Daily Papers

We show how to "compile" human-readable programs into standard decoder-only transformer models. Our compiler, Tracr, generates models with known structure. This structure can be used to design experiments. For example, we use it to study "superposition" in transformers that execute multi-step algorithms. Additionally, the known structure of Tracr-compiled models can serve as ground-truth for evaluating interpretability methods. Commonly, because the "programs" learned by transformers are unknown it is unclear whether an interpretation succeeded. We demonstrate our approach by implementing and examining programs including computing token frequencies, sorting, and parenthesis checking. We provide an open-source implementation of Tracr at https://github.com/google-deepmind/tracr.

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.

Understanding sentences that contain mathematical expressions in text form poses significant challenges. To address this, the importance of converting these expressions into formula images has been highlighted. For instance, the expression ``x equals minus b plus or minus the square root of b squared minus four a c, all over two a'' is more readily comprehensible when displayed as an image x = -b pm sqrt{b^2 - 4ac}{2a}. To develop a text-to-image conversion system, we can break down the process into text-to-LaTeX and LaTeX-to-image conversions, with the latter being managed with by existing various LaTeX engines. However, the former approach has been notably hindered by the severe scarcity of text-to-LaTeX paired data, presenting a significant challenge in the field.In this context, we introduce MathBridge, the first extensive dataset for translating mathematical spoken English into LaTeX, which aims to establish a robust baseline for future research in text-to-LaTeX translation. MathBridge comprises approximately 23 million LaTeX formulas paired with corresponding spoken English expressions. Through comprehensive evaluations, including fine-tuning and testing with data, we discovered that MathBridge significantly enhances pre-trained language models' capabilities for text-to-LaTeX translation. Specifically, for the T5-large model, the sacreBLEU score increased from 4.77 to 46.8, demonstrating substantial enhancement. Our findings indicate the necessity for a new metric specifically for text-to-LaTeX conversion evaluation.

Visual programming languages (VPLs) provide coding without typing texts. VPL makes coding easy to programmers with automatically adding usually used some code structure. Beginners in coding have generally two main challenges; transforming ideas into logical expressions and syntax errors. Syntax errors are impossible with VPLs because of there is no forgotten parentheses and semicolons. VPLs provide to focus on algorithm for programmers. VPL is a new trend for educational robotic environments. In this study, Robot Operating System (ROS) compatible web based visual programming system has been developed for evarobot. ROS provides libraries and tools to help software developers create robot applications. It provides hardware abstraction, device drivers, libraries, visualizers, message-passing, package management, and more. Blockly has been used as VPL for the study and to generate / use blocks (commucation, sensing etc.). Some applications were generated like teleoperation, SLAM and wander etc. In this system, communication between server and client is supported by rosbridge package. Web page connected to ROS which runs on server using roslibjs library. Rosbridge provides a JSON API to ROS functionality for non-ROS programs.

Large Language Models (LLMs) have recently achieved remarkable progress in mathematical reasoning. To enable such capabilities, many existing works distill strong reasoning models into long chains of thought or design algorithms to construct high-quality math QA data for training. However, these efforts primarily focus on generating correct reasoning paths and answers, while largely overlooking the validity of the questions themselves. In this work, we propose Math Question Verification (MathQ-Verify), a novel five-stage pipeline designed to rigorously filter ill-posed or under-specified math problems. MathQ-Verify first performs format-level validation to remove redundant instructions and ensure that each question is syntactically well-formed. It then formalizes each question, decomposes it into atomic conditions, and verifies them against mathematical definitions. Next, it detects logical contradictions among these conditions, followed by a goal-oriented completeness check to ensure the question provides sufficient information for solving. To evaluate this task, we use existing benchmarks along with an additional dataset we construct, containing 2,147 math questions with diverse error types, each manually double-validated. Experiments show that MathQ-Verify achieves state-of-the-art performance across multiple benchmarks, improving the F1 score by up to 25 percentage points over the direct verification baseline. It further attains approximately 90% precision and 63% recall through a lightweight model voting scheme. MathQ-Verify offers a scalable and accurate solution for curating reliable mathematical datasets, reducing label noise and avoiding unnecessary computation on invalid questions. Our code and data are available at https://github.com/scuuy/MathQ-Verify.

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

Large language models show promise for autoformalization, the task of automatically translating natural language into formal languages. However, current autoformalization methods remain limited. The last reported state-of-the-art performance on the ProofNet formalization benchmark for the Lean proof assistant, achieved using Codex for Lean 3, only showed successful formalization of 16.1% of informal statements. Similarly, our evaluation of GPT-4o for Lean 4 only produces successful translations 34.9% of the time. Our analysis shows that the performance of these models is largely limited by their inability to generate formal statements that successfully type-check (i.e., are syntactically correct and consistent with types) - with a whopping 86.6% of GPT-4o errors starting from a type-check failure. In this work, we propose a method to fix this issue through decoding with type-check filtering, where we initially sample a diverse set of candidate formalizations for an informal statement, then use the Lean proof assistant to filter out candidates that do not type-check. Using GPT-4o as a base model, and combining our method with self-consistency, we obtain a +18.3% absolute increase in formalization accuracy, and achieve a new state-of-the-art of 53.2% on ProofNet with Lean 4.

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.

When applying automated speech recognition (ASR) for Belgian Dutch (Van Dyck et al. 2021), the output consists of an unsegmented stream of words, without any punctuation. A next step is to perform segmentation and insert punctuation, making the ASR output more readable and easy to manually correct. As far as we know there is no publicly available punctuation insertion system for Dutch that functions at a usable level. The model we present here is an extension of the models of Guhr et al. (2021) for Dutch and is made publicly available. We trained a sequence classification model, based on the Dutch language model RobBERT (Delobelle et al. 2020). For every word in the input sequence, the models predicts a punctuation marker that follows the word. We have also extended a multilingual model, for cases where the language is unknown or where code switching applies. When performing the task of segmentation, the application of the best models onto out of domain test data, a sliding window of 200 words of the ASR output stream is sent to the classifier, and segmentation is applied when the system predicts a segmenting punctuation sign with a ratio above threshold. Results show to be much better than a machine translation baseline approach.

We introduce {rm C{small LEVER}}, a high-quality, curated benchmark of 161 problems for end-to-end verified code generation in Lean. Each problem consists of (1) the task of generating a specification that matches a held-out ground-truth specification, and (2) the task of generating a Lean implementation that provably satisfies this specification. Unlike prior benchmarks, {rm C{small LEVER}} avoids test-case supervision, LLM-generated annotations, and specifications that leak implementation logic or allow vacuous solutions. All outputs are verified post-hoc using Lean's type checker to ensure machine-checkable correctness. We use {rm C{small LEVER}} to evaluate several few-shot and agentic approaches based on state-of-the-art language models. These methods all struggle to achieve full verification, establishing it as a challenging frontier benchmark for program synthesis and formal reasoning. Our benchmark can be found on GitHub(https://github.com/trishullab/clever) as well as HuggingFace(https://huggingface.co/datasets/amitayusht/clever). All our evaluation code is also available online(https://github.com/trishullab/clever-prover).

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.

Can you find an xy-equation that, when graphed, writes itself on the plane? This idea became internet-famous when a Wikipedia article on Tupper's self-referential formula went viral in 2012. Under scrutiny, the question has two flaws: it is meaningless (it depends on typography) and it is trivial (for reasons we will explain). We fix these flaws by formalizing the problem, and we give a very general solution using techniques from computability theory.

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

We introduce CheckEval, a novel evaluation framework using Large Language Models, addressing the challenges of ambiguity and inconsistency in current evaluation methods. CheckEval addresses these challenges by dividing evaluation criteria into detailed sub-aspects and constructing a checklist of Boolean questions for each, simplifying the evaluation. This approach not only renders the process more interpretable but also significantly enhances the robustness and reliability of results by focusing on specific evaluation dimensions. Validated through a focused case study using the SummEval benchmark, CheckEval indicates a strong correlation with human judgments. Furthermore, it demonstrates a highly consistent Inter-Annotator Agreement. These findings highlight the effectiveness of CheckEval for objective, flexible, and precise evaluations. By offering a customizable and interactive framework, CheckEval sets a new standard for the use of LLMs in evaluation, responding to the evolving needs of the field and establishing a clear method for future LLM-based evaluation.

Automated Test Case Generation (ATCG) is crucial for evaluating software reliability, particularly in competitive programming where robust algorithm assessments depend on diverse and accurate test cases. However, existing ATCG methods often fail to meet complex specifications or generate effective corner cases, limiting their utility. In this work, we introduce Context-Free Grammars with Counters (CCFGs), a formalism that captures both syntactic and semantic structures in input specifications. Using a fine-tuned CodeT5 model, we translate natural language input specifications into CCFGs, enabling the systematic generation of high-quality test cases. Experiments on the CodeContests dataset demonstrate that CCFG-based test cases outperform baseline methods in identifying incorrect algorithms, achieving significant gains in validity and effectiveness. Our approach provides a scalable and reliable grammar-driven framework for enhancing automated competitive programming evaluations.

Large Language Models (LLMs) have limited performance when solving arithmetic reasoning tasks and often provide incorrect answers. Unlike natural language understanding, math problems typically have a single correct answer, making the task of generating accurate solutions more challenging for LLMs. To the best of our knowledge, we are not aware of any LLMs that indicate their level of confidence in their responses which fuels a trust deficit in these models impeding their adoption. To address this deficiency, we propose `MathPrompter', a technique that improves performance of LLMs on arithmetic problems along with increased reliance in the predictions. MathPrompter uses the Zero-shot chain-of-thought prompting technique to generate multiple Algebraic expressions or Python functions to solve the same math problem in different ways and thereby raise the confidence level in the output results. This is in contrast to other prompt based CoT methods, where there is no check on the validity of the intermediate steps followed. Our technique improves over state-of-the-art on the MultiArith dataset (78.7%rightarrow92.5%) evaluated using 175B parameter GPT-based LLM.

As the probability (and thus perplexity) of a text is calculated based on the product of the probabilities of individual tokens, it may happen that one unlikely token significantly reduces the probability (i.e., increase the perplexity) of some otherwise highly probable input, while potentially representing a simple typographical error. Also, given that perplexity is a scalar value that refers to the entire input, information about the probability distribution within it is lost in the calculation (a relatively good text that has one unlikely token and another text in which each token is equally likely they can have the same perplexity value), especially for longer texts. As an alternative to scalar perplexity this research proposes a simple algorithm used to calculate vector values based on n-gram perplexities within the input. Such representations consider the previously mentioned aspects, and instead of a unique value, the relative perplexity of each text token is calculated, and these values are combined into a single vector representing the input.

Handwritten mathematical expression recognition (HMER) is a challenging task that has many potential applications. Recent methods for HMER have achieved outstanding performance with an encoder-decoder architecture. However, these methods adhere to the paradigm that the prediction is made "from one character to another", which inevitably yields prediction errors due to the complicated structures of mathematical expressions or crabbed handwritings. In this paper, we propose a simple and efficient method for HMER, which is the first to incorporate syntax information into an encoder-decoder network. Specifically, we present a set of grammar rules for converting the LaTeX markup sequence of each expression into a parsing tree; then, we model the markup sequence prediction as a tree traverse process with a deep neural network. In this way, the proposed method can effectively describe the syntax context of expressions, alleviating the structure prediction errors of HMER. Experiments on three benchmark datasets demonstrate that our method achieves better recognition performance than prior arts. To further validate the effectiveness of our method, we create a large-scale dataset consisting of 100k handwritten mathematical expression images acquired from ten thousand writers. The source code, new dataset, and pre-trained models of this work will be publicly available.

We describe SeCaV, a sequent calculus verifier for first-order logic in Isabelle/HOL, and the SeCaV Unshortener, an online tool that expands succinct derivations into the full SeCaV syntax. We leverage the power of Isabelle/HOL as a proof checker for our SeCaV derivations. The interactive features of Isabelle/HOL make our system transparent. For instance, the user can simply click on a side condition to see its exact definition. Our formalized soundness and completeness proofs pertain exactly to the calculus as exposed to the user and not just to some model of our tool. Users can also write their derivations in the SeCaV Unshortener, which provides a lighter syntax, and expand them for later verification. We have used both tools in our teaching.

Formula recognition presents significant challenges due to the complicated structure and varied notation of mathematical expressions. Despite continuous advancements in formula recognition models, the evaluation metrics employed by these models, such as BLEU and Edit Distance, still exhibit notable limitations. They overlook the fact that the same formula has diverse representations and is highly sensitive to the distribution of training data, thereby causing the unfairness in formula recognition evaluation. To this end, we propose a Character Detection Matching (CDM) metric, ensuring the evaluation objectivity by designing a image-level rather than LaTex-level metric score. Specifically, CDM renders both the model-predicted LaTeX and the ground-truth LaTeX formulas into image-formatted formulas, then employs visual feature extraction and localization techniques for precise character-level matching, incorporating spatial position information. Such a spatially-aware and character-matching method offers a more accurate and equitable evaluation compared with previous BLEU and Edit Distance metrics that rely solely on text-based character matching. Experimentally, we evaluated various formula recognition models using CDM, BLEU, and ExpRate metrics. Their results demonstrate that the CDM aligns more closely with human evaluation standards and provides a fairer comparison across different models by eliminating discrepancies caused by diverse formula representations.

This paper presents a case study on applying two model checkers, SPIN and DIVINE, to verify key properties of a C++ software framework, known as ADAPRO, originally developed at CERN. SPIN was used for verifying properties on the design level. DIVINE was used for verifying simple test applications that interacted with the implementation. Both model checkers were found to have their own respective sets of pros and cons, but the overall experience was positive. Because both model checkers were used in a complementary manner, they provided valuable new insights into the framework, which would arguably have been hard to gain by traditional testing and analysis tools only. Translating the C++ source code into the modeling language of the SPIN model checker helped to find flaws in the original design. With DIVINE, defects were found in parts of the code base that had already been subject to hundreds of hours of unit tests, integration tests, and acceptance tests. Most importantly, model checking was found to be easy to integrate into the workflow of the software project and bring added value, not only as verification, but also validation methodology. Therefore, using model checking for developing library-level code seems realistic and worth the effort.

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.

Critical Error Detection (CED) in machine translation aims to determine whether a translation is safe to use or contains unacceptable deviations in meaning. While the WMT21 English-German CED dataset provided the first benchmark, it is limited in scale, label balance, domain coverage, and temporal freshness. We present SynCED-EnDe, a new resource consisting of 1,000 gold-labeled and 8,000 silver-labeled sentence pairs, balanced 50/50 between error and non-error cases. SynCED-EnDe draws from diverse 2024-2025 sources (StackExchange, GOV.UK) and introduces explicit error subclasses, structured trigger flags, and fine-grained auxiliary judgments (obviousness, severity, localization complexity, contextual dependency, adequacy deviation). These enrichments enable systematic analyses of error risk and intricacy beyond binary detection. The dataset is permanently hosted on GitHub and Hugging Face, accompanied by documentation, annotation guidelines, and baseline scripts. Benchmark experiments with XLM-R and related encoders show substantial performance gains over WMT21 due to balanced labels and refined annotations. We envision SynCED-EnDe as a community resource to advance safe deployment of MT in information retrieval and conversational assistants, particularly in emerging contexts such as wearable AI devices.

Segmenting text into sentences plays an early and crucial role in many NLP systems. This is commonly achieved by using rule-based or statistical methods relying on lexical features such as punctuation. Although some recent works no longer exclusively rely on punctuation, we find that no prior method achieves all of (i) robustness to missing punctuation, (ii) effective adaptability to new domains, and (iii) high efficiency. We introduce a new model - Segment any Text (SaT) - to solve this problem. To enhance robustness, we propose a new pretraining scheme that ensures less reliance on punctuation. To address adaptability, we introduce an extra stage of parameter-efficient fine-tuning, establishing state-of-the-art performance in distinct domains such as verses from lyrics and legal documents. Along the way, we introduce architectural modifications that result in a threefold gain in speed over the previous state of the art and solve spurious reliance on context far in the future. Finally, we introduce a variant of our model with fine-tuning on a diverse, multilingual mixture of sentence-segmented data, acting as a drop-in replacement and enhancement for existing segmentation tools. Overall, our contributions provide a universal approach for segmenting any text. Our method outperforms all baselines - including strong LLMs - across 8 corpora spanning diverse domains and languages, especially in practically relevant situations where text is poorly formatted. Our models and code, including documentation, are available at https://huggingface.co/segment-any-text under the MIT license.

Exceptional mathematical reasoning ability is one of the key features that demonstrate the power of large language models (LLMs). How to comprehensively define and evaluate the mathematical abilities of LLMs, and even reflect the user experience in real-world scenarios, has emerged as a critical issue. Current benchmarks predominantly concentrate on problem-solving capabilities, which presents a substantial risk of model overfitting and fails to accurately represent genuine mathematical reasoning abilities. In this paper, we argue that if a model really understands a problem, it should be robustly and readily applied across a diverse array of tasks. Motivated by this, we introduce MATHCHECK, a well-designed checklist for testing task generalization and reasoning robustness, as well as an automatic tool to generate checklists efficiently. MATHCHECK includes multiple mathematical reasoning tasks and robustness test types to facilitate a comprehensive evaluation of both mathematical reasoning ability and behavior testing. Utilizing MATHCHECK, we develop MATHCHECK-GSM and MATHCHECK-GEO to assess mathematical textual reasoning and multi-modal reasoning capabilities, respectively, serving as upgraded versions of benchmarks including GSM8k, GeoQA, UniGeo, and Geometry3K. We adopt MATHCHECK-GSM and MATHCHECK-GEO to evaluate over 20 LLMs and 11 MLLMs, assessing their comprehensive mathematical reasoning abilities. Our results demonstrate that while frontier LLMs like GPT-4o continue to excel in various abilities on the checklist, many other model families exhibit a significant decline. Further experiments indicate that, compared to traditional math benchmarks, MATHCHECK better reflects true mathematical abilities and represents mathematical intelligence more linearly, thereby supporting our design. On our MATHCHECK, we can easily conduct detailed behavior analysis to deeply investigate models.

Large Language Models (LLMs) have catalyzed vibe coding, where users leverage LLMs to generate and iteratively refine code through natural language interactions until it passes their vibe check. Vibe check is tied to real-world human preference and goes beyond functionality: the solution should feel right, read cleanly, preserve intent, and remain correct. However, current code evaluation remains anchored to pass@k and captures only functional correctness, overlooking the non-functional instructions that users routinely apply. In this paper, we hypothesize that instruction following is the missing piece underlying vibe check that represents human preference in coding besides functional correctness. To quantify models' code instruction following capabilities with measurable signals, we present VeriCode, a taxonomy of 30 verifiable code instructions together with corresponding deterministic verifiers. We use the taxonomy to augment established evaluation suites, resulting in Vibe Checker, a testbed to assess both code instruction following and functional correctness. Upon evaluating 31 leading LLMs, we show that even the strongest models struggle to comply with multiple instructions and exhibit clear functional regression. Most importantly, a composite score of functional correctness and instruction following correlates the best with human preference, with the latter emerging as the primary differentiator on real-world programming tasks. Our work identifies core factors of the vibe check, providing a concrete path for benchmarking and developing models that better align with user preferences in coding.

In this article we describe an efficient approach to guiding language model text generation with regular expressions and context-free grammars. Our approach adds little to no overhead to the token sequence generation process, and makes guided generation feasible in practice. An implementation is provided in the open source Python library Outlines.

As language models regularly make mistakes when solving math problems, automated identification of errors in the reasoning process becomes increasingly significant for their scalable oversight. In this paper, we introduce ProcessBench for measuring the ability to identify erroneous steps in mathematical reasoning. It consists of 3,400 test cases, primarily focused on competition- and Olympiad-level math problems. Each test case contains a step-by-step solution with error location annotated by human experts. Models are required to identify the earliest step that contains an error, or conclude that all steps are correct. We conduct extensive evaluation on ProcessBench, involving two types of models: process reward models (PRMs) and critic models, where for the latter we prompt general language models to critique each solution step by step. We draw two main observations: (1) Existing PRMs typically fail to generalize to more challenging math problems beyond GSM8K and MATH. They underperform both critic models (i.e., prompted general language models) and our own trained PRM that is straightforwardly fine-tuned on the PRM800K dataset. (2) The best open-source model, QwQ-32B-Preview, has demonstrated the critique capability competitive with the proprietary model GPT-4o, despite that it still lags behind the reasoning-specialized o1-mini. We hope ProcessBench can foster future research in reasoning process assessment, paving the way toward scalable oversight of language models.

This position paper provides a critical but constructive discussion of current practices in benchmarking and evaluative practices in the field of formal reasoning and automated theorem proving. We take the position that open code, open data, and benchmarks that are complete and error-free will accelerate progress in this field. We identify practices that create barriers to contributing to this field and suggest ways to remove them. We also discuss some of the practices that might produce misleading evaluative information. We aim to create discussions that bring together people from various groups contributing to automated theorem proving, autoformalization, and informal reasoning.

Automated code generation with large language models has gained significant traction, but there remains no guarantee on the correctness of generated code. We aim to use formal verification to provide mathematical guarantees that the generated code is correct. However, generating formally verified code with LLMs is hindered by the scarcity of training data and the complexity of formal proofs. To tackle this challenge, we introduce AlphaVerus, a self-improving framework that bootstraps formally verified code generation by iteratively translating programs from a higher-resource language and leveraging feedback from a verifier. AlphaVerus operates in three phases: exploration of candidate translations, Treefinement -- a novel tree search algorithm for program refinement using verifier feedback, and filtering misaligned specifications and programs to prevent reward hacking. Through this iterative process, AlphaVerus enables a LLaMA-3.1-70B model to generate verified code without human intervention or model finetuning. AlphaVerus shows an ability to generate formally verified solutions for HumanEval and MBPP, laying the groundwork for truly trustworthy code-generation agents.

The demonstrated code-understanding capability of LLMs raises the question of whether they can be used for automated program verification, a task that often demands high-level abstract reasoning about program properties, which is challenging for verification tools. We propose a general methodology to combine the power of LLMs and automated reasoners for automated program verification. We formally describe this methodology as a set of derivation rules and prove its soundness. We instantiate the calculus as a sound automated verification procedure, which led to practical improvements on a set of synthetic and competition benchmarks.

Identifying subtle technical errors within complex scientific and technical documents, especially those requiring multimodal interpretation (e.g., formulas in images), presents a significant hurdle for Large Language Models (LLMs) whose inherent error-correction tendencies can mask inaccuracies. This exploratory proof-of-concept (PoC) study investigates structured LLM context conditioning, informed by Persistent Workflow Prompting (PWP) principles, as a methodological strategy to modulate this LLM behavior at inference time. The approach is designed to enhance the reliability of readily available, general-purpose LLMs (specifically Gemini 2.5 Pro and ChatGPT Plus o3) for precise validation tasks, crucially relying only on their standard chat interfaces without API access or model modifications. To explore this methodology, we focused on validating chemical formulas within a single, complex test paper with known textual and image-based errors. Several prompting strategies were evaluated: while basic prompts proved unreliable, an approach adapting PWP structures to rigorously condition the LLM's analytical mindset appeared to improve textual error identification with both models. Notably, this method also guided Gemini 2.5 Pro to repeatedly identify a subtle image-based formula error previously overlooked during manual review, a task where ChatGPT Plus o3 failed in our tests. These preliminary findings highlight specific LLM operational modes that impede detail-oriented validation and suggest that PWP-informed context conditioning offers a promising and highly accessible technique for developing more robust LLM-driven analytical workflows, particularly for tasks requiring meticulous error detection in scientific and technical documents. Extensive validation beyond this limited PoC is necessary to ascertain broader applicability.

We provide here a dataset for tasks related to natural language understanding and natural language inference. The dataset contains logical puzzles in natural language from three domains: comparing puzzles, knighs and knaves, and zebra puzzles. Each puzzle is associated with the entire set of atomic questions that can be generated based on the relations and individuals occurring in the text. For each question we provide the correct answer: entailment, contradiction or ambiguity. The answer's correctness is verified against theorem provers. Good puzzles have two properties: (i) each piece of information is necessary and (ii) no unnecessary information is provided. These properties make puzzles interesting candidates for machine comprehension tasks.

As large language models (LLMs) become more powerful and are deployed more autonomously, it will be increasingly important to prevent them from causing harmful outcomes. Researchers have investigated a variety of safety techniques for this purpose, e.g. using models to review the outputs of other models, or red-teaming techniques to surface subtle failure modes. However, researchers have not evaluated whether such techniques still ensure safety if the model is itself intentionally trying to subvert them. In this paper, we develop and evaluate pipelines of safety techniques ("protocols") that are robust to intentional subversion. We investigate a scenario in which we want to solve a sequence of programming problems, using access to a powerful but untrusted model (in our case, GPT-4), access to a less powerful trusted model (in our case, GPT-3.5), and limited access to high-quality trusted labor. We investigate protocols that aim to never submit solutions containing backdoors, which we operationalize here as logical errors that are not caught by test cases. We investigate a range of protocols and test each against strategies that the untrusted model could use to subvert them. One protocol is what we call trusted editing. This protocol first asks GPT-4 to write code, and then asks GPT-3.5 to rate the suspiciousness of that code. If the code is below some suspiciousness threshold, it is submitted. Otherwise, GPT-3.5 edits the solution to remove parts that seem suspicious and then submits the edited code. Another protocol is untrusted monitoring. This protocol asks GPT-4 to write code, and then asks another instance of GPT-4 whether the code is backdoored, using various techniques to prevent the GPT-4 instances from colluding. These protocols improve substantially on simple baselines.

High-quality, large-scale corpora are the cornerstone of building foundation models. In this work, we introduce MathPile, a diverse and high-quality math-centric corpus comprising about 9.5 billion tokens. Throughout its creation, we adhered to the principle of ``less is more'', firmly believing in the supremacy of data quality over quantity, even in the pre-training phase. Our meticulous data collection and processing efforts included a complex suite of preprocessing, prefiltering, language identification, cleaning, filtering, and deduplication, ensuring the high quality of our corpus. Furthermore, we performed data contamination detection on downstream benchmark test sets to eliminate duplicates. We hope our MathPile can help to enhance the mathematical reasoning abilities of language models. We plan to open-source different versions of \mathpile with the scripts used for processing, to facilitate future developments in this field.

Text Normalization is an integral part of any text-to-speech synthesis system. In a natural language text, there are elements such as numbers, dates, abbreviations, etc. that belong to other semiotic classes. They are called non-standard words (NSW) and need to be expanded into ordinary words. For this purpose, it is necessary to identify the semiotic class of each NSW. The taxonomy of semiotic classes adapted to the Lithuanian language is presented in the work. Sets of rules are created for detecting and expanding NSWs based on regular expressions. Experiments with three completely different data sets were performed and the accuracy was assessed. Causes of errors are explained and recommendations are given for the development of text normalization rules.

We introduce refutationally complete superposition calculi for intentional and extensional clausal lambda-free higher-order logic, two formalisms that allow partial application and applied variables. The calculi are parameterized by a term order that need not be fully monotonic, making it possible to employ the lambda-free higher-order lexicographic path and Knuth-Bendix orders. We implemented the calculi in the Zipperposition prover and evaluated them on Isabelle/HOL and TPTP benchmarks. They appear promising as a stepping stone towards complete, highly efficient automatic theorem provers for full higher-order logic.

Chinese Spell Checking (CSC) aims to detect and correct erroneous characters for user-generated text in the Chinese language. Most of the Chinese spelling errors are misused semantically, phonetically or graphically similar characters. Previous attempts noticed this phenomenon and try to use the similarity for this task. However, these methods use either heuristics or handcrafted confusion sets to predict the correct character. In this paper, we propose a Chinese spell checker called ReaLiSe, by directly leveraging the multimodal information of the Chinese characters. The ReaLiSe model tackles the CSC task by (1) capturing the semantic, phonetic and graphic information of the input characters, and (2) selectively mixing the information in these modalities to predict the correct output. Experiments on the SIGHAN benchmarks show that the proposed model outperforms strong baselines by a large margin.

In infilling tasks, sub-tokens, representing instances where a complete token is segmented into two parts, often emerge at the boundaries of prefixes, middles, and suffixes. Traditional methods focused on training models at the token level, leading to sub-optimal performance in character-level infilling tasks during the inference stage. Alternately, some approaches considered character-level infilling, but they relied on predicting sub-tokens in inference, yet this strategy diminished ability in character-level infilling tasks due to the large perplexity of the model on sub-tokens. In this paper, we introduce FIM-SE, which stands for Fill-In-the-Middle with both Starting and Ending character constraints. The proposed method addresses character-level infilling tasks by utilizing a line-level format to avoid predicting any sub-token in inference. In addition, we incorporate two special tokens to signify the rest of the incomplete lines, thereby enhancing generation guidance. Extensive experiments demonstrate that our proposed approach surpasses previous methods, offering a significant advantage. Code is available at https://github.com/SenseLLM/FIM-SE.

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.

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.

Input constraints are useful for many software development tasks. For example, input constraints of a function enable the generation of valid inputs, i.e., inputs that follow these constraints, to test the function deeper. API functions of deep learning (DL) libraries have DL specific input constraints, which are described informally in the free form API documentation. Existing constraint extraction techniques are ineffective for extracting DL specific input constraints. To fill this gap, we design and implement a new technique, DocTer, to analyze API documentation to extract DL specific input constraints for DL API functions. DocTer features a novel algorithm that automatically constructs rules to extract API parameter constraints from syntactic patterns in the form of dependency parse trees of API descriptions. These rules are then applied to a large volume of API documents in popular DL libraries to extract their input parameter constraints. To demonstrate the effectiveness of the extracted constraints, DocTer uses the constraints to enable the automatic generation of valid and invalid inputs to test DL API functions. Our evaluation on three popular DL libraries (TensorFlow, PyTorch, and MXNet) shows that the precision of DocTer in extracting input constraints is 85.4%. DocTer detects 94 bugs from 174 API functions, including one previously unknown security vulnerability that is now documented in the CVE database, while a baseline technique without input constraints detects only 59 bugs. Most (63) of the 94 bugs are previously unknown, 54 of which have been fixed or confirmed by developers after we report them. In addition, DocTer detects 43 inconsistencies in documents, 39 of which are fixed or confirmed.

Grammatical error correction aims to correct ungrammatical sentences automatically. Recently, some work has demonstrated the excellent capabilities of closed-source Large Language Models (LLMs, e.g., ChatGPT) in grammatical error correction. However, the potential of open-source LLMs remains unexplored. In this paper, we introduced GrammarGPT, an open-source LLM, to preliminary explore its potential for native Chinese grammatical error correction. The core recipe of GrammarGPT is to leverage the hybrid dataset of ChatGPT-generated and human-annotated. For grammatical errors with clues, we proposed a heuristic method to guide ChatGPT to generate ungrammatical sentences by providing those clues. For grammatical errors without clues, we collected ungrammatical sentences from publicly available websites and manually corrected them. In addition, we employed an error-invariant augmentation method to enhance the ability of the model to correct native Chinese grammatical errors. We ultimately constructed about 1k parallel data and utilized these data to fine-tune open-source LLMs (e.g., Phoenix, released by The Chinese University of Hong Kong, Shenzhen) with instruction tuning. The experimental results show that GrammarGPT outperforms the existing SOTA system significantly. Although model parameters are 20x larger than the SOTA baseline, the required amount of data for instruction tuning is 1200x smaller, illustrating the potential of open-source LLMs on native CGEC. Our GrammarGPT ranks 3^{rd} on NLPCC2023 SharedTask1, demonstrating our approach's effectiveness. The code and data are available at https://github.com/FreedomIntelligence/GrammarGPT.

Recent advancements in large language models (LLMs) have substantially enhanced their mathematical reasoning abilities. However, these models still struggle with complex problems that require multiple reasoning steps, frequently leading to logical or numerical errors. While numerical mistakes can be largely addressed by integrating a code interpreter, identifying logical errors within intermediate steps is more challenging. Moreover, manually annotating these steps for training is not only expensive but also labor-intensive, requiring the expertise of professional annotators. In our study, we introduce an innovative approach that bypasses the need for process annotations (from human or GPTs) by utilizing the Monte Carlo Tree Search (MCTS) framework. This technique automatically generates both the process supervision and the step-level evaluation signals. Our method iteratively trains the policy and value models, leveraging the capabilities of a well-pretrained LLM to progressively enhance its mathematical reasoning skills. Furthermore, we propose an efficient inference strategy-step-level beam search, where the value model is crafted to assist the policy model (i.e., LLM) in navigating more effective reasoning paths, rather than solely relying on prior probabilities. The experimental results on both in-domain and out-of-domain datasets demonstrate that even without GPT-4 or human-annotated process supervision, our AlphaMath framework achieves comparable or superior results to previous state-of-the-art methods.

In this paper, we present a rule-based sentence boundary disambiguation Python package that works out-of-the-box for 22 languages. We aim to provide a realistic segmenter which can provide logical sentences even when the format and domain of the input text is unknown. In our work, we adapt the Golden Rules Set (a language-specific set of sentence boundary exemplars) originally implemented as a ruby gem - pragmatic_segmenter - which we ported to Python with additional improvements and functionality. PySBD passes 97.92% of the Golden Rule Set exemplars for English, an improvement of 25% over the next best open-source Python tool.

This report overviews our ongoing work in enriching chain-of-thoughts datasets requiring arithmetical reasoning with the integration of non-parametric components, such as a calculator. We conduct an analysis of prominent relevant datasets such as GSM8K, Ape210K, AQuA-RAT, and MathQA and propose a machine-processable HTML-like format specifically tailored for working with semi-structured chains. By converting the datasets into this unified format, we enable the effective integration of large language models and symbolic systems, empowering them to tackle arithmetical reasoning tasks more efficiently.

Proof automation is crucial to large-scale formal mathematics and software/hardware verification projects in ITPs. Sophisticated tools called hammers have been developed to provide general-purpose proof automation in ITPs such as Coq and Isabelle, leveraging the power of ATPs. An important component of a hammer is the translation algorithm from the ITP's logical system to the ATP's logical system. In this paper, we propose a novel translation algorithm for ITPs based on dependent type theory. The algorithm is implemented in Lean 4 under the name Lean-auto. When combined with ATPs, Lean-auto provides general-purpose, ATP-based proof automation in Lean 4 for the first time. Soundness of the main translation procedure is guaranteed, and experimental results suggest that our algorithm is sufficiently complete to automate the proof of many problems that arise in practical uses of Lean 4. We also find that Lean-auto solves more problems than existing tools on Lean 4's math library Mathlib4.

While slow-thinking large language models (LLMs) exhibit reflection-like reasoning, commonly referred to as the "aha moment:, their ability to generate informative critiques and refine prior solutions remains limited. In this paper, we introduce Double-Checker, a principled framework designed to enhance the reasoning capabilities of slow-thinking LLMs by fostering explicit self-critique and iterative refinement of their previous solutions. By fine-tuning on our curated 1,730 self-critical instances, Double-Checker empowers long-CoT LLMs to iteratively critique and refine their outputs during inference until they evaluate their solutions as correct under self-generated critiques. We validate the efficacy of Double-Checker across a comprehensive suite of reasoning benchmarks, demonstrating that iterative self-critique significantly enhances the reasoning capabilities of long-CoT LLMs. Notably, our Double-Checker increases the pass@1 performance on challenging AIME benchmarks from 4.4% to 18.2% compared to the original long-CoT LLMs. These results highlight a promising direction for developing more trustworthy and effective LLMs capable of structured self-critique. Our codes and data are available at https://github.com/XinXU-USTC/DoubleChecker

While pre-trained Chinese language models have demonstrated impressive performance on a wide range of NLP tasks, the Chinese Spell Checking (CSC) task remains a challenge. Previous research has explored using information such as glyphs and phonetics to improve the ability to distinguish misspelled characters, with good results. However, the generalization ability of these models is not well understood: it is unclear whether they incorporate glyph-phonetic information and, if so, whether this information is fully utilized. In this paper, we aim to better understand the role of glyph-phonetic information in the CSC task and suggest directions for improvement. Additionally, we propose a new, more challenging, and practical setting for testing the generalizability of CSC models. All code is made publicly available.

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 .

We perform a thorough analysis of the formal and informal statements in the miniF2F benchmark from the perspective of an AI system that is tasked to participate in a math Olympiad consisting of the problems in miniF2F. In such setting, the model has to read and comprehend the problems in natural language, formalize them in Lean language, then proceed with proving the problems, and it will get credit for each problem if the formal proof corresponds to the original informal statement presented to the model. Our evaluation results reveal that the best accuracy of such pipeline can be about 36% using the SoTA models in the literature, considerably lower than the individual SoTA accuracies, 97% and 69% reported in the autoformalization and theorem proving literature. Analyzing the failure modes, we trace back a considerable portion of this drop to discrepancies between the formal and informal statements for more than half of the problems in miniF2F. We proceed with correcting all the errors, discrepancies and simplifications in formal and informal statements, and present the miniF2F-v2 with fully verified formal and informal statements and proofs. Evaluating the full theorem proving pipeline on miniF2F-v2 leads to the best accuracy of 70%, a significant improvement from the 40% on the original miniF2F, yet indicating considerable misalignment between the autoformalization models and theorem provers. Our deep analysis suggests that a higher quality benchmark can help the community better evaluate progress in the field of formal reasoning and also better diagnose the failure and success modes of autoformalization and theorem proving models. Our dataset is available at https://github.com/roozbeh-yz/miniF2F_v2.

We investigate the mathematical capabilities of ChatGPT by testing it on publicly available datasets, as well as hand-crafted ones, and measuring its performance against other models trained on a mathematical corpus, such as Minerva. We also test whether ChatGPT can be a useful assistant to professional mathematicians by emulating various use cases that come up in the daily professional activities of mathematicians (question answering, theorem searching). In contrast to formal mathematics, where large databases of formal proofs are available (e.g., the Lean Mathematical Library), current datasets of natural-language mathematics, used to benchmark language models, only cover elementary mathematics. We address this issue by introducing a new dataset: GHOSTS. It is the first natural-language dataset made and curated by working researchers in mathematics that (1) aims to cover graduate-level mathematics and (2) provides a holistic overview of the mathematical capabilities of language models. We benchmark ChatGPT on GHOSTS and evaluate performance against fine-grained criteria. We make this new dataset publicly available to assist a community-driven comparison of ChatGPT with (future) large language models in terms of advanced mathematical comprehension. We conclude that contrary to many positive reports in the media (a potential case of selection bias), ChatGPT's mathematical abilities are significantly below those of an average mathematics graduate student. Our results show that ChatGPT often understands the question but fails to provide correct solutions. Hence, if your goal is to use it to pass a university exam, you would be better off copying from your average peer!

Math reasoning is becoming an ever increasing area of focus as we scale large language models. However, even the previously-toughest evals like MATH are now close to saturated by frontier models (90.0% for o1-mini and 86.5% for Gemini 1.5 Pro). We introduce HARP, Human Annotated Reasoning Problems (for Math), consisting of 5,409 problems from the US national math competitions (A(J)HSME, AMC, AIME, USA(J)MO). Of these, 4,780 have answers that are automatically check-able (with libraries such as SymPy). These problems range six difficulty levels, with frontier models performing relatively poorly on the hardest bracket of 197 problems (average accuracy 41.1% for o1-mini, and 9.6% for Gemini 1.5 Pro). Our dataset also features multiple choices (for 4,110 problems) and an average of two human-written, ground-truth solutions per problem, offering new avenues of research that we explore briefly. We report evaluations for many frontier models and share some interesting analyses, such as demonstrating that frontier models across families intrinsically scale their inference-time compute for more difficult problems. Finally, we open source all code used for dataset construction (including scraping) and all code for evaluation (including answer checking) to enable future research at: https://github.com/aadityasingh/HARP.

Formal mathematical reasoning remains a critical challenge for artificial intelligence, hindered by limitations of existing benchmarks in scope and scale. To address this, we present FormalMATH, a large-scale Lean4 benchmark comprising 5,560 formally verified problems spanning from high-school Olympiad challenges to undergraduate-level theorems across diverse domains (e.g., algebra, applied mathematics, calculus, number theory, and discrete mathematics). To mitigate the inefficiency of manual formalization, we introduce a novel human-in-the-loop autoformalization pipeline that integrates: (1) specialized large language models (LLMs) for statement autoformalization, (2) multi-LLM semantic verification, and (3) negation-based disproof filtering strategies using off-the-shelf LLM-based provers. This approach reduces expert annotation costs by retaining 72.09% of statements before manual verification while ensuring fidelity to the original natural-language problems. Our evaluation of state-of-the-art LLM-based theorem provers reveals significant limitations: even the strongest models achieve only 16.46% success rate under practical sampling budgets, exhibiting pronounced domain bias (e.g., excelling in algebra but failing in calculus) and over-reliance on simplified automation tactics. Notably, we identify a counterintuitive inverse relationship between natural-language solution guidance and proof success in chain-of-thought reasoning scenarios, suggesting that human-written informal reasoning introduces noise rather than clarity in the formal reasoning settings. We believe that FormalMATH provides a robust benchmark for benchmarking formal mathematical reasoning.

A primary concern regarding training large language models (LLMs) is whether they abuse copyrighted online text. With the increasing training data scale and the prevalence of LLMs in daily lives, two problems arise: 1) false positive membership inference results misled by similar examples; 2) membership inference methods are usually too complex for end users to understand and use. To address these issues, we propose an alternative insert-and-detect methodology, advocating that web users and content platforms employ \textit{unique identifiers} for reliable and independent membership inference. Users and platforms can create their identifiers, embed them in copyrighted text, and independently detect them in future LLMs. As an initial demonstration, we introduce \textbf{ghost sentences} and a user-friendly last-k words test, allowing end users to chat with LLMs for membership inference. Ghost sentences consist primarily of unique passphrases of random natural words, which can come with customized elements to bypass possible filter rules. The last-k words test requires a significant repetition time of ghost sentences~(ge10). For cases with fewer repetitions, we designed an extra perplexity test, as LLMs exhibit high perplexity when encountering unnatural passphrases. We also conduct a comprehensive study on the memorization and membership inference of ghost sentences, examining factors such as training data scales, model sizes, repetition times, insertion positions, wordlist of passphrases, alignment, etc. Our study shows the possibility of applying ghost sentences in real scenarios and provides instructions for the potential application.

Autoformalization, which translates natural language mathematics into machine-verifiable formal statements, is critical for using formal mathematical reasoning to solve math problems stated in natural language. While Large Language Models can generate syntactically correct formal statements, they often fail to preserve the original problem's semantic intent. This limitation arises from the LLM approaches' treating autoformalization as a simplistic translation task which lacks mechanisms for self-reflection and iterative refinement that human experts naturally employ. To address these issues, we propose ReForm, a Reflective Autoformalization method that tightly integrates semantic consistency evaluation into the autoformalization process. This enables the model to iteratively generate formal statements, assess its semantic fidelity, and self-correct identified errors through progressive refinement. To effectively train this reflective model, we introduce Prospective Bounded Sequence Optimization (PBSO), which employs different rewards at different sequence positions to ensure that the model develops both accurate autoformalization and correct semantic validations, preventing superficial critiques that would undermine the purpose of reflection. Extensive experiments across four autoformalization benchmarks demonstrate that ReForm achieves an average improvement of 17.2 percentage points over the strongest baselines. To further ensure evaluation reliability, we introduce ConsistencyCheck, a benchmark of 859 expert-annotated items that not only validates LLMs as judges but also reveals that autoformalization is inherently difficult: even human experts produce semantic errors in up to 38.5% of cases.

Large Language Models (LLMs) are often asked to generate structured outputs that obey precise syntactic rules, such as code snippets or formatted data. Grammar-constrained decoding (GCD) can guarantee that LLM outputs matches such rules by masking out tokens that will provably lead to outputs that do not belong to a specified context-free grammar (CFG). To guarantee soundness, GCD algorithms have to compute how a given LLM subword tokenizer can align with the tokens used by a given context-free grammar and compute token masks based on this information. Doing so efficiently is challenging and existing GCD algorithms require tens of minutes to preprocess common grammars. We present a new GCD algorithm together with an implementation that offers 17.71x faster offline preprocessing than existing approaches while preserving state-of-the-art efficiency in online mask computation.

Software testing plays a critical role in ensuring that systems behave as intended. However, existing automated testing approaches struggle to match the capabilities of human engineers due to key limitations such as test locality, lack of general reliability, and business logic blindness. In this work, we propose a novel framework that leverages functional programming and type systems to translate Scala backend code into formal Lean representations. Our pipeline automatically generates theorems that specify the intended behavior of APIs and database operations, and uses LLM-based provers to verify them. When a theorem is proved, the corresponding logic is guaranteed to be correct and no further testing is needed. If the negation of a theorem is proved instead, it confirms a bug. In cases where neither can be proved, human intervention is required. We evaluate our method on realistic backend systems and find that it can formally verify over 50% of the test requirements, which suggests that half of a testing engineer's workload can be automated. Additionally, with an average cost of only $2.19 per API, LLM-based verification is significantly more cost-effective than manual testing and can be scaled easily through parallel execution. Our results indicate a promising direction for scalable, AI-powered software testing, with the potential to greatly improve engineering productivity as models continue to advance.

In this work, we measure the impact of affixal negation on modern English large language models (LLMs). In affixal negation, the negated meaning is expressed through a negative morpheme, which is potentially challenging for LLMs as their tokenizers are often not morphologically plausible. We conduct extensive experiments using LLMs with different subword tokenization methods, which lead to several insights on the interaction between tokenization performance and negation sensitivity. Despite some interesting mismatches between tokenization accuracy and negation detection performance, we show that models can, on the whole, reliably recognize the meaning of affixal negation.

Large Language Models (LLMs) are highly sensitive to subtle, non-semantic variations in prompt phrasing and formatting. In this work, we present the first systematic evaluation of 5 methods for improving prompt robustness within a unified experimental framework. We benchmark these techniques on 8 models from Llama, Qwen and Gemma families across 52 tasks from Natural Instructions dataset. Our evaluation covers robustness methods from both fine-tuned and in-context learning paradigms, and tests their generalization against multiple types of distribution shifts. Finally, we extend our analysis to GPT-4.1 and DeepSeek V3 to assess frontier models' current robustness to format perturbations. Our findings offer actionable insights into the relative effectiveness of these robustness methods, enabling practitioners to make informed decisions when aiming for stable and reliable LLM performance in real-world applications. Code: https://github.com/AIRI-Institute/when-punctuation-matters.

Reasoning methods such as chain-of-thought prompting and self-consistency have shown immense potential to improve the accuracy of large language models across various reasoning tasks. However such methods involve generation of lengthy reasoning chains, which substantially increases token consumption, computational cost, and latency. To address this inefficiency, we propose ProofSketch, a verification-guided reasoning framework that integrates symbolic closure computation, lexicographic verification and adaptive sketch generation. Our experiments show that ProofSketch consistently reduces token usage while improving accuracy, demonstrating that this approach offers a promising path for efficient and trustworthy reasoning.

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.

We present the KL3M tokenizers, a family of specialized tokenizers for legal, financial, and governmental text. Despite established work on tokenization, specialized tokenizers for professional domains remain understudied. Our paper offers two main contributions to this area. First, we introduce domain-specific BPE tokenizers for legal, financial, and governmental text. Our kl3m-004-128k-cased tokenizer uses 9-17% fewer tokens than GPT-4o and Llama3 for domain-specific documents, despite having a smaller vocabulary. For specialized terminology, our cased tokenizer is even more efficient, using up to 83% fewer tokens for legal terms and 39% fewer tokens for financial terms. Second, we develop character-level BPE tokenizers (4K, 8K, and 16K vocabulary sizes) for text correction tasks like OCR post-processing. These tokenizers keep consistent token boundaries between error-containing and correct text, making it easier for models to learn correction patterns. These tokenizers help professional applications by fitting more text in context windows, reducing computational needs, and preserving the meaning of domain-specific terms. Our analysis shows these efficiency gains directly benefit the processing of long legal and financial documents. We release all tokenizers and code through GitHub and Hugging Face to support further research in specialized tokenization.

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.

Spreadsheets are widely used for table manipulation and presentation. Stylistic formatting of these tables is an important property for both presentation and analysis. As a result, popular spreadsheet software, such as Excel, supports automatically formatting tables based on rules. Unfortunately, writing such formatting rules can be challenging for users as it requires knowledge of the underlying rule language and data logic. We present CORNET, a system that tackles the novel problem of automatically learning such formatting rules from user examples in the form of formatted cells. CORNET takes inspiration from advances in inductive programming and combines symbolic rule enumeration with a neural ranker to learn conditional formatting rules. To motivate and evaluate our approach, we extracted tables with over 450K unique formatting rules from a corpus of over 1.8M real worksheets. Since we are the first to introduce conditional formatting, we compare CORNET to a wide range of symbolic and neural baselines adapted from related domains. Our results show that CORNET accurately learns rules across varying evaluation setups. Additionally, we show that CORNET finds shorter rules than those that a user has written and discovers rules in spreadsheets that users have manually formatted.

We propose utilizing background operators for mathematical reasoning in large language models (LLMs). To achieve this, we define a set of fundamental mathematical predicates as the basic building blocks. For each mathematical problem, we develop a Prolog solution that includes problem-specific predicates and intermediate predicates derived from these background operators, ensuring that each solution adheres to the defined operator set. We introduce the MATH-Prolog corpus, which is derived from the counting and probability categories of the MATH corpus. For efficient data augmentation, we apply K-fold cross-validated self-training. This method incrementally generates new Prolog solutions for each fold, incorporating those verified as correct into the training set throughout the model training process. Our experimental results demonstrate that 5-fold crossvalidated self-training effectively identifies new, accurate Prolog solutions, achieving an accuracy of 84.6% on the cross-validated set, and 84.8% on the test set during fine-tuning the Meta-Llama-3.1-8B-Instruct model. This approach successfully uncovers new solutions with fully computable inference steps for previously unseen problems. Additionally, incorporating the background mathematical predicates into the prompt enhances solution coverage.

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\%).

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.

Recent advances in automated test generation utilises language models to produce unit tests. While effective, language models tend to generate many incorrect tests with respect to both syntax and semantics. Although such incorrect tests can be easily detected and discarded, they constitute a "missed opportunity" -- if fixed, they are often valuable as they directly add testing value (they effectively target the underlying program logic to be tested) and indirectly form good seeds for generating additional tests. To this end, we propose a simple technique for repairing some of these incorrect tests through a combination of rule-based static analysis and re-prompting. We evaluate this simple approach, named YATE, on a set of 6 open-source projects and show that it can effectively produce tests that cover on average 32.06% more lines and kill 21.77% more mutants than a plain LLM-based method. We also compare YATE with four other LLM-based methods, namely HITS, SYMPROMPT, TESTSPARK and COVERUP and show that it produces tests that cover substantially more code. YATE achieves 22% higher line coverage, 20% higher branch coverage and kill 20% more mutants at a comparable cost (number of calls to LLMs).

Chain-of-thought prompting~(CoT) and tool augmentation have been validated in recent work as effective practices for improving large language models~(LLMs) to perform step-by-step reasoning on complex math-related tasks. However, most existing math reasoning datasets may be not able to fully evaluate and analyze the ability of LLMs in manipulating tools and performing reasoning, as they may only require very few invocations of tools or miss annotations for evaluating intermediate reasoning steps. To address the issue, we construct CARP, a new Chinese dataset consisting of 4,886 computation-intensive algebra problems with formulated annotations on intermediate steps. In CARP, we test four LLMs with CoT prompting, and find that they are all prone to make mistakes at the early steps of the solution, leading to wrong answers. Based on this finding, we propose a new approach that can deliberate the reasoning steps with tool interfaces, namely DELI. In DELI, we first initialize a step-by-step solution based on retrieved exemplars, then iterate two deliberation procedures that check and refine the intermediate steps of the generated solution, from the perspectives of tool manipulation and natural language reasoning, until obtaining converged solutions or reaching the maximum turn. Experimental results on CARP and six other datasets show that the proposed DELI mostly outperforms competitive baselines, and can further boost the performance of existing CoT methods. Our data and code are available in https://github.com/RUCAIBox/CARP.

Mathematical verfier achieves success in mathematical reasoning tasks by validating the correctness of solutions. However, existing verifiers are trained with binary classification labels, which are not informative enough for the model to accurately assess the solutions. To mitigate the aforementioned insufficiency of binary labels, we introduce step-wise natural language feedbacks as rationale labels (i.e., the correctness of the current step and the explanations). In this paper, we propose Math-Minos, a natural language feedback enhanced verifier by constructing automatically-generated training data and a two-stage training paradigm for effective training and efficient inference. Our experiments reveal that a small set (30k) of natural language feedbacks can significantly boost the performance of the verifier by the accuracy of 1.6\% (86.6\% rightarrow 88.2\%) on GSM8K and 0.8\% (37.8\% rightarrow 38.6\%) on MATH. We have released our code and data for further exploration.

Autoformalization, the conversion of natural language mathematics into formal languages, offers significant potential for advancing mathematical reasoning. However, existing efforts are limited to formal languages with substantial online corpora and struggle to keep pace with rapidly evolving languages like Lean 4. To bridge this gap, we propose a new benchmark Formalization for Lean~4 (\name) designed to evaluate the autoformalization capabilities of large language models (LLMs). This benchmark encompasses a comprehensive assessment of questions, answers, formal statements, and proofs. Additionally, we introduce a Process-Supervised Verifier (PSV) model that leverages the precise feedback from Lean 4 compilers to enhance autoformalization. Our experiments demonstrate that the PSV method improves autoformalization, enabling higher accuracy using less filtered training data. Furthermore, when fine-tuned with data containing detailed process information, PSV can leverage the data more effectively, leading to more significant improvements in autoformalization for Lean 4. Our dataset and code are available at https://github.com/rookie-joe/PDA.

We introduce ProofNet, a benchmark for autoformalization and formal proving of undergraduate-level mathematics. The ProofNet benchmarks consists of 371 examples, each consisting of a formal theorem statement in Lean 3, a natural language theorem statement, and a natural language proof. The problems are primarily drawn from popular undergraduate pure mathematics textbooks and cover topics such as real and complex analysis, linear algebra, abstract algebra, and topology. We intend for ProofNet to be a challenging benchmark that will drive progress in autoformalization and automatic theorem proving. We report baseline results on statement autoformalization via in-context learning. Moreover, we introduce two novel statement autoformalization methods: prompt retrieval and distilled backtranslation.

Using large language models (LLMs) to generate source code from natural language prompts is a popular and promising idea with a wide range of applications. One of its limitations is that the generated code can be faulty at times, often in a subtle way, despite being presented to the user as correct. In this paper, we explore ways in which formal methods can assist with increasing the quality of code generated by an LLM. Instead of emitting code in a target language directly, we propose that the user guides the LLM to first generate an opaque intermediate representation, in the verification-aware language Dafny, that can be automatically validated for correctness against agreed on specifications. The correct Dafny program is then compiled to the target language and returned to the user. All user-system interactions throughout the procedure occur via natural language; Dafny code is never exposed. We describe our current prototype and report on its performance on the HumanEval Python code generation benchmarks.

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.

We introduce a new type of programming challenge called programming puzzles, as an objective and comprehensive evaluation of program synthesis, and release an open-source dataset of Python Programming Puzzles (P3). Each puzzle is defined by a short Python program f, and the goal is to find an input which makes f return True. The puzzles are objective in that each one is specified entirely by the source code of its verifier f, so evaluating f is all that is needed to test a candidate solution. They do not require an answer key or input/output examples, nor do they depend on natural language understanding. The dataset is comprehensive in that it spans problems of a range of difficulties and domains, ranging from trivial string manipulation problems, to classic programming puzzles (e.g., Tower of Hanoi), to interview/competitive-programming problems (e.g., dynamic programming), to longstanding open problems in algorithms and mathematics (e.g., factoring). We develop baseline enumerative program synthesis, GPT-3 and Codex solvers that are capable of solving puzzles -- even without access to any reference solutions -- by learning from their own past solutions. Codex performs best, solving up to 18% of 397 test problems with a single try and 80% of the problems with 1,000 tries per problem. In a small user study, we find a positive correlation between puzzle-solving performance and coding experience, and between the puzzle difficulty for humans and AI solvers. Therefore, further improvements on P3 could have a significant impact on many program synthesis areas.

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

Legacy software systems, written in outdated languages like MUMPS and mainframe assembly, pose challenges in efficiency, maintenance, staffing, and security. While LLMs offer promise for modernizing these systems, their ability to understand legacy languages is largely unknown. This paper investigates the utilization of LLMs to generate documentation for legacy code using two datasets: an electronic health records (EHR) system in MUMPS and open-source applications in IBM mainframe Assembly Language Code (ALC). We propose a prompting strategy for generating line-wise code comments and a rubric to evaluate their completeness, readability, usefulness, and hallucination. Our study assesses the correlation between human evaluations and automated metrics, such as code complexity and reference-based metrics. We find that LLM-generated comments for MUMPS and ALC are generally hallucination-free, complete, readable, and useful compared to ground-truth comments, though ALC poses challenges. However, no automated metrics strongly correlate with comment quality to predict or measure LLM performance. Our findings highlight the limitations of current automated measures and the need for better evaluation metrics for LLM-generated documentation in legacy systems.

Punctuation plays a vital role in structuring meaning, yet current models often struggle to restore it accurately in transcripts of spontaneous speech, especially in the presence of disfluencies such as false starts and backtracking. These limitations hinder the performance of downstream tasks like translation, text to speech, summarization, etc. where sentence boundaries are critical for preserving quality. In this work, we introduce Cadence, a generalist punctuation restoration model adapted from a pretrained large language model. Cadence is designed to handle both clean written text and highly spontaneous spoken transcripts. It surpasses the previous state of the art in performance while expanding support from 14 to all 22 Indian languages and English. We conduct a comprehensive analysis of model behavior across punctuation types and language families, identifying persistent challenges under domain shift and with rare punctuation marks. Our findings demonstrate the efficacy of utilizing pretrained language models for multilingual punctuation restoration and highlight Cadence practical value for low resource NLP pipelines at scale.

We introduce a novel framework named ClarifyGPT, which aims to enhance code generation by empowering LLMs with the ability to identify ambiguous requirements and ask targeted clarifying questions. In particular, ClarifyGPT first detects whether a given requirement is ambiguous by performing a code consistency check. If it is ambiguous, ClarifyGPT prompts an LLM to generate targeted clarifying questions. After receiving question responses, ClarifyGPT refines the ambiguous requirement and inputs it into the same LLM to generate a final code solution. To evaluate our ClarifyGPT, we first conduct a human evaluation involving ten participants who use ClarifyGPT for code generation on two publicly available benchmarks: MBPP-sanitized and MBPP-ET. The results show that ClarifyGPT elevates the performance (Pass@1) of GPT-4 from 70.96% to 80.80% on MBPP-sanitized. Furthermore, to perform large-scale automated evaluations of ClarifyGPT across different LLMs and benchmarks without requiring user participation, we introduce a high-fidelity simulation method to simulate user responses. The automated evaluation results also demonstrate that ClarifyGPT can significantly enhance code generation performance compared to the baselines. In particular, ClarifyGPT improves the average performance of GPT-4 and ChatGPT across four benchmarks from 68.02% to 75.75% and from 58.55% to 67.22%, respectively. We believe that ClarifyGPT can effectively facilitate the practical application of LLMs in real-world development environments.

Code has been shown to be effective in enhancing the mathematical reasoning abilities of large language models due to its precision and accuracy. Previous works involving continued mathematical pretraining often include code that utilizes math-related packages, which are primarily designed for fields such as engineering, machine learning, signal processing, or module testing, rather than being directly focused on mathematical reasoning. In this paper, we introduce a novel method for generating mathematical code accompanied with corresponding reasoning steps for continued pretraining. Our approach begins with the construction of a high-quality mathematical continued pretraining dataset by incorporating math-related web data, code using mathematical packages, math textbooks, and synthetic data. Next, we construct reasoning steps by extracting LaTeX expressions, the conditions needed for the expressions, and the results of the expressions from the previously collected dataset. Based on this extracted information, we generate corresponding code to accurately capture the mathematical reasoning process. Appending the generated code to each reasoning step results in data consisting of paired natural language reasoning steps and their corresponding code. Combining this data with the original dataset results in a 19.2B-token high-performing mathematical pretraining corpus, which we name MathCode-Pile. Training several popular base models with this corpus significantly improves their mathematical abilities, leading to the creation of the MathCoder2 family of models. All of our data processing and training code is open-sourced, ensuring full transparency and easy reproducibility of the entire data collection and training pipeline. The code is released at https://github.com/mathllm/MathCoder2 .

Writing competitive programming problems is exacting. Authors must: set constraints, input distributions, and edge cases that rule out shortcuts; target specific algorithms (e.g., max-flow, dynamic programming, data structures); and calibrate complexity beyond the reach of most competitors. We argue that this makes for an ideal test of general large language model capabilities and study whether they can do this reliably. We introduce AutoCode, which uses multiple rounds of validation to yield competition-grade problem statements and test cases. On held-out problems, AutoCode test suites approach 99% consistency with official judgments, a significant improvement over current state-of-the-art methods like HardTests, which achieve less than 81%. Furthermore, starting with a random seed problem, AutoCode can create novel variants with reference and brute-force solutions. By cross-verifying these generated solutions against test cases, we can further filter out malformed problems. Our system ensures high correctness, as verified by human experts. AutoCode successfully produces novel problems judged by Grandmaster-level (top 0.3%) competitive programmers to be of contest quality.

Context: Bugs in code are inevitable and can lead to severe consequences, ranging from security vulnerabilities to operational failures. Debugging software remains challenging despite advances in testing and verification, often requiring extensive manual effort. Learning-based automated program repair (APR) has shown promise in reducing the time, effort, and cost of manually fixing bugs. However, existing techniques face several challenges, including language-dependent strategies, limited bug context utilization, and difficulties in handling bugs that span multiple locations in the code. Objective: This paper introduces MultiMend, a learning-based APR approach designed to improve repair performance on multiple programming languages with language-independent context augmentation and multi-hunk patch generation. Method: MultiMend fine-tunes a pre-trained encoder-decoder transformer model (CodeT5) to generate bug-fixing patches. It embeds source code lines and applies retrieval-augmented generation to augment the buggy context with relevant lines during patch generation. The approach systematically constructs patches for multi-hunk bugs to reduce the needed patch validations. We evaluate MultiMend on four benchmarks with four programming languages and compare it with state-of-the-art methods. Results: Experimental results show that MultiMend achieves competitive effectiveness and efficiency against compared tools. Across all benchmarks, MultiMend fixes 2,077 bugs, of which 1,455 are identical to the developer's patch, and 106 are for multi-hunk bugs. Both context augmentation and multi-hunk patch generation positively contribute to the results. Conclusion: MultiMend shows promising performance across benchmarks. The findings highlight its applicability to real-world software maintenance and its potential to reduce manual debugging efforts.

Code generation, symbolic math reasoning, and other tasks require LLMs to produce outputs that are both syntactically and semantically correct. Constrained LLM generation is a promising direction to enforce adherence to formal grammar, but prior works have empirically observed that strict enforcement of formal constraints often diminishes the reasoning capabilities of LLMs. In this work, we first provide a theoretical explanation for why constraining LLM outputs to very restrictive grammars that only allow syntactically valid final answers reduces the reasoning capabilities of the model. Second, we demonstrate that by augmenting the output grammar with carefully designed additional rules, it is always possible to preserve the reasoning capabilities of the LLM while ensuring syntactic and semantic correctness in its outputs. Building on these theoretical insights, we propose a reasoning-augmented constrained decoding algorithm, CRANE, which effectively balances the correctness of constrained generation with the flexibility of unconstrained generation. Experiments on multiple open-source LLMs and benchmarks show that CRANE significantly outperforms both state-of-the-art constrained decoding strategies and standard unconstrained decoding, showing up to 10% points accuracy improvement over baselines on challenging symbolic reasoning benchmarks GSM-symbolic and FOLIO.

Large Language Models (LLMs) have demonstrated impressive problem-solving capabilities in mathematics through step-by-step reasoning chains. However, they are susceptible to reasoning errors that impact the quality of subsequent reasoning chains and the final answer due to language models' autoregressive token-by-token generating nature. Recent works have proposed adopting external verifiers to guide the generation of reasoning paths, but existing works utilize models that have been trained with step-by-step labels to assess the correctness of token-by-token reasoning chains. Consequently, they struggle to recognize discriminative details of tokens within a reasoning path and lack the ability to evaluate whether an intermediate reasoning path is on a promising track toward the correct final answer. To amend the lack of sound and token-grained math-verification signals, we devise a novel training scheme for verifiers that apply token-level supervision with the expected cumulative reward (i.e., value). Furthermore, we propose a practical formulation of the cumulative reward by reducing it to finding the probability of future correctness of the final answer and thereby enabling the empirical estimation of the value. Experimental results on mathematical reasoning benchmarks show that Token-Supervised Value Model (TVM) can outperform step-by-step verifiers on GSM8K and MATH with Mistral and Llama.

Large language models (LLMs) have scaled up to unlock a wide range of complex reasoning tasks with the aid of various prompting methods. However, current prompting methods generate natural language intermediate steps to help reasoning, which can cause imperfect task reduction and confusion. To mitigate such limitations, we explore code prompting, a neural symbolic prompting method with both zero-shot and few-shot versions which triggers code as intermediate steps. We conduct experiments on 7 widely-used benchmarks involving symbolic reasoning and arithmetic reasoning. Code prompting generally outperforms chain-of-thought (CoT) prompting. To further understand the performance and limitations of code prompting, we perform extensive ablation studies and error analyses, and identify several exclusive advantages of using symbolic promptings compared to natural language. We also consider the ensemble of code prompting and CoT prompting to combine the strengths of both. Finally, we show through experiments how code annotations and their locations affect code prompting.

Given the rapid ascent of large language models (LLMs), we study the question: (How) can large language models help in reviewing of scientific papers or proposals? We first conduct some pilot studies where we find that (i) GPT-4 outperforms other LLMs (Bard, Vicuna, Koala, Alpaca, LLaMa, Dolly, OpenAssistant, StableLM), and (ii) prompting with a specific question (e.g., to identify errors) outperforms prompting to simply write a review. With these insights, we study the use of LLMs (specifically, GPT-4) for three tasks: 1. Identifying errors: We construct 13 short computer science papers each with a deliberately inserted error, and ask the LLM to check for the correctness of these papers. We observe that the LLM finds errors in 7 of them, spanning both mathematical and conceptual errors. 2. Verifying checklists: We task the LLM to verify 16 closed-ended checklist questions in the respective sections of 15 NeurIPS 2022 papers. We find that across 119 {checklist question, paper} pairs, the LLM had an 86.6% accuracy. 3. Choosing the "better" paper: We generate 10 pairs of abstracts, deliberately designing each pair in such a way that one abstract was clearly superior than the other. The LLM, however, struggled to discern these relatively straightforward distinctions accurately, committing errors in its evaluations for 6 out of the 10 pairs. Based on these experiments, we think that LLMs have a promising use as reviewing assistants for specific reviewing tasks, but not (yet) for complete evaluations of papers or proposals.

Language models have demonstrated remarkable performance in solving reasoning tasks; however, even the strongest models still occasionally make reasoning mistakes. Recently, there has been active research aimed at improving reasoning accuracy, particularly by using pretrained language models to "self-correct" their mistakes via multi-round prompting. In this paper, we follow this line of work but focus on understanding the usefulness of incorporating "error-correction" data directly into the pretraining stage. This data consists of erroneous solution steps immediately followed by their corrections. Using a synthetic math dataset, we show promising results: this type of pretrain data can help language models achieve higher reasoning accuracy directly (i.e., through simple auto-regression, without multi-round prompting) compared to pretraining on the same amount of error-free data. We also delve into many details, such as (1) how this approach differs from beam search, (2) how such data can be prepared, (3) whether masking is needed on the erroneous tokens, (4) the amount of error required, (5) whether such data can be deferred to the fine-tuning stage, and many others.

Grammar serves as a cornerstone in programming languages and software engineering, providing frameworks to define the syntactic space and program structure. Existing research demonstrates the effectiveness of grammar-based code representations in small-scale models, showing their ability to reduce syntax errors and enhance performance. However, as language models scale to the billion level or beyond, syntax-level errors become rare, making it unclear whether grammar information still provides performance benefits. To explore this, we develop a series of billion-scale GrammarCoder models, incorporating grammar rules in the code generation process. Experiments on HumanEval (+) and MBPP (+) demonstrate a notable improvement in code generation accuracy. Further analysis shows that grammar-based representations enhance LLMs' ability to discern subtle code differences, reducing semantic errors caused by minor variations. These findings suggest that grammar-based code representations remain valuable even in billion-scale models, not only by maintaining syntax correctness but also by improving semantic differentiation.

Code large language models (Code LLMs) have made significant progress in code generation by translating natural language descriptions into functional code; however, real-world applications often demand stricter adherence to detailed requirements such as coding style, line count, and structural constraints, beyond mere correctness. To address this, the paper introduces forward and backward constraints generation to improve the instruction-following capabilities of Code LLMs in controlled code generation, ensuring outputs align more closely with human-defined guidelines. The authors further present IFEvalCode, a multilingual benchmark comprising 1.6K test samples across seven programming languages (Python, Java, JavaScript, TypeScript, Shell, C++, and C#), with each sample featuring both Chinese and English queries. Unlike existing benchmarks, IFEvalCode decouples evaluation into two metrics: correctness (Corr.) and instruction-following (Instr.), enabling a more nuanced assessment. Experiments on over 40 LLMs reveal that closed-source models outperform open-source ones in controllable code generation and highlight a significant gap between the models' ability to generate correct code versus code that precisely follows instructions.

Portable Document Format (PDF) files are dominantly used for storing and disseminating scientific research, legal documents, and tax information. LaTeX is a popular application for creating PDF documents. Despite its advantages, LaTeX is not WYSWYG -- what you see is what you get, i.e., the LaTeX source and rendered PDF images look drastically different, especially for formulae and tables. This gap makes it hard to modify or export LaTeX sources for formulae and tables from PDF images, and existing work is still limited. First, prior work generates LaTeX sources in a single iteration and struggles with complex LaTeX formulae. Second, existing work mainly recognizes and extracts LaTeX sources for formulae; and is incapable or ineffective for tables. This paper proposes LATTE, the first iterative refinement framework for LaTeX recognition. Specifically, we propose delta-view as feedback, which compares and pinpoints the differences between a pair of rendered images of the extracted LaTeX source and the expected correct image. Such delta-view feedback enables our fault localization model to localize the faulty parts of the incorrect recognition more accurately and enables our LaTeX refinement model to repair the incorrect extraction more accurately. LATTE improves the LaTeX source extraction accuracy of both LaTeX formulae and tables, outperforming existing techniques as well as GPT-4V by at least 7.07% of exact match, with a success refinement rate of 46.08% (formula) and 25.51% (table).

Large language models trained on code have shown great potential to increase productivity of software developers. Several execution-based benchmarks have been proposed to evaluate functional correctness of model-generated code on simple programming problems. Nevertheless, it is expensive to perform the same evaluation on complex real-world projects considering the execution cost. On the contrary, static analysis tools such as linters, which can detect errors without running the program, haven't been well explored for evaluating code generation models. In this work, we propose a static evaluation framework to quantify static errors in Python code completions, by leveraging Abstract Syntax Trees. Compared with execution-based evaluation, our method is not only more efficient, but also applicable to code in the wild. For experiments, we collect code context from open source repos to generate one million function bodies using public models. Our static analysis reveals that Undefined Name and Unused Variable are the most common errors among others made by language models. Through extensive studies, we also show the impact of sampling temperature, model size, and context on static errors in code completions.

We present a novel method of performing spelling correction on short input strings, such as search queries or individual words. At its core lies a procedure for generating artificial typos which closely follow the error patterns manifested by humans. This procedure is used to train the production spelling correction model based on a transformer architecture. This model is currently served in the HubSpot product search. We show that our approach to typo generation is superior to the widespread practice of adding noise, which ignores human patterns. We also demonstrate how our approach may be extended to resource-scarce settings and train spelling correction models for Arabic, Greek, Russian, and Setswana languages, without using any labeled data.

We present GlotScript, an open resource and tool for low resource writing system identification. GlotScript-R is a resource that provides the attested writing systems for more than 7,000 languages. It is compiled by aggregating information from existing writing system resources. GlotScript-T is a writing system identification tool that covers all 161 Unicode 15.0 scripts. For an input text, it returns its script distribution where scripts are identified by ISO 15924 codes. We also present two use cases for GlotScript. First, we demonstrate that GlotScript supports cleaning multilingual corpora such as mC4 and OSCAR. Second, we analyze the tokenization of a number of language models such as GPT-4 using GlotScript and provide insights on the coverage of low resource scripts and languages by each language model. We hope that GlotScript will become a useful resource for work on low resource languages in the NLP community. GlotScript-R and GlotScript-T are available at https://github.com/cisnlp/GlotScript.

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.

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.

As a vital stage of automated rule checking (ARC), rule interpretation of regulatory texts requires considerable effort. However, interpreting regulatory clauses with implicit properties or complex computational logic is still challenging due to the lack of domain knowledge and limited expressibility of conventional logic representations. Thus, LLM-FuncMapper, an approach to identifying predefined functions needed to interpret various regulatory clauses based on the large language model (LLM), is proposed. First, by systematically analysis of building codes, a series of atomic functions are defined to capture shared computational logics of implicit properties and complex constraints, creating a database of common blocks for interpreting regulatory clauses. Then, a prompt template with the chain of thought is developed and further enhanced with a classification-based tuning strategy, to enable common LLMs for effective function identification. Finally, the proposed approach is validated with statistical analysis, experiments, and proof of concept. Statistical analysis reveals a long-tail distribution and high expressibility of the developed function database, with which almost 100% of computer-processible clauses can be interpreted and represented as computer-executable codes. Experiments show that LLM-FuncMapper achieve promising results in identifying relevant predefined functions for rule interpretation. Further proof of concept in automated rule interpretation also demonstrates the possibility of LLM-FuncMapper in interpreting complex regulatory clauses. To the best of our knowledge, this study is the first attempt to introduce LLM for understanding and interpreting complex regulatory clauses, which may shed light on further adoption of LLM in the construction domain.

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.

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

Recent advancements in AI safety have led to increased efforts in training and red-teaming large language models (LLMs) to mitigate unsafe content generation. However, these safety mechanisms may not be comprehensive, leaving potential vulnerabilities unexplored. This paper introduces MathPrompt, a novel jailbreaking technique that exploits LLMs' advanced capabilities in symbolic mathematics to bypass their safety mechanisms. By encoding harmful natural language prompts into mathematical problems, we demonstrate a critical vulnerability in current AI safety measures. Our experiments across 13 state-of-the-art LLMs reveal an average attack success rate of 73.6\%, highlighting the inability of existing safety training mechanisms to generalize to mathematically encoded inputs. Analysis of embedding vectors shows a substantial semantic shift between original and encoded prompts, helping explain the attack's success. This work emphasizes the importance of a holistic approach to AI safety, calling for expanded red-teaming efforts to develop robust safeguards across all potential input types and their associated risks.

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.

As large language models (LLMs) become increasingly capable, concerns over the unauthorized use of copyrighted and licensed content in their training data have grown, especially in the context of code. Open-source code, often protected by open source licenses (e.g, GPL), poses legal and ethical challenges when used in pretraining. Detecting whether specific code samples were included in LLM training data is thus critical for transparency, accountability, and copyright compliance. We propose SynPrune, a syntax-pruned membership inference attack method tailored for code. Unlike prior MIA approaches that treat code as plain text, SynPrune leverages the structured and rule-governed nature of programming languages. Specifically, it identifies and excludes consequent tokens that are syntactically required and not reflective of authorship, from attribution when computing membership scores. Experimental results show that SynPrune consistently outperforms the state-of-the-arts. Our method is also robust across varying function lengths and syntax categories.

Recent LLMs have demonstrated remarkable performance in solving exam-like math word problems. However, the degree to which these numerical reasoning skills are effective in real-world scenarios, particularly in expert domains, is still largely unexplored. This paper introduces DocMath-Eval, a comprehensive benchmark specifically designed to evaluate the numerical reasoning and problem-solving capabilities of LLMs in the context of understanding and analyzing financial documents containing both text and tables. We evaluate a wide spectrum of 19 LLMs, including those specialized in coding and finance. We also incorporate different prompting strategies (i.e., Chain-of-Thoughts and Program-of-Thoughts) to comprehensively assess the capabilities and limitations of existing LLMs in DocMath-Eval. We found that, although the current best-performing system (i.e., GPT-4), can perform well on simple problems such as calculating the rate of increase in a financial metric within a short document context, it significantly lags behind human experts in more complex problems grounded in longer contexts. We believe DocMath-Eval can be used as a valuable benchmark to evaluate LLMs' capabilities to solve challenging numerical reasoning problems in expert domains. We will release the benchmark and code at https://github.com/yale-nlp/DocMath-Eval.

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

In this paper, we aim to do code completion based on implementing a Neural Network from Li et. al.. Our contribution is that we use an encoding that is in-between character and word encoding called Byte Pair Encoding (BPE). We use this on the source code files treating them as natural text without first going through the abstract syntax tree (AST). We have implemented two models: an attention-enhanced LSTM and a pointer network, where the pointer network was originally introduced to solve out of vocabulary problems. We are interested to see if BPE can replace the need for the pointer network for code completion.

Text data can pose a risk of harm. However, the risks are not fully understood, and how to handle, present, and discuss harmful text in a safe way remains an unresolved issue in the NLP community. We provide an analytical framework categorising harms on three axes: (1) the harm type (e.g., misinformation, hate speech or racial stereotypes); (2) whether a harm is sought as a feature of the research design if explicitly studying harmful content (e.g., training a hate speech classifier), versus unsought if harmful content is encountered when working on unrelated problems (e.g., language generation or part-of-speech tagging); and (3) who it affects, from people (mis)represented in the data to those handling the data and those publishing on the data. We provide advice for practitioners, with concrete steps for mitigating harm in research and in publication. To assist implementation we introduce HarmCheck -- a documentation standard for handling and presenting harmful text in research.

Policy Compliance Detection (PCD) is a task we encounter when reasoning over texts, e.g. legal frameworks. Previous work to address PCD relies heavily on modeling the task as a special case of Recognizing Textual Entailment. Entailment is applicable to the problem of PCD, however viewing the policy as a single proposition, as opposed to multiple interlinked propositions, yields poor performance and lacks explainability. To address this challenge, more recent proposals for PCD have argued for decomposing policies into expression trees consisting of questions connected with logic operators. Question answering is used to obtain answers to these questions with respect to a scenario. Finally, the expression tree is evaluated in order to arrive at an overall solution. However, this work assumes expression trees are provided by experts, thus limiting its applicability to new policies. In this work, we learn how to infer expression trees automatically from policy texts. We ensure the validity of the inferred trees by introducing constrained decoding using a finite state automaton to ensure the generation of valid trees. We determine through automatic evaluation that 63% of the expression trees generated by our constrained generation model are logically equivalent to gold trees. Human evaluation shows that 88% of trees generated by our model are correct.

Code contains security and functional bugs. The process of identifying and localizing them is difficult and relies on human labor. In this work, we present a novel approach (FLAG) to assist human debuggers. FLAG is based on the lexical capabilities of generative AI, specifically, Large Language Models (LLMs). Here, we input a code file then extract and regenerate each line within that file for self-comparison. By comparing the original code with an LLM-generated alternative, we can flag notable differences as anomalies for further inspection, with features such as distance from comments and LLM confidence also aiding this classification. This reduces the inspection search space for the designer. Unlike other automated approaches in this area, FLAG is language-agnostic, can work on incomplete (and even non-compiling) code and requires no creation of security properties, functional tests or definition of rules. In this work, we explore the features that help LLMs in this classification and evaluate the performance of FLAG on known bugs. We use 121 benchmarks across C, Python and Verilog; with each benchmark containing a known security or functional weakness. We conduct the experiments using two state of the art LLMs in OpenAI's code-davinci-002 and gpt-3.5-turbo, but our approach may be used by other models. FLAG can identify 101 of the defects and helps reduce the search space to 12-17% of source code.

We present Dyve, a dynamic process verifier that enhances reasoning error detection in large language models by integrating fast and slow thinking, inspired by Kahneman's Systems Theory. Dyve adaptively applies immediate token-level confirmation System 1 for straightforward steps and comprehensive analysis System 2 for complex ones. Leveraging a novel step-wise consensus-filtered process supervision technique, combining Monte Carlo estimation with LLM based evaluation, Dyve curates high-quality supervision signals from noisy data. Experimental results on ProcessBench and the MATH dataset confirm that Dyve significantly outperforms existing process-based verifiers and boosts performance in Best-of-N settings.

This paper gives three formulas for the pseudoinverse of a matrix product A = CR. The first is sometimes correct, the second is always correct, and the third is almost never correct. But that third randomized pseudoinverse A^+_r may be very useful when A is a very large matrix. 1. A^+ = R^+C^+ when A = CR and C has independent columns and R has independent rows. 2. A^+ = (C^+CR)^+(CRR^+)^+ is always correct. 3. A^+_r = (P^TCR)^+P^TCRQ(CRQ)^+ = A^+ only when rank(P^TA) = rank(AQ) = rank(A) with A = CR.

Recently, the Natural Language Inference (NLI) task has been studied for semi-structured tables that do not have a strict format. Although neural approaches have achieved high performance in various types of NLI, including NLI between semi-structured tables and texts, they still have difficulty in performing a numerical type of inference, such as counting. To handle a numerical type of inference, we propose a logical inference system for reasoning between semi-structured tables and texts. We use logical representations as meaning representations for tables and texts and use model checking to handle a numerical type of inference between texts and tables. To evaluate the extent to which our system can perform inference with numerical comparatives, we make an evaluation protocol that focuses on numerical understanding between semi-structured tables and texts in English. We show that our system can more robustly perform inference between tables and texts that requires numerical understanding compared with current neural approaches.

Despite the much discussed capabilities of today's language models, they are still prone to silly and unexpected commonsense failures. We consider a retrospective verification approach that reflects on the correctness of LM outputs, and introduce Vera, a general-purpose model that estimates the plausibility of declarative statements based on commonsense knowledge. Trained on ~7M commonsense statements created from 19 QA datasets and two large-scale knowledge bases, and with a combination of three training objectives, Vera is a versatile model that effectively separates correct from incorrect statements across diverse commonsense domains. When applied to solving commonsense problems in the verification format, Vera substantially outperforms existing models that can be repurposed for commonsense verification, and it further exhibits generalization capabilities to unseen tasks and provides well-calibrated outputs. We find that Vera excels at filtering LM-generated commonsense knowledge and is useful in detecting erroneous commonsense statements generated by models like ChatGPT in real-world settings.

Pre-trained Programming Language Models (PPLMs) achieved many recent states of the art results for many code-related software engineering tasks. Though some studies use data flow or propose tree-based models that utilize Abstract Syntax Tree (AST), most PPLMs do not fully utilize the rich syntactical information in source code. Still, the input is considered a sequence of tokens. There are two issues; the first is computational inefficiency due to the quadratic relationship between input length and attention complexity. Second, any syntactical information, when needed as an extra input to the current PPLMs, requires the model to be pre-trained from scratch, wasting all the computational resources already used for pre-training the current models. In this work, we propose Named Entity Recognition (NER) adapters, lightweight modules that can be inserted into Transformer blocks to learn type information extracted from the AST. These adapters can be used with current PPLMs such as CodeBERT, GraphCodeBERT, and CodeT5. We train the NER adapters using a novel Token Type Classification objective function (TTC). We insert our proposed work in CodeBERT, building CodeBERTER, and evaluate the performance on two tasks of code refinement and code summarization. CodeBERTER improves the accuracy of code refinement from 16.4 to 17.8 while using 20% of training parameter budget compared to the fully fine-tuning approach, and the BLEU score of code summarization from 14.75 to 15.90 while reducing 77% of training parameters compared to the fully fine-tuning approach.

Due to the fast pace of life and online communications and the prevalence of English and the QWERTY keyboard, people tend to forgo using diacritics, make typographical errors (typos) when typing in other languages. Restoring diacritics and correcting spelling is important for proper language use and the disambiguation of texts for both humans and downstream algorithms. However, both of these problems are typically addressed separately: the state-of-the-art diacritics restoration methods do not tolerate other typos, but classical spellcheckers also cannot deal adequately with all the diacritics missing. In this work, we tackle both problems at once by employing the newly-developed universal ByT5 byte-level seq2seq transformer model that requires no language-specific model structures. For a comparison, we perform diacritics restoration on benchmark datasets of 12 languages, with the addition of Lithuanian. The experimental investigation proves that our approach is able to achieve results (> 98%) comparable to the previous state-of-the-art, despite being trained less and on fewer data. Our approach is also able to restore diacritics in words not seen during training with > 76% accuracy. Our simultaneous diacritics restoration and typos correction approach reaches > 94% alpha-word accuracy on the 13 languages. It has no direct competitors and strongly outperforms classical spell-checking or dictionary-based approaches. We also demonstrate all the accuracies to further improve with more training. Taken together, this shows the great real-world application potential of our suggested methods to more data, languages, and error classes.

Assurance cases can be used to argue for the safety of products in safety engineering. In safety-critical areas, the construction of assurance cases is indispensable. Trustworthiness Derivation Trees (TDTs) enhance assurance cases by incorporating formal methods, rendering it possible for automatic reasoning about assurance cases. We present Trustworthiness Derivation Tree Analyzer (Trusta), a desktop application designed to automatically construct and verify TDTs. The tool has a built-in Prolog interpreter in its backend, and is supported by the constraint solvers Z3 and MONA. Therefore, it can solve constraints about logical formulas involving arithmetic, sets, Horn clauses etc. Trusta also utilizes large language models to make the creation and evaluation of assurance cases more convenient. It allows for interactive human examination and modification. We evaluated top language models like ChatGPT-3.5, ChatGPT-4, and PaLM 2 for generating assurance cases. Our tests showed a 50%-80% similarity between machine-generated and human-created cases. In addition, Trusta can extract formal constraints from text in natural languages, facilitating an easier interpretation and validation process. This extraction is subject to human review and correction, blending the best of automated efficiency with human insight. To our knowledge, this marks the first integration of large language models in automatic creating and reasoning about assurance cases, bringing a novel approach to a traditional challenge. Through several industrial case studies, Trusta has proven to quickly find some subtle issues that are typically missed in manual inspection, demonstrating its practical value in enhancing the assurance case development process.

Formulas involving fundamental mathematical constants had a great impact on various fields of science and mathematics, for example aiding in proofs of irrationality of constants. However, the discovery of such formulas has historically remained scarce, often perceived as an act of mathematical genius by great mathematicians such as Ramanujan, Euler, and Gauss. Recent efforts to automate the discovery of formulas for mathematical constants, such as the Ramanujan Machine project, relied on exhaustive search. Despite several successful discoveries, exhaustive search remains limited by the space of options that can be covered and by the need for vast amounts of computational resources. Here we propose a fundamentally different method to search for conjectures on mathematical constants: through analysis of integer sequences. We introduce the Enumerated Signed-continued-fraction Massey Approve (ESMA) algorithm, which builds on the Berlekamp-Massey algorithm to identify patterns in integer sequences that represent mathematical constants. The ESMA algorithm found various known formulas for e, e^2, tan(1), and ratios of values of Bessel functions. The algorithm further discovered a large number of new conjectures for these constants, some providing simpler representations and some providing faster numerical convergence than the corresponding simple continued fractions. Along with the algorithm, we present mathematical tools for manipulating continued fractions. These connections enable us to characterize what space of constants can be found by ESMA and quantify its algorithmic advantage in certain scenarios. Altogether, this work continues in the development of augmenting mathematical intuition by computer algorithms, to help reveal mathematical structures and accelerate mathematical research.

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

Recently, large language models have presented promising results in aiding formal mathematical reasoning. However, their performance is restricted due to the scarcity of formal theorem-proving data, which requires additional effort to be extracted from raw formal language corpora. Meanwhile, a significant amount of human-written formal language corpora remains underutilized. To address this issue, we propose LEAN-GitHub, a dataset consisting of large-scale formal data extracted from almost all Lean 4 repositories on GitHub. After fine-tuning InternLM-math-plus on this dataset, our model achieved accuracies of 48.8% with a single pass and 54.5% with 64 passes on the Lean 4 miniF2F test, surpassing state-of-the-art method at 52%. And it also achieves state-of-the-art on two other Lean 4 benchmarks (ProofNet and Putnam) targeting different fields/levels of math. These results demonstrate that our proposed dataset is beneficial for formal reasoning on a wide range of math topics. We open-source our model at https://GitHub. com/InternLM/InternLM-Math and our data at https://huggingface.co/ datasets/InternLM/Lean-GitHub

Verifying the reliability of complex, multi-step reasoning in Large Language Models (LLMs) remains a fundamental challenge, as existing methods often lack both faithfulness and precision. To address this issue, we propose the Graph of Verification (GoV) framework. GoV offers three key contributions: First, it explicitly models the underlying deductive process as a directed acyclic graph (DAG), whether this structure is implicit or explicitly constructed. Second, it enforces a topological order over the DAG to guide stepwise verification. Third, GoV introduces the notion of customizable node blocks, which flexibly define the verification granularity, from atomic propositions to full paragraphs, while ensuring that all requisite premises derived from the graph are provided as contextual input for each verification unit. We evaluate GoV on the Number Triangle Summation task and the ProcessBench benchmark with varying levels of reasoning complexity. Experimental results show that GoV substantially improves verification accuracy, faithfulness, and error localization when compared to conventional end-to-end verification approaches. Our code and data are available at https://github.com/Frevor/Graph-of-Verification.