trade off between parallelization and expressivity. We propose implicit SSMs, which iterate a transformation until convergence to a fixed point. Theoretically, we show that implicit SSMs implement the non-linear state-transitions of RNNs. Empirically, we find that only approximate fixed-point convergence suffices, enabling the design of a scalable training curriculum that largely retains parallelization, with full convergence required only for a small subset of tokens. Our approach demonstrates superior state-tracking capabilities on regular languages, surpassing transformers and SSMs. We further scale implicit SSMs to natural language reasoning tasks and pretraining of large-scale language models up to 1.3B parameters on 207B tokens - representing, to our knowledge, the largest implicit model trained to date. Notably, our implicit models outperform their explicit counterparts on standard benchmarks.

While recently Large Language Models (LLMs) have achieved remarkable successes, they are vulnerable to certain jailbreaking attacks that lead to generation of inappropriate or harmful content. Manual red-teaming requires finding adversarial prompts that cause such jailbreaking, e.g. by appending a suffix to a given instruction, which is inefficient and time-consuming. On the other hand, automatic adversarial prompt generation often leads to semantically meaningless attacks that can easily be detected by perplexity-based filters, may require gradient information from the TargetLLM, or do not scale well due to time-consuming discrete optimization processes over the token space. In this paper, we present a novel method that uses another LLM, called the AdvPrompter, to generate human-readable adversarial prompts in seconds, sim800times faster than existing optimization-based approaches. We train the AdvPrompter using a novel algorithm that does not require access to the gradients of the TargetLLM. This process alternates between two steps: (1) generating high-quality target adversarial suffixes by optimizing the AdvPrompter predictions, and (2) low-rank fine-tuning of the AdvPrompter with the generated adversarial suffixes. The trained AdvPrompter generates suffixes that veil the input instruction without changing its meaning, such that the TargetLLM is lured to give a harmful response. Experimental results on popular open source TargetLLMs show state-of-the-art results on the AdvBench dataset, that also transfer to closed-source black-box LLM APIs. Further, we demonstrate that by fine-tuning on a synthetic dataset generated by AdvPrompter, LLMs can be made more robust against jailbreaking attacks while maintaining performance, i.e. high MMLU scores.

With the rapid development and widespread application of Large Language Models (LLMs), rigorous evaluation has become particularly crucial. This research adopts a novel perspective, focusing on evaluating the core computational reasoning ability of LLMs, defined as the capacity of model to accurately understand rules, and execute logically computing operations. This capability assesses the reliability of LLMs as precise executors, and is critical to advanced tasks such as complex code generation and multi-step problem-solving. We propose an evaluation framework based on Universal Turing Machine (UTM) simulation. This framework requires LLMs to strictly follow instructions and track dynamic states, such as tape content and read/write head position, during multi-step computations. To enable standardized evaluation, we developed TMBench, a benchmark for systematically studying the computational reasoning capabilities of LLMs. TMBench provides several key advantages, including knowledge-agnostic evaluation, adjustable difficulty, foundational coverage through Turing machine encoding, and unlimited capacity for instance generation, ensuring scalability as models continue to evolve. We find that model performance on TMBench correlates strongly with performance on other recognized reasoning benchmarks (Pearson correlation coefficient is 0.73), clearly demonstrating that computational reasoning is a significant dimension for measuring the deep capabilities of LLMs. Code and data are available at https://github.com/HaitaoWuTJU/Turing-Machine-Bench.

We present SuperCoder2.0, an advanced autonomous system designed to enhance software development through artificial intelligence. The system combines an AI-native development approach with intelligent agents to enable fully autonomous coding. Key focus areas include a retry mechanism with error output traceback, comprehensive code rewriting and replacement using Abstract Syntax Tree (ast) parsing to minimize linting issues, code embedding technique for retrieval-augmented generation, and a focus on localizing methods for problem-solving rather than identifying specific line numbers. The methodology employs a three-step hierarchical search space reduction approach for code base navigation and bug localization:utilizing Retrieval Augmented Generation (RAG) and a Repository File Level Map to identify candidate files, (2) narrowing down to the most relevant files using a File Level Schematic Map, and (3) extracting 'relevant locations' within these files. Code editing is performed through a two-part module comprising CodeGeneration and CodeEditing, which generates multiple solutions at different temperature values and replaces entire methods or classes to maintain code integrity. A feedback loop executes repository-level test cases to validate and refine solutions. Experiments conducted on the SWE-bench Lite dataset demonstrate SuperCoder2.0's effectiveness, achieving correct file localization in 84.33% of cases within the top 5 candidates and successfully resolving 34% of test instances. This performance places SuperCoder2.0 fourth globally on the SWE-bench leaderboard. The system's ability to handle diverse repositories and problem types highlights its potential as a versatile tool for autonomous software development. Future work will focus on refining the code editing process and exploring advanced embedding models for improved natural language to code mapping.

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

Large Language Models (LLMs) pre-trained on code have recently emerged as the dominant approach to program synthesis. However, these models are trained using next-token prediction, which ignores the syntax and semantics of code. We propose RLCF, that further trains a pre-trained LLM via reinforcement learning, using feedback from a grounding function that scores the quality of the code. The grounding function uses (i) compiler-derived feedback on whether the code it generates passes a set of correctness checks; and (ii) feedback from a different LLM that compares the generated code to a reference code. RLCF is model- and language-agnostic. We empirically evaluate it on the MBJP and MathQA tasks for Java. Our experiments show that RLCF raises the odds that an LLM-generated program compiles, is executable, and produces the right output on tests, often allowing LLMs to match the performance of 2x-8x larger LLMs.

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

As large language models (LLMs) excel at code reasoning, a natural question arises: can an LLM execute programs (i.e., act as an interpreter) purely based on a programming language's formal semantics? If so, it will enable rapid prototyping of new programming languages and language features. We study this question using the imperative language IMP (a subset of C), formalized via small-step operational semantics (SOS) and rewriting-based operational semantics (K-semantics). We introduce three evaluation sets-Human-Written, LLM-Translated, and Fuzzer- Generated-whose difficulty is controlled by code-complexity metrics spanning the size, control-flow, and data-flow axes. Given a program and its semantics formalized with SOS/K-semantics, models are evaluated on three tasks ranging from coarse to fine: (1) final-state prediction, (2) semantic rule prediction, and (3) execution trace prediction. To distinguish pretraining memorization from semantic competence, we define two nonstandard semantics obtained through systematic mutations of the standard rules. Across strong code/reasoning LLMs, performance drops under nonstandard semantics despite high performance under the standard one. We further find that (i) there are patterns to different model failures, (ii) most reasoning models perform exceptionally well on coarse grained tasks involving reasoning about highly complex programs often containing nested loop depths beyond five, and surprisingly, (iii) providing formal semantics helps on simple programs but often hurts on more complex ones. Overall, the results show a promise that LLMs could serve as programming language interpreters, but points to the lack of their robust semantics understanding. We release the benchmark and the supporting code at https://github.com/EngineeringSoftware/PLSemanticsBench.

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.

Recent advancements, such as DeepSeek-Prover-V2-671B and Kimina-Prover-Preview-72B, demonstrate a prevailing trend in leveraging reinforcement learning (RL)-based large-scale training for automated theorem proving. Surprisingly, we discover that even without any training, careful neuro-symbolic coordination of existing off-the-shelf reasoning models and tactic step provers can achieve comparable performance. This paper introduces DSP+, an improved version of the Draft, Sketch, and Prove framework, featuring a fine-grained and integrated neuro-symbolic enhancement for each phase: (1) In the draft phase, we prompt reasoning models to generate concise natural-language subgoals to benefit the sketch phase, removing thinking tokens and references to human-written proofs; (2) In the sketch phase, subgoals are autoformalized with hypotheses to benefit the proving phase, and sketch lines containing syntactic errors are masked according to predefined rules; (3) In the proving phase, we tightly integrate symbolic search methods like Aesop with step provers to establish proofs for the sketch subgoals. Experimental results show that, without any additional model training or fine-tuning, DSP+ solves 80.7\%, 32.8\%, and 24 out of 644 problems from miniF2F, ProofNet, and PutnamBench, respectively, while requiring fewer budgets compared to state-of-the-arts. DSP+ proves imo\_2019\_p1, an IMO problem in miniF2F that is not solved by any prior work. Additionally, DSP+ generates proof patterns comprehensible by human experts, facilitating the identification of formalization errors; For example, eight wrongly formalized statements in miniF2F are discovered. Our results highlight the potential of classical reasoning patterns besides the RL-based training. All components will be open-sourced.

Recent advancements in Large Language Models (LLMs) have significantly enhanced their code generation capabilities. However, their robustness against adversarial misuse, particularly through multi-turn malicious coding prompts, remains underexplored. In this work, we introduce code decomposition attacks, where a malicious coding task is broken down into a series of seemingly benign subtasks across multiple conversational turns to evade safety filters. To facilitate systematic evaluation, we introduce , a large-scale benchmark designed to evaluate the robustness of code LLMs against both single-turn and multi-turn malicious prompts. Empirical results across open- and closed-source models reveal persistent vulnerabilities, especially under multi-turn scenarios. Fine-tuning on MOCHA improves rejection rates while preserving coding ability, and importantly, enhances robustness on external adversarial datasets with up to 32.4% increase in rejection rates without any additional supervision.

Understanding the structure and function of circuits is crucial for electronic design automation (EDA). Circuits can be formulated as And-Inverter graphs (AIGs), enabling efficient implementation of representation learning through graph neural networks (GNNs). Masked modeling paradigms have been proven effective in graph representation learning. However, masking augmentation to original circuits will destroy their logical equivalence, which is unsuitable for circuit representation learning. Moreover, existing masked modeling paradigms often prioritize structural information at the expense of abstract information such as circuit function. To address these limitations, we introduce MGVGA, a novel constrained masked modeling paradigm incorporating masked gate modeling (MGM) and Verilog-AIG alignment (VGA). Specifically, MGM preserves logical equivalence by masking gates in the latent space rather than in the original circuits, subsequently reconstructing the attributes of these masked gates. Meanwhile, large language models (LLMs) have demonstrated an excellent understanding of the Verilog code functionality. Building upon this capability, VGA performs masking operations on original circuits and reconstructs masked gates under the constraints of equivalent Verilog codes, enabling GNNs to learn circuit functions from LLMs. We evaluate MGVGA on various logic synthesis tasks for EDA and show the superior performance of MGVGA compared to previous state-of-the-art methods. Our code is available at https://github.com/wuhy68/MGVGA.

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

Competition-level code generation tasks pose significant challenges for current state-of-the-art large language models (LLMs). For example, on the LiveCodeBench-Hard dataset, models such as O1-Mini and O1-Preview achieve pass@1 rates of only 0.366 and 0.143, respectively. While tree search techniques have proven effective in domains like mathematics and general coding, their potential in competition-level code generation remains under-explored. In this work, we propose a novel token-level tree search method specifically designed for code generation. Leveraging Qwen2.5-Coder-32B-Instruct, our approach achieves a pass rate of 0.305 on LiveCodeBench-Hard, surpassing the pass@100 performance of GPT4o-0513 (0.245). Furthermore, by integrating Chain-of-Thought (CoT) prompting, we improve our method's performance to 0.351, approaching O1-Mini's pass@1 rate. To ensure reproducibility, we report the average number of generations required per problem by our tree search method on the test set. Our findings underscore the potential of tree search to significantly enhance performance on competition-level code generation tasks. This opens up new possibilities for large-scale synthesis of challenging code problems supervised fine-tuning (SFT) data, advancing competition-level code generation tasks.

This paper introduces VeriThoughts, a novel dataset designed for reasoning-based Verilog code generation. We establish a new benchmark framework grounded in formal verification methods to evaluate the quality and correctness of generated hardware descriptions. Additionally, we present a suite of specialized small-scale models optimized specifically for Verilog generation. Our work addresses the growing need for automated hardware design tools that can produce verifiably correct implementations from high-level specifications, potentially accelerating the hardware development process while maintaining rigorous correctness guarantees. Our code and data are available at https://github.com/wilyub/VeriThoughts{this URL}.

Large language models (LLMs) are a new and powerful tool for a wide span of applications involving natural language and demonstrate impressive code generation abilities. In this paper, we explore the capabilitity of state-of-the-art LLMs, including closed-source options like OpenAI GPT-4 and open-source alternatives like Meta AI Codellama, to automatically generate tests and use these tests to validate and verify compiler implementations of a directive-based programming paradigm, OpenACC. Our approach entails exploring various prompt engineering techniques including a code template, retrieval-augmented generation (RAG) with code template, expressive prompt using RAG with code template, one-shot example, and RAG with one-shot example. This paper focusses on (a) exploring the capabilities of the latest LLMs for code generation, (b) investigating prompt and fine tuning methods, and (c) analyzing the outcome of LLMs generated tests

This paper introduces a new method for adversarial attacks on large language models (LLMs) called the Single-Turn Crescendo Attack (STCA). Building on the multi-turn crescendo attack method introduced by Russinovich, Salem, and Eldan (2024), which gradually escalates the context to provoke harmful responses, the STCA achieves similar outcomes in a single interaction. By condensing the escalation into a single, well-crafted prompt, the STCA bypasses typical moderation filters that LLMs use to prevent inappropriate outputs. This technique reveals vulnerabilities in current LLMs and emphasizes the importance of stronger safeguards in responsible AI (RAI). The STCA offers a novel method that has not been previously explored.

Large language models (LLMs) have shown strong performance in Verilog generation from natural language description. However, ensuring the functional correctness of the generated code remains a significant challenge. This paper introduces a method that integrates verification insights from testbench into the training of Verilog generation LLMs, aligning the training with the fundamental goal of hardware design: functional correctness. The main obstacle in using LLMs for Verilog code generation is the lack of sufficient functional verification data, particularly testbenches paired with design specifications and code. To address this problem, we introduce an automatic testbench generation pipeline that decomposes the process and uses feedback from the Verilog compiler simulator (VCS) to reduce hallucination and ensure correctness. We then use the testbench to evaluate the generated codes and collect them for further training, where verification insights are introduced. Our method applies reinforcement learning (RL), specifically direct preference optimization (DPO), to align Verilog code generation with functional correctness by training preference pairs based on testbench outcomes. In evaluations on VerilogEval-Machine, VerilogEval-Human, RTLLM v1.1, RTLLM v2, and VerilogEval v2, our approach consistently outperforms state-of-the-art baselines in generating functionally correct Verilog code. We open source all training code, data, and models at https://anonymous.4open.science/r/VeriPrefer-E88B.

Pre-tokenization, the initial step in many modern tokenization pipelines, segments text into smaller units called pretokens, typically splitting on whitespace and punctuation. While this process encourages having full, individual words as tokens, it introduces a fundamental limitation in most tokenization algorithms such as Byte Pair Encoding (BPE). Specifically, pre-tokenization causes the distribution of tokens in a corpus to heavily skew towards common, full-length words. This skewed distribution limits the benefits of expanding to larger vocabularies, since the additional tokens appear with progressively lower counts. To overcome this barrier, we propose BoundlessBPE, a modified BPE algorithm that relaxes the pretoken boundary constraint. Our approach selectively merges two complete pretokens into a larger unit we term a superword. Superwords are not necessarily semantically cohesive. For example, the pretokens " of" and " the" might be combined to form the superword " of the". This merging strategy results in a substantially more uniform distribution of tokens across a corpus than standard BPE, and compresses text more effectively, with an approximate 20% increase in bytes per token.

Graph neural networks (GNNs) have been shown to be highly sensitive to the choice of aggregation function. While summing over a node's neighbours can approximate any permutation-invariant function over discrete inputs, Cohen-Karlik et al. [2020] proved there are set-aggregation problems for which summing cannot generalise to unbounded inputs, proposing recurrent neural networks regularised towards permutation-invariance as a more expressive aggregator. We show that these results carry over to the graph domain: GNNs equipped with recurrent aggregators are competitive with state-of-the-art permutation-invariant aggregators, on both synthetic benchmarks and real-world problems. However, despite the benefits of recurrent aggregators, their O(V) depth makes them both difficult to parallelise and harder to train on large graphs. Inspired by the observation that a well-behaved aggregator for a GNN is a commutative monoid over its latent space, we propose a framework for constructing learnable, commutative, associative binary operators. And with this, we construct an aggregator of O(log V) depth, yielding exponential improvements for both parallelism and dependency length while achieving performance competitive with recurrent aggregators. Based on our empirical observations, our proposed learnable commutative monoid (LCM) aggregator represents a favourable tradeoff between efficient and expressive aggregators.

Pretrained using large amount of data, autoregressive language models are able to generate high quality sequences. However, these models do not perform well under hard lexical constraints as they lack fine control of content generation process. Progressive insertion-based transformers can overcome the above limitation and efficiently generate a sequence in parallel given some input tokens as constraint. These transformers however may fail to support hard lexical constraints as their generation process is more likely to terminate prematurely. The paper analyses such early termination problems and proposes the Entity-constrained insertion transformer (ENCONTER), a new insertion transformer that addresses the above pitfall without compromising much generation efficiency. We introduce a new training strategy that considers predefined hard lexical constraints (e.g., entities to be included in the generated sequence). Our experiments show that ENCONTER outperforms other baseline models in several performance metrics rendering it more suitable in practical applications. Our code is available at https://github.com/LARC-CMU-SMU/Enconter

Large language models (LLMs) frequently refuse to respond to pseudo-malicious instructions: semantically harmless input queries triggering unnecessary LLM refusals due to conservative safety alignment, significantly impairing user experience. Collecting such instructions is crucial for evaluating and mitigating over-refusals, but existing instruction curation methods, like manual creation or instruction rewriting, either lack scalability or fail to produce sufficiently diverse and effective refusal-inducing prompts. To address these limitations, we introduce EVOREFUSE, a prompt optimization approach that generates diverse pseudo-malicious instructions consistently eliciting confident refusals across LLMs. EVOREFUSE employs an evolutionary algorithm exploring the instruction space in more diverse directions than existing methods via mutation strategies and recombination, and iteratively evolves seed instructions to maximize evidence lower bound on LLM refusal probability. Using EVOREFUSE, we create two novel datasets: EVOREFUSE-TEST, a benchmark of 582 pseudo-malicious instructions that outperforms the next-best benchmark with 140.41% higher average refusal triggering rate across 9 LLMs, 34.86% greater lexical diversity, and 40.03% improved LLM response confidence scores; and EVOREFUSE-ALIGN, which provides 3,000 pseudo-malicious instructions with responses for supervised and preference-based alignment training. LLAMA3.1-8B-INSTRUCT supervisedly fine-tuned on EVOREFUSE-ALIGN achieves up to 14.31% fewer over-refusals than models trained on the second-best alignment dataset, without compromising safety. Our analysis with EVOREFUSE-TEST reveals models trigger over-refusals by overly focusing on sensitive keywords while ignoring broader context.

Despite careful safety alignment, current large language models (LLMs) remain vulnerable to various attacks. To further unveil the safety risks of LLMs, we introduce a Safety Concept Activation Vector (SCAV) framework, which effectively guides the attacks by accurately interpreting LLMs' safety mechanisms. We then develop an SCAV-guided attack method that can generate both attack prompts and embedding-level attacks with automatically selected perturbation hyperparameters. Both automatic and human evaluations demonstrate that our attack method significantly improves the attack success rate and response quality while requiring less training data. Additionally, we find that our generated attack prompts may be transferable to GPT-4, and the embedding-level attacks may also be transferred to other white-box LLMs whose parameters are known. Our experiments further uncover the safety risks present in current LLMs. For example, in our evaluation of seven open-source LLMs, we observe an average attack success rate of 99.14%, based on the classic keyword-matching criterion. Finally, we provide insights into the safety mechanism of LLMs. The code is available at https://github.com/SproutNan/AI-Safety_SCAV.

Large language models (LLMs) excel at complex reasoning when they include intermediate steps, known as "chains of thought" (CoTs). However, these rationales are often overly verbose, even for simple problems, leading to wasted context, increased latency, and higher energy consumption. We observe that verbose, English-heavy CoTs and concise, math-centric CoTs occupy distinct regions in the model's residual-stream activation space. By extracting and injecting a "steering vector" to transition between these modes, we can reliably shift generation toward more concise reasoning, effectively compressing CoTs without retraining. We formalize this approach as Activation-Steered Compression (ASC), an inference-time technique that shortens reasoning traces by directly modifying hidden representations. In addition, we provide a theoretical analysis of the impact of ASC on the output distribution, derived from a closed-form KL-divergence-bounded constraint to regulate steering strength. Using only 100 paired verbose and concise examples, ASC achieves up to 67.43% reduction in CoT length on MATH500 and GSM8K datasets, while maintaining accuracy across 7B, 8B, and 32B parameter models. As a training-free method, ASC introduces negligible runtime overhead and, on MATH500, delivers an average 2.73x speedup in end-to-end reasoning wall-clock time on an 8B model. This makes ASC a practical and efficient tool for streamlining the deployment of reasoning-capable LLMs in latency- or cost-sensitive settings. The code is available at: https://github.com/ArminAzizi98/ASC

Jailbreaks on large language models (LLMs) have recently received increasing attention. For a comprehensive assessment of LLM safety, it is essential to consider jailbreaks with diverse attributes, such as contextual coherence and sentiment/stylistic variations, and hence it is beneficial to study controllable jailbreaking, i.e. how to enforce control on LLM attacks. In this paper, we formally formulate the controllable attack generation problem, and build a novel connection between this problem and controllable text generation, a well-explored topic of natural language processing. Based on this connection, we adapt the Energy-based Constrained Decoding with Langevin Dynamics (COLD), a state-of-the-art, highly efficient algorithm in controllable text generation, and introduce the COLD-Attack framework which unifies and automates the search of adversarial LLM attacks under a variety of control requirements such as fluency, stealthiness, sentiment, and left-right-coherence. The controllability enabled by COLD-Attack leads to diverse new jailbreak scenarios which not only cover the standard setting of generating fluent (suffix) attack with continuation constraint, but also allow us to address new controllable attack settings such as revising a user query adversarially with paraphrasing constraint, and inserting stealthy attacks in context with position constraint. Our extensive experiments on various LLMs (Llama-2, Mistral, Vicuna, Guanaco, GPT-3.5, and GPT-4) show COLD-Attack's broad applicability, strong controllability, high success rate, and attack transferability. Our code is available at https://github.com/Yu-Fangxu/COLD-Attack.

LangProp is a framework for iteratively optimizing code generated by large language models (LLMs) in a supervised/reinforcement learning setting. While LLMs can generate sensible solutions zero-shot, the solutions are often sub-optimal. Especially for code generation tasks, it is likely that the initial code will fail on certain edge cases. LangProp automatically evaluates the code performance on a dataset of input-output pairs, as well as catches any exceptions, and feeds the results back to the LLM in the training loop, so that the LLM can iteratively improve the code it generates. By adopting a metric- and data-driven training paradigm for this code optimization procedure, one could easily adapt findings from traditional machine learning techniques such as imitation learning, DAgger, and reinforcement learning. We demonstrate the first proof of concept of automated code optimization for autonomous driving in CARLA, showing that LangProp can generate interpretable and transparent driving policies that can be verified and improved in a metric- and data-driven way. Our code will be open-sourced and is available at https://github.com/shuishida/LangProp.

Recent theoretical work has identified surprisingly simple reasoning problems, such as checking if two nodes in a graph are connected or simulating finite-state machines, that are provably unsolvable by standard transformers that answer immediately after reading their input. However, in practice, transformers' reasoning can be improved by allowing them to use a "chain of thought" or "scratchpad", i.e., generate and condition on a sequence of intermediate tokens before answering. Motivated by this, we ask: Does such intermediate generation fundamentally extend the computational power of a decoder-only transformer? We show that the answer is yes, but the amount of increase depends crucially on the amount of intermediate generation. For instance, we find that transformer decoders with a logarithmic number of decoding steps (w.r.t. the input length) push the limits of standard transformers only slightly, while a linear number of decoding steps, assuming a slight generalization to standard pre-norm, adds a clear new ability (under standard complexity conjectures): recognizing all regular languages. Our results also imply that linear steps keep transformer decoders within context-sensitive languages, and polynomial steps with generalized pre-norm make them recognize exactly the class of polynomial-time solvable problems -- the first exact characterization of a type of transformers in terms of standard complexity classes. Together, our results provide a nuanced framework for understanding how the length of a transformer's chain of thought or scratchpad impacts its reasoning power.

Recent advancements in LLM-based agents have led to significant progress in automatic software engineering, particularly in software maintenance and evolution. Despite these encouraging advances, current research faces two major challenges. First, SOTA performance primarily depends on closed-source models, which significantly limits the technology's accessibility, and potential for customization in diverse SE tasks. Second, these models are predominantly trained on static code data, lacking a deep understanding of the dynamic interactions, iterative problem-solving processes, and evolutionary characteristics inherent in software development. To address these challenges, our study adopts a software engineering perspective. We recognize that real-world software maintenance and evolution processes encompass not only static code data but also developers' thought processes, utilization of external tools, and the interaction between different functional personnel. Consequently, we introduce the Lingma SWE-GPT series, comprising Lingma SWE-GPT 7B and 72B. By learning from and simulating real-world code submission activities, Lingma SWE-GPT systematically incorporates the dynamic interactions and iterative problem-solving inherent in software development process, thereby achieving a more comprehensive understanding of software improvement processes. We conducted experimental evaluations using SWE-bench Verified benchmark. The results demonstrate that Lingma SWE-GPT 72B successfully resolves 30.20% of the GitHub issues, marking a significant improvement in automatic issue resolution (22.76% relative improvement compared to Llama 3.1 405B), approaching the performance of closed-source models (31.80\% issues of GPT-4o resolved). Notably, Lingma SWE-GPT 7B resolves 18.20% of the issues, highlighting the potential for applying smaller models to ASE tasks.

Effective prompt design is essential for improving the planning capabilities of large language model (LLM)-driven agents. However, existing structured prompting strategies are typically limited to single-agent, plan-only settings, and often evaluate performance solely based on task accuracy - overlooking critical factors such as token efficiency, modularity, and scalability in multi-agent environments. To address these limitations, we introduce CodeAgents, a prompting framework that codifies multi-agent reasoning and enables structured, token-efficient planning in multi-agent systems. In CodeAgents, all components of agent interaction - Task, Plan, Feedback, system roles, and external tool invocations - are codified into modular pseudocode enriched with control structures (e.g., loops, conditionals), boolean logic, and typed variables. This design transforms loosely connected agent plans into cohesive, interpretable, and verifiable multi-agent reasoning programs. We evaluate the proposed framework across three diverse benchmarks - GAIA, HotpotQA, and VirtualHome - using a range of representative LLMs. Results show consistent improvements in planning performance, with absolute gains of 3-36 percentage points over natural language prompting baselines. On VirtualHome, our method achieves a new state-of-the-art success rate of 56%. In addition, our approach reduces input and output token usage by 55-87% and 41-70%, respectively, underscoring the importance of token-aware evaluation metrics in the development of scalable multi-agent LLM systems. The code and resources are available at: https://anonymous.4open.science/r/CodifyingAgent-5A86

Despite the advancements in training Large Language Models (LLMs) with alignment techniques to enhance the safety of generated content, these models remain susceptible to jailbreak, an adversarial attack method that exposes security vulnerabilities in LLMs. Notably, the Greedy Coordinate Gradient (GCG) method has demonstrated the ability to automatically generate adversarial suffixes that jailbreak state-of-the-art LLMs. However, the optimization process involved in GCG is highly time-consuming, rendering the jailbreaking pipeline inefficient. In this paper, we investigate the process of GCG and identify an issue of Indirect Effect, the key bottleneck of the GCG optimization. To this end, we propose the Model Attack Gradient Index GCG (MAGIC), that addresses the Indirect Effect by exploiting the gradient information of the suffix tokens, thereby accelerating the procedure by having less computation and fewer iterations. Our experiments on AdvBench show that MAGIC achieves up to a 1.5x speedup, while maintaining Attack Success Rates (ASR) on par or even higher than other baselines. Our MAGIC achieved an ASR of 74% on the Llama-2 and an ASR of 54% when conducting transfer attacks on GPT-3.5. Code is available at https://github.com/jiah-li/magic.

Software testing and verification are critical for ensuring the reliability and security of modern software systems. Traditionally, formal verification techniques, such as model checking and theorem proving, have provided rigorous frameworks for detecting bugs and vulnerabilities. However, these methods often face scalability challenges when applied to complex, real-world programs. Recently, the advent of Large Language Models (LLMs) has introduced a new paradigm for software analysis, leveraging their ability to understand insecure coding practices. Although LLMs demonstrate promising capabilities in tasks such as bug prediction and invariant generation, they lack the formal guarantees of classical methods. This paper presents a comprehensive study of state-of-the-art software testing and verification, focusing on three key approaches: classical formal methods, LLM-based analysis, and emerging hybrid techniques, which combine their strengths. We explore each approach's strengths, limitations, and practical applications, highlighting the potential of hybrid systems to address the weaknesses of standalone methods. We analyze whether integrating formal rigor with LLM-driven insights can enhance the effectiveness and scalability of software verification, exploring their viability as a pathway toward more robust and adaptive testing frameworks.

In this paper we present a novel solution that combines the capabilities of Large Language Models (LLMs) with Formal Verification strategies to verify and automatically repair software vulnerabilities. Initially, we employ Bounded Model Checking (BMC) to locate the software vulnerability and derive a counterexample. The counterexample provides evidence that the system behaves incorrectly or contains a vulnerability. The counterexample that has been detected, along with the source code, are provided to the LLM engine. Our approach involves establishing a specialized prompt language for conducting code debugging and generation to understand the vulnerability's root cause and repair the code. Finally, we use BMC to verify the corrected version of the code generated by the LLM. As a proof of concept, we create ESBMC-AI based on the Efficient SMT-based Context-Bounded Model Checker (ESBMC) and a pre-trained Transformer model, specifically gpt-3.5-turbo, to detect and fix errors in C programs. Our experimentation involved generating a dataset comprising 1000 C code samples, each consisting of 20 to 50 lines of code. Notably, our proposed method achieved an impressive success rate of up to 80% in repairing vulnerable code encompassing buffer overflow and pointer dereference failures. We assert that this automated approach can effectively incorporate into the software development lifecycle's continuous integration and deployment (CI/CD) process.

We introduce the AutoGRAMS framework for programming multi-step interactions with language models. AutoGRAMS represents AI agents as a graph, where each node can execute either a language modeling instruction or traditional code. Likewise, transitions in the graph can be governed by either language modeling decisions or traditional branch logic. AutoGRAMS supports using variables as memory and allows nodes to call other AutoGRAMS graphs as functions. We show how AutoGRAMS can be used to design highly sophisticated agents, including self-referential agents that can modify their own graph. AutoGRAMS's graph-centric approach aids interpretability, controllability, and safety during the design, development, and deployment of AI agents. We provide our framework as open source at https://github.com/autograms/autograms .

The rapid advancement of Large Language Models (LLMs) has brought about remarkable generative capabilities but also raised concerns about their potential misuse. While strategies like supervised fine-tuning and reinforcement learning from human feedback have enhanced their safety, these methods primarily focus on natural languages, which may not generalize to other domains. This paper introduces CodeAttack, a framework that transforms natural language inputs into code inputs, presenting a novel environment for testing the safety generalization of LLMs. Our comprehensive studies on state-of-the-art LLMs including GPT-4, Claude-2, and Llama-2 series reveal a new and universal safety vulnerability of these models against code input: CodeAttack bypasses the safety guardrails of all models more than 80\% of the time. We find that a larger distribution gap between CodeAttack and natural language leads to weaker safety generalization, such as encoding natural language input with data structures. Furthermore, we give our hypotheses about the success of CodeAttack: the misaligned bias acquired by LLMs during code training, prioritizing code completion over avoiding the potential safety risk. Finally, we analyze potential mitigation measures. These findings highlight new safety risks in the code domain and the need for more robust safety alignment algorithms to match the code capabilities of LLMs.

We propose Token Turing Machines (TTM), a sequential, autoregressive Transformer model with memory for real-world sequential visual understanding. Our model is inspired by the seminal Neural Turing Machine, and has an external memory consisting of a set of tokens which summarise the previous history (i.e., frames). This memory is efficiently addressed, read and written using a Transformer as the processing unit/controller at each step. The model's memory module ensures that a new observation will only be processed with the contents of the memory (and not the entire history), meaning that it can efficiently process long sequences with a bounded computational cost at each step. We show that TTM outperforms other alternatives, such as other Transformer models designed for long sequences and recurrent neural networks, on two real-world sequential visual understanding tasks: online temporal activity detection from videos and vision-based robot action policy learning. Code is publicly available at: https://github.com/google-research/scenic/tree/main/scenic/projects/token_turing

Recent studies operationalize self-improvement through coding agents that edit their own codebases. They grow a tree of self-modifications through expansion strategies that favor higher software engineering benchmark performance, assuming that this implies more promising subsequent self-modifications. However, we identify a mismatch between the agent's self-improvement potential (metaproductivity) and its coding benchmark performance, namely the Metaproductivity-Performance Mismatch. Inspired by Huxley's concept of clade, we propose a metric (CMP) that aggregates the benchmark performances of the descendants of an agent as an indicator of its potential for self-improvement. We show that, in our self-improving coding agent development setting, access to the true CMP is sufficient to simulate how the G\"odel Machine would behave under certain assumptions. We introduce the Huxley-G\"odel Machine (HGM), which, by estimating CMP and using it as guidance, searches the tree of self-modifications. On SWE-bench Verified and Polyglot, HGM outperforms prior self-improving coding agent development methods while using less wall-clock time. Last but not least, HGM demonstrates strong transfer to other coding datasets and large language models. The agent optimized by HGM on SWE-bench Verified with GPT-5-mini and evaluated on SWE-bench Lite with GPT-5 achieves human-level performance, matching the best officially checked results of human-engineered coding agents. Our code is available at https://github.com/metauto-ai/HGM.

Modular neural networks without additional training have recently been shown to surpass end-to-end neural networks on challenging vision-language tasks. The latest such methods simultaneously introduce LLM-based code generation to build programs and a number of skill-specific, task-oriented modules to execute them. In this paper, we focus on ViperGPT and ask where its additional performance comes from and how much is due to the (state-of-art, end-to-end) BLIP-2 model it subsumes vs. additional symbolic components. To do so, we conduct a controlled study (comparing end-to-end, modular, and prompting-based methods across several VQA benchmarks). We find that ViperGPT's reported gains over BLIP-2 can be attributed to its selection of task-specific modules, and when we run ViperGPT using a more task-agnostic selection of modules, these gains go away. Additionally, ViperGPT retains much of its performance if we make prominent alterations to its selection of modules: e.g. removing or retaining only BLIP-2. Finally, we compare ViperGPT against a prompting-based decomposition strategy and find that, on some benchmarks, modular approaches significantly benefit by representing subtasks with natural language, instead of code.

Sparse Autoencoders (SAEs) have emerged as a promising solution for decomposing large language model representations into interpretable features. However, Paulo and Belrose (2025) have highlighted instability across different initialization seeds, and Heap et al. (2025) have pointed out that SAEs may not capture model-internal features. These problems likely stem from training SAEs on external datasets - either collected from the Web or generated by another model - which may contain out-of-distribution (OOD) data beyond the model's generalisation capabilities. This can result in hallucinated SAE features, which we term "Fake Features", that misrepresent the model's internal activations. To address these issues, we propose FaithfulSAE, a method that trains SAEs on the model's own synthetic dataset. Using FaithfulSAEs, we demonstrate that training SAEs on less-OOD instruction datasets results in SAEs being more stable across seeds. Notably, FaithfulSAEs outperform SAEs trained on web-based datasets in the SAE probing task and exhibit a lower Fake Feature Ratio in 5 out of 7 models. Overall, our approach eliminates the dependency on external datasets, advancing interpretability by better capturing model-internal features while highlighting the often neglected importance of SAE training datasets.

Large Language Models (LLMs) have demonstrated impressive capabilities in code generation. However, current evaluation datasets suffer from issues such as the lack of runnable test cases, deviation from the distribution of real-world code, and the ability to evaluate only the Python language. These limitations undermine the credibility of the evaluation results. To address these limitations, we introduce MRG-Bench (Multi-language Repository-level Code Generation Benchmark), a novel dataset that provides a more accurate evaluation of LLMs in practical repository-level code generation tasks. MRG-Bench has three main features: (1) practical data sourced from real-world code repositories that align to the practical distribution, (2) multiple programming languages support, including Python, Java, and Go, and (3) project-level runnable test cases to assess the quality of the generated code. Based on MRG-Bench, we conducted extensive experiments including large language models, long-context models, and RAG-related methods. These evaluation results demonstrate that current repository-level code generation techniques suffer from significant performance deficiencies. To further investigate why models fail, we designed novel experiments to annotate the underlying causes of generation errors. The results explicitly show that the majority of methods suffer from "difficulty in understanding user requirements," failing to comprehend their assigned tasks accurately. Moreover, the impact of different repository-level contexts on this issue exhibits significant disparities across different programming languages, suggesting that, in practice, specialized contextual information needs to be designed for different languages.

Open-ended text generation with autoregressive language models (LMs) is one of the core tasks in natural language processing. However, maximization-based decoding methods (e.g., greedy/beam search) often lead to the degeneration problem, i.e., the generated text is unnatural and contains undesirable repetitions. Existing solutions to this problem either introduce randomness prone to incoherence or require a look-ahead mechanism that demands extra computational overhead. In this study, we formulate open-ended text generation from a new perspective, i.e., we view it as an exploration process within a directed graph. Thereby, we understand the phenomenon of degeneration as circular loops within the directed graph. Based on our formulation, we propose a novel decoding method -- momentum decoding -- which encourages the LM to greedily explore new nodes outside the current graph. Meanwhile, it also allows the LM to return to the existing nodes with a momentum downgraded by a pre-defined resistance function. We extensively test our approach on three benchmarks from different domains through automatic and human evaluations. The results show that momentum decoding performs comparably with the current state of the art while enjoying notably improved inference speed and computation FLOPs. Furthermore, we conduct a detailed analysis to reveal the merits and inner workings of our approach. Our codes and other related resources are publicly available at https://github.com/gmftbyGMFTBY/MomentumDecoding.

Autoregressive large language models (LLMs) have made remarkable progress in various natural language generation tasks. However, they incur high computation cost and latency resulting from the autoregressive token-by-token generation. To address this issue, several approaches have been proposed to reduce computational cost using early-exit strategies. These strategies enable faster text generation using reduced computation without applying the full computation graph to each token. While existing token-level early exit methods show promising results for online inference, they cannot be readily applied for batch inferencing and Key-Value caching. This is because they have to wait until the last token in a batch exits before they can stop computing. This severely limits the practical application of such techniques. In this paper, we propose a simple and effective token-level early exit method, SkipDecode, designed to work seamlessly with batch inferencing and KV caching. It overcomes prior constraints by setting up a singular exit point for every token in a batch at each sequence position. It also guarantees a monotonic decrease in exit points, thereby eliminating the need to recompute KV Caches for preceding tokens. Rather than terminating computation prematurely as in prior works, our approach bypasses lower to middle layers, devoting most of the computational resources to upper layers, allowing later tokens to benefit from the compute expenditure by earlier tokens. Our experimental results show that SkipDecode can obtain 2x to 5x inference speedups with negligible regression across a variety of tasks. This is achieved using OPT models of 1.3 billion and 6.7 billion parameters, all the while being directly compatible with batching and KV caching optimization techniques.

Recent advances have demonstrated the promising capabilities of large language models (LLMs) in generating register-transfer level (RTL) code, such as Verilog. However, existing LLM-based frameworks still face significant challenges in accurately handling the complexity of real-world RTL designs, particularly those that are large-scale and involve multi-level module instantiations. To address this issue, we present ComplexVCoder, an open-source LLM-driven framework that enhances both the generation quality and efficiency of complex Verilog code. Specifically, we introduce a two-stage generation mechanism, which leverages an intermediate representation to enable a more accurate and structured transition from natural language descriptions to intricate Verilog designs. In addition, we introduce a rule-based alignment method and a domain-specific retrieval-augmented generation (RAG) to further improve the correctness of the synthesized code by incorporating relevant design knowledge during generation. To evaluate our approach, we construct a comprehensive dataset comprising 55 complex Verilog designs derived from real-world implementations. We also release an open-source benchmark suite for systematically assessing the quality of auto-generated RTL code together with the ComplexVCoder framework. Experimental results show that ComplexVCoder outperforms SOTA frameworks such as CodeV and RTLCoder by 14.6% and 22.2%, respectively, in terms of function correctness on complex Verilog benchmarks. Furthermore, ComplexVcoder achieves comparable generation performances in terms of functionality correctness using a lightweight 32B model (Qwen2.5), rivaling larger-scale models such as GPT-3.5 and DeepSeek-V3.

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.

We study lossless acceleration for seq2seq generation with a novel decoding algorithm -- Aggressive Decoding. Unlike the previous efforts (e.g., non-autoregressive decoding) speeding up seq2seq generation at the cost of quality loss, our approach aims to yield the identical (or better) generation compared with autoregressive decoding but in a significant speedup, achieved by innovative cooperation of aggressive decoding and verification that are both efficient due to parallel computing. We propose two Aggressive Decoding paradigms for 2 kinds of seq2seq tasks: 1) For the seq2seq tasks whose inputs and outputs are highly similar (e.g., Grammatical Error Correction), we propose Input-guided Aggressive Decoding (IAD) that aggressively copies from the input sentence as drafted decoded tokens to verify in parallel; 2) For other general seq2seq tasks (e.g., Machine Translation), we propose Generalized Aggressive Decoding (GAD) that first employs an additional non-autoregressive decoding model for aggressive decoding and then verifies in parallel in the autoregressive manner. We test Aggressive Decoding on the most popular 6-layer Transformer model on GPU in multiple seq2seq tasks: 1) For IAD, we show that it can introduce a 7x-9x speedup for the Transformer in Grammatical Error Correction and Text Simplification tasks with the identical results as greedy decoding; 2) For GAD, we observe a 3x-5x speedup with the identical or even better quality in two important seq2seq tasks: Machine Translation and Abstractive Summarization. Moreover, Aggressive Decoding can benefit even more from stronger computing devices that are better at parallel computing. Given the lossless quality as well as significant and promising speedup, we believe Aggressive Decoding may potentially evolve into a de facto standard for efficient and lossless seq2seq generation in the near future.

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,

LLM-assisted hardware verification is gaining substantial attention due to its potential to significantly reduce the cost and effort of crafting effective testbenches. It also serves as a critical enabler for LLM-aided end-to-end hardware language design. However, existing current LLMs often struggle with Register Transfer Level (RTL) code generation, resulting in testbenches that exhibit functional errors in Hardware Description Languages (HDL) logic. Motivated by the strong performance of LLMs in Python code generation under inference-time sampling strategies, and their promising capabilities as judge agents, we propose PRO-V a fully program generation multi-agent system for robust RTL verification. Pro-V incorporates an efficient best-of-n iterative sampling strategy to enhance the correctness of generated testbenches. Moreover, it introduces an LLM-as-a-judge aid validation framework featuring an automated prompt generation pipeline. By converting rule-based static analysis from the compiler into natural language through in-context learning, this pipeline enables LLMs to assist the compiler in determining whether verification failures stem from errors in the RTL design or the testbench. PRO-V attains a verification accuracy of 87.17% on golden RTL implementations and 76.28% on RTL mutants. Our code is open-sourced at https://github.com/stable-lab/Pro-V.

In this paper, we study the problem of generating obstinate (over-stability) adversarial examples by word substitution in NLP, where input text is meaningfully changed but the model's prediction does not, even though it should. Previous word substitution approaches have predominantly focused on manually designed antonym-based strategies for generating obstinate adversarial examples, which hinders its application as these strategies can only find a subset of obstinate adversarial examples and require human efforts. To address this issue, in this paper, we introduce a novel word substitution method named GradObstinate, a gradient-based approach that automatically generates obstinate adversarial examples without any constraints on the search space or the need for manual design principles. To empirically evaluate the efficacy of GradObstinate, we conduct comprehensive experiments on five representative models (Electra, ALBERT, Roberta, DistillBERT, and CLIP) finetuned on four NLP benchmarks (SST-2, MRPC, SNLI, and SQuAD) and a language-grounding benchmark (MSCOCO). Extensive experiments show that our proposed GradObstinate generates more powerful obstinate adversarial examples, exhibiting a higher attack success rate compared to antonym-based methods. Furthermore, to show the transferability of obstinate word substitutions found by GradObstinate, we replace the words in four representative NLP benchmarks with their obstinate substitutions. Notably, obstinate substitutions exhibit a high success rate when transferred to other models in black-box settings, including even GPT-3 and ChatGPT. Examples of obstinate adversarial examples found by GradObstinate are available at https://huggingface.co/spaces/anonauthors/SecretLanguage.

State-based sequence models like RWKV-7 offer a compelling alternative to Transformer architectures, achieving linear complexity while demonstrating greater expressive power in short-context scenarios and enabling state tracking beyond the \(TC^0\) complexity class. However, RWKV-7 lacks mechanisms for token-parameter interactions and native scalability, limiting its adaptability and growth without retraining. In this paper, we propose Meta-State, a novel extension to RWKV-7 that replaces attention mechanisms with a fully state-driven approach, integrating token-parameter interactions through a Self-State Encoder (SSE) mechanism. The SSE repurposes a portion of the RWKV-7 Weighted Key-Value (WKV) state as transformation weights to encode token-parameter interactions in a linear, state-driven manner without introducing new trainable matrices or softmax operations, while preserving the autoregressive property of token processing. Meta-State supports progressive model scaling by expanding the WKV state and parameter tokens, reusing existing parameters without retraining. Our approach bridges the gap between state-based modeling, token-parameter interactions, and scalable architectures, offering a flexible framework for efficient and adaptable sequence modeling with linear complexity and constant memory usage.