Daily Papers

We introduce the Formally Verified Automated Programming Progress Standards, or FVAPPS, a benchmark of 4715 samples for writing programs and proving their correctness, the largest formal verification benchmark, including 1083 curated and quality controlled samples. Previously, APPS provided a benchmark and dataset for programming puzzles to be completed in Python and checked against unit tests, of the kind seen in technical assessments in the software engineering industry. Building upon recent approaches for benchmarks in interactive theorem proving, we generalize the unit tests to Lean 4 theorems given without proof (i.e., using Lean's "sorry" keyword). On the 406 theorems of 100 randomly selected samples, Sonnet correctly proves 30% and Gemini correctly proves 18%. We challenge the machine learning and program synthesis communities to solve both each general purpose programming problem and its associated correctness specifications. The benchmark is available at https://huggingface.co/datasets/quinn-dougherty/fvapps.

Having reliable specifications is an unavoidable challenge in achieving verifiable correctness, robustness, and interpretability of AI systems. Existing specifications for neural networks are in the paradigm of data as specification. That is, the local neighborhood centering around a reference input is considered to be correct (or robust). While existing specifications contribute to verifying adversarial robustness, a significant problem in many research domains, our empirical study shows that those verified regions are somewhat tight, and thus fail to allow verification of test set inputs, making them impractical for some real-world applications. To this end, we propose a new family of specifications called neural representation as specification, which uses the intrinsic information of neural networks - neural activation patterns (NAPs), rather than input data to specify the correctness and/or robustness of neural network predictions. We present a simple statistical approach to mining neural activation patterns. To show the effectiveness of discovered NAPs, we formally verify several important properties, such as various types of misclassifications will never happen for a given NAP, and there is no ambiguity between different NAPs. We show that by using NAP, we can verify a significant region of the input space, while still recalling 84% of the data on MNIST. Moreover, we can push the verifiable bound to 10 times larger on the CIFAR10 benchmark. Thus, we argue that NAPs can potentially be used as a more reliable and extensible specification for neural network verification.

Despite recent progress in generating hardware RTL code with LLMs, existing solutions still suffer from a substantial gap between practical application scenarios and the requirements of real-world RTL code development. Prior approaches either focus on overly simplified hardware descriptions or depend on extensive human guidance to process complex specifications, limiting their scalability and automation potential. In this paper, we address this gap by proposing an LLM agent system, termed Spec2RTL-Agent, designed to directly process complex specification documentation and generate corresponding RTL code implementations, advancing LLM-based RTL code generation toward more realistic application settings. To achieve this goal, Spec2RTL-Agent introduces a novel multi-agent collaboration framework that integrates three key enablers: (1) a reasoning and understanding module that translates specifications into structured, step-by-step implementation plans; (2) a progressive coding and prompt optimization module that iteratively refines the code across multiple representations to enhance correctness and synthesisability for RTL conversion; and (3) an adaptive reflection module that identifies and traces the source of errors during generation, ensuring a more robust code generation flow. Instead of directly generating RTL from natural language, our system strategically generates synthesizable C++ code, which is then optimized for HLS. This agent-driven refinement ensures greater correctness and compatibility compared to naive direct RTL generation approaches. We evaluate Spec2RTL-Agent on three specification documents, showing it generates accurate RTL code with up to 75% fewer human interventions than existing methods. This highlights its role as the first fully automated multi-agent system for RTL generation from unstructured specs, reducing reliance on human effort in hardware design.

Although large language models (LLMs) have been largely successful in generating functionally correct programs, conditioning models to produce efficient solutions while ensuring correctness remains a challenge. Further, unreliability in benchmarking code efficiency is a hurdle across varying hardware specifications for popular interpreted languages such as Python. In this paper, we present ECCO, a reproducible benchmark for evaluating program efficiency via two paradigms: natural language (NL) based code generation and history-based code editing. On ECCO, we adapt and thoroughly investigate the three most promising existing LLM-based approaches: in-context learning, iterative refinement with execution or NL feedback, and fine-tuning conditioned on execution and editing history. While most methods degrade functional correctness and moderately increase program efficiency, we find that adding execution information often helps maintain functional correctness, and NL feedback enhances more on efficiency. We release our benchmark to support future work on LLM-based generation of efficient code.

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

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

Large Language Models (LLMs) have demonstrated impressive capabilities in automated code generation but frequently produce code that fails formal verification, an essential requirement for hardware and safety-critical domains. To overcome this fundamental limitation, we previously proposed PREFACE, a model-agnostic framework based on reinforcement learning (RL) that iteratively repairs the prompts provided to frozen LLMs, systematically steering them toward generating formally verifiable Dafny code without costly fine-tuning. This work presents Proof2Silicon, a novel end-to-end synthesis framework that embeds the previously proposed PREFACE flow to enable the generation of correctness-by-construction hardware directly from natural language specifications. Proof2Silicon operates by: (1) leveraging PREFACE's verifier-driven RL agent to optimize prompt generation iteratively, ensuring Dafny code correctness; (2) automatically translating verified Dafny programs into synthesizable high-level C using Dafny's Python backend and PyLog; and (3) employing Vivado HLS to produce RTL implementations. Evaluated rigorously on a challenging 100-task benchmark, PREFACE's RL-guided prompt optimization consistently improved Dafny verification success rates across diverse LLMs by up to 21%. Crucially, Proof2Silicon achieved an end-to-end hardware synthesis success rate of up to 72%, generating RTL designs through Vivado HLS synthesis flows. These results demonstrate a robust, scalable, and automated pipeline for LLM-driven, formally verified hardware synthesis, bridging natural-language specification and silicon realization.

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 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.

Formal verification is the next frontier for ensuring the correctness of code generated by Large Language Models (LLMs). While methods that co-generate code and formal specifications in formal languages, like Dafny, can, in principle, prove alignment with user intent, progress is bottlenecked by specification quality evaluation. Current benchmarks rely on matching against ground-truth specifications, a manual and expertise-intensive process that has limited existing datasets to a few hundred simple problems and also suffers from a reliability issue. To address this, we introduce VeriEquivBench, a new benchmark with 2,389 complex algorithmic problems that probe the limitations of current models in both code generation and formal reasoning. Our evaluation framework replaces ground-truth matching with a formally grounded metric, the equivalence score, and rigorously verifies the quality of generated specifications and code. Our results show that generating formally verifiable code remains a profound challenge for state-of-the-art LLMs. This underscores both the difficulty of the task and the need for benchmarks like VeriEquivBench to drive progress toward scalable and reliable coding agents.

Despite the significant strides made by generative AI in just a few short years, its future progress is constrained by the challenge of building modular and robust systems. This capability has been a cornerstone of past technological revolutions, which relied on combining components to create increasingly sophisticated and reliable systems. Cars, airplanes, computers, and software consist of components-such as engines, wheels, CPUs, and libraries-that can be assembled, debugged, and replaced. A key tool for building such reliable and modular systems is specification: the precise description of the expected behavior, inputs, and outputs of each component. However, the generality of LLMs and the inherent ambiguity of natural language make defining specifications for LLM-based components (e.g., agents) both a challenging and urgent problem. In this paper, we discuss the progress the field has made so far-through advances like structured outputs, process supervision, and test-time compute-and outline several future directions for research to enable the development of modular and reliable LLM-based systems through improved specifications.

The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO, showing significant progress. However, these studies intertwined multiple skills simultaneously, i.e., problem-solving, reasoning, and writing formal specifications, making it hard to precisely identify the LLMs' strengths and weaknesses in each task. This paper focuses on formal verification, an immediate application scenario of formal reasoning, and decomposes it into six sub-tasks. We constructed 18k high-quality instruction-response pairs across five mainstream formal specification languages (Coq, Lean4, Dafny, ACSL, and TLA+) in six formal-verification-related tasks by distilling GPT-4o. They are split into a 14k+ fine-tuning dataset FM-alpaca and a 4k benchmark FM-Bench. We found that LLMs are good at writing proof segments when given either the code, or the detailed description of proof steps. Also, the fine-tuning brought about a nearly threefold improvement at most. Interestingly, we observed that fine-tuning with formal data also enhances mathematics, reasoning, and coding abilities. We hope our findings inspire further research. Fine-tuned models are released to facilitate subsequent studies

In recent years, researchers have proposed numerous benchmarks to evaluate the impressive coding capabilities of large language models (LLMs). However, existing benchmarks primarily focus on assessing the correctness of code generated by LLMs, while neglecting other critical dimensions that also significantly impact code quality. Therefore, this paper proposes the RACE benchmark, which comprehensively evaluates the quality of code generated by LLMs across 4 dimensions: Readability, mAintainability, Correctness, and Efficiency. Specifically, considering the demand-dependent nature of dimensions beyond correctness, we design various types of user requirements for each dimension to assess the model's ability to generate correct code that also meets user demands. We evaluate 18 representative LLMs on RACE and find that: 1) the current LLMs' ability to generate high-quality code on demand does not yet meet the requirements of software development; 2) readability serves as a critical indicator of the overall quality of generated code; 3) most LLMs exhibit an inherent preference for specific coding style. These findings can help researchers gain a deeper understanding of the coding capabilities of current LLMs and shed light on future directions for model improvement.

Scientific documents record research findings and valuable human knowledge, comprising a vast corpus of high-quality data. Leveraging multi-modality data extracted from these documents and assessing large models' abilities to handle scientific document-oriented tasks is therefore meaningful. Despite promising advancements, large models still perform poorly on multi-page scientific document extraction and understanding tasks, and their capacity to process within-document data formats such as charts and equations remains under-explored. To address these issues, we present DocGenome, a structured document benchmark constructed by annotating 500K scientific documents from 153 disciplines in the arXiv open-access community, using our custom auto-labeling pipeline. DocGenome features four key characteristics: 1) Completeness: It is the first dataset to structure data from all modalities including 13 layout attributes along with their LaTeX source codes. 2) Logicality: It provides 6 logical relationships between different entities within each scientific document. 3) Diversity: It covers various document-oriented tasks, including document classification, visual grounding, document layout detection, document transformation, open-ended single-page QA and multi-page QA. 4) Correctness: It undergoes rigorous quality control checks conducted by a specialized team. We conduct extensive experiments to demonstrate the advantages of DocGenome and objectively evaluate the performance of large models on our benchmark.

Despite its crucial role in research experiments, code correctness is often presumed only on the basis of the perceived quality of results. This assumption comes with the risk of erroneous outcomes and potentially misleading findings. To address this issue, we posit that the current focus on reproducibility should go hand in hand with the emphasis on software quality. We present a case study in which we identify and fix three bugs in widely used implementations of the state-of-the-art Conformer architecture. Through experiments on speech recognition and translation in various languages, we demonstrate that the presence of bugs does not prevent the achievement of good and reproducible results, which however can lead to incorrect conclusions that potentially misguide future research. As a countermeasure, we propose a Code-quality Checklist and release pangoliNN, a library dedicated to testing neural models, with the goal of promoting coding best practices and improving research software quality within the NLP community.

Software specifications are essential for ensuring the reliability of software systems. Existing specification extraction approaches, however, suffer from limited generalizability and require manual efforts. The recent emergence of Large Language Models (LLMs), which have been successfully applied to numerous software engineering tasks, offers a promising avenue for automating this process. In this paper, we conduct the first empirical study to evaluate the capabilities of LLMs for generating software specifications from software comments or documentation. We evaluate LLMs' performance with Few Shot Learning (FSL), enabling LLMs to generalize from a small number of examples, as well as different prompt construction strategies, and compare the performance of LLMs with traditional approaches. Additionally, we conduct a comparative diagnosis of the failure cases from both LLMs and traditional methods, identifying their unique strengths and weaknesses. Lastly, we conduct extensive experiments on 15 state of the art LLMs, evaluating their performance and cost effectiveness for generating software specifications. Our results show that with FSL, LLMs outperform traditional methods (by 5.6%), and more sophisticated prompt construction strategies can further enlarge this performance gap (up to 5.1 to 10.0%). Yet, LLMs suffer from their unique challenges, such as ineffective prompts and the lack of domain knowledge, which together account for 53 to 60% of LLM unique failures. The strong performance of open source models (e.g., StarCoder) makes closed source models (e.g., GPT 3 Davinci) less desirable due to size and cost. Our study offers valuable insights for future research to improve specification generation.

Accuracy is an important concern for suppliers of artificial intelligence (AI) services, but considerations beyond accuracy, such as safety (which includes fairness and explainability), security, and provenance, are also critical elements to engender consumers' trust in a service. Many industries use transparent, standardized, but often not legally required documents called supplier's declarations of conformity (SDoCs) to describe the lineage of a product along with the safety and performance testing it has undergone. SDoCs may be considered multi-dimensional fact sheets that capture and quantify various aspects of the product and its development to make it worthy of consumers' trust. Inspired by this practice, we propose FactSheets to help increase trust in AI services. We envision such documents to contain purpose, performance, safety, security, and provenance information to be completed by AI service providers for examination by consumers. We suggest a comprehensive set of declaration items tailored to AI and provide examples for two fictitious AI services in the appendix of the paper.

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.

To evaluate code large language models (LLMs), research has relied on a few small manually curated benchmarks, such as HumanEval and MBPP, which represent a narrow part of the real-world software domains. In this work, we introduce round-trip correctness (RTC) as an alternative evaluation method. RTC allows Code LLM evaluation on a broader spectrum of real-world software domains without the need for costly human curation. RTC rests on the idea that we can ask a model to make a prediction (e.g., describe some code using natural language), feed that prediction back (e.g., synthesize code from the predicted description), and check if this round-trip leads to code that is semantically equivalent to the original input. We show how to employ RTC to evaluate code synthesis and editing. We find that RTC strongly correlates with model performance on existing narrow-domain code synthesis benchmarks while allowing us to expand to a much broader set of domains and tasks which was not previously possible without costly human annotations.

Large language models (LLMs), such as ChatGPT and Copilot, are transforming software development by automating code generation and, arguably, enable rapid prototyping, support education, and boost productivity. Therefore, correctness and quality of the generated code should be on par with manually written code. To assess the current state of LLMs in generating correct code of high quality, we conducted controlled experiments with ChatGPT and Copilot: we let the LLMs generate simple algorithms in Java and Python along with the corresponding unit tests and assessed the correctness and the quality (coverage) of the generated (test) codes. We observed significant differences between the LLMs, between the languages, between algorithm and test codes, and over time. The present paper reports these results together with the experimental methods allowing repeated and comparable assessments for more algorithms, languages, and LLMs over time.

In order to properly train a machine learning model, data must be properly collected. To guarantee a proper data collection, verifying that the collected data set holds certain properties is a possible solution. For example, guaranteeing that the data set contains samples across the whole input space, or that the data set is balanced w.r.t. different classes. We present a formal approach for verifying a set of arbitrarily stated properties over a data set. The proposed approach relies on the transformation of the data set into a first order logic formula, which can be later verified w.r.t. the different properties also stated in the same logic. A prototype tool, which uses the z3 solver, has been developed; the prototype can take as an input a set of properties stated in a formal language and formally verify a given data set w.r.t. to the given set of properties. Preliminary experimental results show the feasibility and performance of the proposed approach, and furthermore the flexibility for expressing properties of interest.

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).

Language models (LMs) are susceptible to in-context reward hacking, where they exploit flaws in tainted or faulty written specifications or rubrics to achieve high scores without fulfilling the user's true intent. We introduce Specification Self-Correction (SSC), a novel, test-time framework that enables an LM to identify and correct flaws within its own guiding specification. SSC employs a multi-step inference process where the model first generates a response based on a potentially tainted specification, critiques its output, and then revises the specification itself to remove the exploitable loophole. A final, more robust response is then generated using this self-corrected specification. Across experiments spanning creative writing and agentic coding tasks with several LMs, we demonstrate that while models initially game tainted specifications in 50-70\% of cases, the SSC process reduces this vulnerability by over 90\%. This dynamic repair occurs at inference time, requires no weight modification, and leads to more robustly aligned model behavior. Code at https://github.com/vicgalle/specification-self-correction .

Code generation has largely improved development efficiency in the era of large language models (LLMs). With the ability to follow instructions, current LLMs can be prompted to generate code solutions given detailed descriptions in natural language. Many research efforts are being devoted to improving the correctness of LLM-generated code, and many benchmarks are proposed to evaluate the correctness comprehensively. Despite the focus on correctness, the time efficiency of LLM-generated code solutions is under-explored. Current correctness benchmarks are not suitable for time efficiency evaluation since their test cases cannot well distinguish the time efficiency of different code solutions. Besides, the current execution time measurement is not stable and comprehensive, threatening the validity of the time efficiency evaluation. To address the challenges in the time efficiency evaluation of code generation, we propose COFFE, a code generation benchmark for evaluating the time efficiency of LLM-generated code solutions. COFFE contains 398 and 358 problems for function-level and file-level code generation, respectively. To improve the distinguishability, we design a novel stressful test case generation approach with contracts and two new formats of test cases to improve the accuracy of generation. For the time evaluation metric, we propose efficienct@k based on CPU instruction count to ensure a stable and solid comparison between different solutions. We evaluate 14 popular LLMs on COFFE and identify four findings. Based on the findings, we draw some implications for LLM researchers and software practitioners to facilitate future research and usage of LLMs in code generation.

Generating accurate and calibrated confidence estimates is critical for deploying LLMs in high-stakes or user-facing applications, and remains an open challenge. Prior research has often framed confidence as a problem of eliciting a model's "self-knowledge", i.e., the ability of an LLM to judge whether its own answers are correct; this approach implicitly assumes that there is some privileged information about the answer's correctness that is accessible to the model itself. However, our experiments reveal that an LLM attempting to predict the correctness of its own outputs generally performs no better than an unrelated LLM. Moreover, we hypothesize that a key factor in building a "Correctness Model" (CM) is exposure to a target model's historical predictions. We propose multiple methods to inject this historical correctness information, creating a Generalized Correctness Model (GCM). We first show that GCMs can be trained on the correctness data from many LLMs and learn patterns for correctness prediction applicable across datasets and models. We then use CMs as a lens for studying the source of correctness prediction ability and its generalization, systematically controlling their training data and finding that answer phrasing is a strong predictor for correctness. We further explore alternative methods of injecting history without training an LLM, finding that including history as in-context examples can help improve correctness prediction, and post-hoc calibration can provide complementary reductions in calibration error. We evaluate GCMs based on Qwen3-8B across 5 model families and the MMLU and TriviaQA datasets, as well as on a downstream selective prediction task, finding that reliable LLM confidence estimation is a generalizable and model-agnostic skill learned by systematically encoding correctness history rather than a model-specific skill reliant on self-introspection.

We present and test the largest benchmark for vericoding, LLM-generation of formally verified code from formal specifications - in contrast to vibe coding, which generates potentially buggy code from a natural language description. Our benchmark contains 12,504 formal specifications, with 3,029 in Dafny, 2,334 in Verus/Rust and 7,141 in Lean. Of these, 6,174 are new unseen problems. We find vericoding success rates of 27% in Lean, 44% in Verus/Rust and 82% in Dafny using off-the-shelf LLMs. Adding natural-language descriptions does not significantly improve performance. We also find that LLM progress has improved progress on pure Dafny verification from 68% to 96% over the past year. The benchmark and vericoding results are shared at https://github.com/Beneficial-AI-Foundation/vericoding-benchmark

We introduce gec-metrics, a library for using and developing grammatical error correction (GEC) evaluation metrics through a unified interface. Our library enables fair system comparisons by ensuring that everyone conducts evaluations using a consistent implementation. Moreover, it is designed with a strong focus on API usage, making it highly extensible. It also includes meta-evaluation functionalities and provides analysis and visualization scripts, contributing to developing GEC evaluation metrics. Our code is released under the MIT license and is also distributed as an installable package. The video is available on YouTube.

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.

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

Large language models (LLMs) are increasingly applied in diverse real-world scenarios, each governed by bespoke behavioral and safety specifications (spec) custom-tailored by users or organizations. These spec, categorized into safety-spec and behavioral-spec, vary across scenarios and evolve with changing preferences and requirements. We formalize this challenge as specification alignment, focusing on LLMs' ability to follow dynamic, scenario-specific spec from both behavioral and safety perspectives. To address this challenge, we propose Align3, a lightweight method that employs Test-Time Deliberation (TTD) with hierarchical reflection and revision to reason over the specification boundaries. We further present SpecBench, a unified benchmark for measuring specification alignment, covering 5 scenarios, 103 spec, and 1,500 prompts. Experiments on 15 reasoning and 18 instruct models with several TTD methods, including Self-Refine, TPO, and MoreThink, yield three key findings: (i) test-time deliberation enhances specification alignment; (ii) Align3 advances the safety-helpfulness trade-off frontier with minimal overhead; (iii) SpecBench effectively reveals alignment gaps. These results highlight the potential of test-time deliberation as an effective strategy for reasoning over the real-world specification boundaries.

Recent Language Models (LMs) achieve breakthrough performance in code generation when trained on human-authored problems, even solving some competitive-programming problems. Self-play has proven useful in games such as Go, and thus it is natural to ask whether LMs can generate their own instructive programming problems to improve their performance. We show that it is possible for an LM to synthesize programming problems and solutions, which are filtered for correctness by a Python interpreter. The LM's performance is then seen to improve when it is fine-tuned on its own synthetic problems and verified solutions; thus the model 'improves itself' using the Python interpreter. Problems are specified formally as programming puzzles [Schuster et al., 2021], a code-based problem format where solutions can easily be verified for correctness by execution. In experiments on publicly-available LMs, test accuracy more than doubles. This work demonstrates the potential for code LMs, with an interpreter, to generate instructive problems and improve their own performance.

Large language models (LLMs) are increasingly integrated in software development, but ensuring correctness in LLM-generated code remains challenging and often requires costly manual review. Verifiable code generation -- jointly generating code, specifications, and proofs of code-specification alignment -- offers a promising path to address this limitation and further unleash LLMs' benefits in coding. Yet, there exists a significant gap in evaluation: current benchmarks often lack support for end-to-end verifiable code generation. In this paper, we introduce Verina (Verifiable Code Generation Arena), a high-quality benchmark enabling a comprehensive and modular evaluation of code, specification, and proof generation as well as their compositions. Verina consists of 189 manually curated coding tasks in Lean, with detailed problem descriptions, reference implementations, formal specifications, and extensive test suites. Our extensive evaluation of state-of-the-art LLMs reveals significant challenges in verifiable code generation, especially in proof generation, underscoring the need for improving LLM-based theorem provers in verification domains. The best model, OpenAI o4-mini, generates only 61.4% correct code, 51.0% sound and complete specifications, and 3.6% successful proofs, with one trial per task. We hope Verina will catalyze progress in verifiable code generation by providing a rigorous and comprehensive benchmark. We release our dataset on https://huggingface.co/datasets/sunblaze-ucb/verina and our evaluation code on https://github.com/sunblaze-ucb/verina.

Existing evaluation benchmarks of language models of code (code LMs) focus almost exclusively on whether the LMs can generate functionally-correct code. In real-world software engineering, developers think beyond functional correctness. They have requirements on "how" a functionality should be implemented to meet overall system design objectives like efficiency, security, and maintainability. They would also trust the code LMs more if the LMs demonstrate robust understanding of requirements and code semantics. We propose a new benchmark NoFunEval to evaluate code LMs on non-functional requirements and simple classification instances for both functional and non-functional requirements. We propose a prompting method, Coding Concepts (CoCo), as a way for a developer to communicate the domain knowledge to the LMs. We conduct an extensive evaluation of twenty-two code LMs. Our finding is that they generally falter when tested on our benchmark, hinting at fundamental blindspots in their training setups. Surprisingly, even the classification accuracy on functional-correctness instances derived from the popular HumanEval benchmark is low, calling in question the depth of their comprehension and the source of their success in generating functionally-correct code in the first place. We will release our benchmark and evaluation scripts publicly at https://aka.ms/NoFunEval.

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.

Recent advances in Large Language Models (LLMs) have sparked growing interest in applying them to Electronic Design Automation (EDA) tasks, particularly Register Transfer Level (RTL) code generation. While several RTL datasets have been introduced, most focus on syntactic validity rather than functional validation with tests, leading to training examples that compile but may not implement the intended behavior. We present VERICODER, a model for RTL code generation fine-tuned on a dataset validated for functional correctness. This fine-tuning dataset is constructed using a novel methodology that combines unit test generation with feedback-directed refinement. Given a natural language specification and an initial RTL design, we prompt a teacher model (GPT-4o-mini) to generate unit tests and iteratively revise the RTL design based on its simulation results using the generated tests. If necessary, the teacher model also updates the tests to ensure they comply with the natural language specification. As a result of this process, every example in our dataset is functionally validated, consisting of a natural language description, an RTL implementation, and passing tests. Fine-tuned on this dataset of over 125,000 examples, VERICODER achieves state-of-the-art metrics in functional correctness on VerilogEval and RTLLM, with relative gains of up to 71.7% and 27.4% respectively. An ablation study further shows that models trained on our functionally validated dataset outperform those trained on functionally non-validated datasets, underscoring the importance of high-quality datasets in RTL code generation.

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

This is the first paper in a series of work we have accomplished over the past three years. In this paper, we have constructed a consistent formal plane geometry system. This will serve as a crucial bridge between IMO-level plane geometry challenges and readable AI automated reasoning. Within this formal framework, we have been able to seamlessly integrate modern AI models with our formal system. AI is now capable of providing deductive reasoning solutions to IMO-level plane geometry problems, just like handling other natural languages, and these proofs are readable, traceable, and verifiable. We propose the geometry formalization theory (GFT) to guide the development of the geometry formal system. Based on the GFT, we have established the FormalGeo, which consists of 88 geometric predicates and 196 theorems. It can represent, validate, and solve IMO-level geometry problems. we also have crafted the FGPS (formal geometry problem solver) in Python. It serves as both an interactive assistant for verifying problem-solving processes and an automated problem solver. We've annotated the formalgeo7k and formalgeo-imo datasets. The former contains 6,981 (expand to 133,818 through data augmentation) geometry problems, while the latter includes 18 (expand to 2,627 and continuously increasing) IMO-level challenging geometry problems. All annotated problems include detailed formal language descriptions and solutions. Implementation of the formal system and experiments validate the correctness and utility of the GFT. The backward depth-first search method only yields a 2.42% problem-solving failure rate, and we can incorporate deep learning techniques to achieve lower one. The source code of FGPS and datasets are available at https://github.com/BitSecret/FGPS.

We propose a novel dynamic safety framework that optimizes language model (LM) safety reasoning at inference time without modifying model weights. Building on recent advances in self-critique methods, our approach leverages a meta-critique mechanism that iteratively updates safety prompts-termed specifications-to drive the critique and revision process adaptively. This test-time optimization not only improves performance against adversarial jailbreak requests but also in diverse general safety-related tasks, such as avoiding moral harm or pursuing honest responses. Our empirical evaluations across several language models demonstrate that dynamically optimized safety prompts yield significantly higher safety scores compared to fixed system prompts and static self-critique defenses. Code to be released at https://github.com/vicgalle/meta-self-critique.git .

FormalSpecCpp is a dataset designed to fill the gap in standardized benchmarks for verifying formal specifications in C++ programs. To the best of our knowledge, this is the first comprehensive collection of C++ programs with well-defined preconditions and postconditions. It provides a structured benchmark for evaluating specification inference tools and testing theaccuracy of generated specifications. Researchers and developers can use this dataset to benchmark specification inference tools,fine-tune Large Language Models (LLMs) for automated specification generation, and analyze the role of formal specifications in improving program verification and automated testing. By making this dataset publicly available, we aim to advance research in program verification, specification inference, and AI-assisted software development. The dataset and the code are available at https://github.com/MadhuNimmo/FormalSpecCpp.

Training large language models (LLMs) for external tool usage is a rapidly expanding field, with recent research focusing on generating synthetic data to address the shortage of available data. However, the absence of systematic data quality checks poses complications for properly training and testing models. To that end, we propose two approaches for assessing the reliability of data for training LLMs to use external tools. The first approach uses intuitive, human-defined correctness criteria. The second approach uses a model-driven assessment with in-context evaluation. We conduct a thorough evaluation of data quality on two popular benchmarks, followed by an extrinsic evaluation that showcases the impact of data quality on model performance. Our results demonstrate that models trained on high-quality data outperform those trained on unvalidated data, even when trained with a smaller quantity of data. These findings empirically support the significance of assessing and ensuring the reliability of training data for tool-using LLMs.

There is a growing line of research on verifying the correctness of language models' outputs. At the same time, LMs are being used to tackle complex queries that require reasoning. We introduce CoverBench, a challenging benchmark focused on verifying LM outputs in complex reasoning settings. Datasets that can be used for this purpose are often designed for other complex reasoning tasks (e.g., QA) targeting specific use-cases (e.g., financial tables), requiring transformations, negative sampling and selection of hard examples to collect such a benchmark. CoverBench provides a diversified evaluation for complex claim verification in a variety of domains, types of reasoning, relatively long inputs, and a variety of standardizations, such as multiple representations for tables where available, and a consistent schema. We manually vet the data for quality to ensure low levels of label noise. Finally, we report a variety of competitive baseline results to show CoverBench is challenging and has very significant headroom. The data is available at https://huggingface.co/datasets/google/coverbench .

Ensuring that Software Requirements Specifications (SRS) align with higher-level organizational or national requirements is vital, particularly in regulated environments such as finance and aerospace. In these domains, maintaining consistency, adhering to regulatory frameworks, minimizing errors, and meeting critical expectations are essential for the reliable functioning of systems. The widespread adoption of large language models (LLMs) highlights their immense potential, yet there remains considerable scope for improvement in retrieving relevant information and enhancing reasoning capabilities. This study demonstrates that integrating a robust Graph-RAG framework with advanced prompt engineering techniques, such as Chain of Thought and Tree of Thought, can significantly enhance performance. Compared to baseline RAG methods and simple prompting strategies, this approach delivers more accurate and context-aware results. While this method demonstrates significant improvements in performance, it comes with challenges. It is both costly and more complex to implement across diverse contexts, requiring careful adaptation to specific scenarios. Additionally, its effectiveness heavily relies on having complete and accurate input data, which may not always be readily available, posing further limitations to its scalability and practicality.

We introduce Codex, a GPT language model fine-tuned on publicly available code from GitHub, and study its Python code-writing capabilities. A distinct production version of Codex powers GitHub Copilot. On HumanEval, a new evaluation set we release to measure functional correctness for synthesizing programs from docstrings, our model solves 28.8% of the problems, while GPT-3 solves 0% and GPT-J solves 11.4%. Furthermore, we find that repeated sampling from the model is a surprisingly effective strategy for producing working solutions to difficult prompts. Using this method, we solve 70.2% of our problems with 100 samples per problem. Careful investigation of our model reveals its limitations, including difficulty with docstrings describing long chains of operations and with binding operations to variables. Finally, we discuss the potential broader impacts of deploying powerful code generation technologies, covering safety, security, and economics.

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.

One of the biggest challenges of natural language generation (NLG) is the proper handling of named entities. Named entities are a common source of grammar mistakes such as wrong prepositions, wrong article handling, or incorrect entity inflection. Without factoring linguistic representation, such errors are often underrepresented when evaluating on a small set of arbitrarily picked argument values, or when translating a dataset from a linguistically simpler language, like English, to a linguistically complex language, like Russian. However, for some applications, broadly precise grammatical correctness is critical -- native speakers may find entity-related grammar errors silly, jarring, or even offensive. To enable the creation of more linguistically diverse NLG datasets, we release a Corpus of Linguistically Significant Entities (CLSE) annotated by linguist experts. The corpus includes 34 languages and covers 74 different semantic types to support various applications from airline ticketing to video games. To demonstrate one possible use of CLSE, we produce an augmented version of the Schema-Guided Dialog Dataset, SGD-CLSE. Using the CLSE's entities and a small number of human translations, we create a linguistically representative NLG evaluation benchmark in three languages: French (high-resource), Marathi (low-resource), and Russian (highly inflected language). We establish quality baselines for neural, template-based, and hybrid NLG systems and discuss the strengths and weaknesses of each approach.

Recent advances in long chain-of-thought (CoT) reasoning have largely prioritized answer accuracy and token efficiency, while overlooking aspects critical to trustworthiness. We argue that usable reasoning systems must be trustworthy, characterized by three properties: interpretability, faithfulness, and reliability. To this end, we propose ReFIne, a new training framework that integrates supervised fine-tuning with GRPO to encourage models to: (i) improve interpretability by producing structured, tag-based traces with high-level planning that are easier for humans to follow; (ii) enhance faithfulness by explicitly disclosing the decisive information guiding each solution, with consistent cross-section references; and (iii) promote reliability by providing self-assessments of both the derivation's soundness and the confidence of the final answer. We apply ReFIne to the Qwen3 models at multiple scales (1.7B/4B/8B) and evaluate across mathematical benchmarks of varying difficulty. Our experimental results show that ReFIne models generate clearer and better-structured reasoning traces (interpretability +44.0%), more faithfully expose their underlying decision process (faithfulness +18.8%), and offer informative confidence estimates (reliability +42.4%). These findings highlight an overlooked but important direction: reasoning models should be optimized not only for accuracy, but also for broader dimensions of trustworthiness. Our code is available at: https://github.com/Trustworthy-ML-Lab/Training_Trustworthy_LRM_with_Refine

Common-sense reasoning is a key language model capability because it encapsulates not just specific factual knowledge but rather general language and world understanding. Measuring common-sense reasoning, therefore, is crucial for language models of different sizes and applications. One of the most widely used benchmarks for evaluating such capabilities is HellaSwag; however, in this paper, we show that it has severe construct validity issues. These issues range from basic ungrammaticality and numerous typos to misleading prompts or equally correct options. Furthermore, we show that if models are evaluated only on answer texts, or with "Lorem ipsum dolor..." instead of the question, more than 65% of model predictions remain the same, and this cannot be attributed merely to contamination. Since benchmark scores are an essential part of model selection in both research and commercial applications, these validity issues can have severe consequences. In particular, knowing that taking benchmark scores at face value is ubiquitous, inadequate evaluation leads to ill-informed decisions about models. In this paper, we thoroughly investigate critical validity issues posed by HellaSwag and illustrate them with various evaluations using generative language models of different sizes. We argue that this benchmark does not accurately measure common-sense reasoning and, therefore, should not be used for evaluation in its current state. Based on the results of our study, we propose requirements that should be met by future common-sense reasoning benchmarks. In addition, we release GoldenSwag, a corrected subset of HellaSwag, which, to our belief, facilitates acceptable common-sense reasoning evaluation.

Translating software written in legacy languages to modern languages, such as C to Rust, has significant benefits in improving memory safety while maintaining high performance. However, manual translation is cumbersome, error-prone, and produces unidiomatic code. Large language models (LLMs) have demonstrated promise in producing idiomatic translations, but offer no correctness guarantees as they lack the ability to capture all the semantics differences between the source and target languages. To resolve this issue, we propose SACTOR, an LLM-driven C-to-Rust zero-shot translation tool using a two-step translation methodology: an "unidiomatic" step to translate C into Rust while preserving semantics, and an "idiomatic" step to refine the code to follow Rust's semantic standards. SACTOR utilizes information provided by static analysis of the source C program to address challenges such as pointer semantics and dependency resolution. To validate the correctness of the translated result from each step, we use end-to-end testing via the foreign function interface to embed our translated code segment into the original code. We evaluate the translation of 200 programs from two datasets and two case studies, comparing the performance of GPT-4o, Claude 3.5 Sonnet, Gemini 2.0 Flash, Llama 3.3 70B and DeepSeek-R1 in SACTOR. Our results demonstrate that SACTOR achieves high correctness and improved idiomaticity, with the best-performing model (DeepSeek-R1) reaching 93% and (GPT-4o, Claude 3.5, DeepSeek-R1) reaching 84% correctness (on each dataset, respectively), while producing more natural and Rust-compliant translations compared to existing methods.

Large language models (LLMs), exemplified by ChatGPT, have gained considerable attention for their excellent natural language processing capabilities. Nonetheless, these LLMs present many challenges, particularly in the realm of trustworthiness. Therefore, ensuring the trustworthiness of LLMs emerges as an important topic. This paper introduces TrustLLM, a comprehensive study of trustworthiness in LLMs, including principles for different dimensions of trustworthiness, established benchmark, evaluation, and analysis of trustworthiness for mainstream LLMs, and discussion of open challenges and future directions. Specifically, we first propose a set of principles for trustworthy LLMs that span eight different dimensions. Based on these principles, we further establish a benchmark across six dimensions including truthfulness, safety, fairness, robustness, privacy, and machine ethics. We then present a study evaluating 16 mainstream LLMs in TrustLLM, consisting of over 30 datasets. Our findings firstly show that in general trustworthiness and utility (i.e., functional effectiveness) are positively related. Secondly, our observations reveal that proprietary LLMs generally outperform most open-source counterparts in terms of trustworthiness, raising concerns about the potential risks of widely accessible open-source LLMs. However, a few open-source LLMs come very close to proprietary ones. Thirdly, it is important to note that some LLMs may be overly calibrated towards exhibiting trustworthiness, to the extent that they compromise their utility by mistakenly treating benign prompts as harmful and consequently not responding. Finally, we emphasize the importance of ensuring transparency not only in the models themselves but also in the technologies that underpin trustworthiness. Knowing the specific trustworthy technologies that have been employed is crucial for analyzing their effectiveness.

The ModelWriter platform provides a generic framework for automated traceability analysis. In this paper, we demonstrate how this framework can be used to trace the consistency and completeness of technical documents that consist of a set of System Installation Design Principles used by Airbus to ensure the correctness of aircraft system installation. We show in particular, how the platform allows the integration of two types of reasoning: reasoning about the meaning of text using semantic parsing and description logic theorem proving; and reasoning about document structure using first-order relational logic and finite model finding for traceability analysis.

Large language models (LLMs) often struggle with maintaining accuracy across a sequence of intermediate reasoning steps in mathematical reasoning, leading to error propagation that undermines the final result. The current methodology to mitigate this issue primarily involves using a verifier model to assess the correctness of generated solution candidates, focusing either on the overall reasoning path or on an incomplete reasoning path. By rethinking this approach, we argue that assessing potentials of incomplete reasoning paths could be more advantageous as it guides towards correct final answers, transforming the task into a planning problem. Our proposed verifier, the Outcome-supervision Value Model (OVM), employs outcome supervision for training, offering an efficient and intuitive method for planning by prioritizing steps that lead to accurate conclusions over mere per-step correctness. Furthermore, the OVM eschews the need for labor-intensive annotations on step-level correctness, enhancing its scalability. Our experiments on two multi-step mathematical reasoning datasets, GSM8K and Game of 24, demonstrate the superior performance of the OVM model. Notably, in GSM8K, our OVM-7B model achieves state-of-the-art results among LLMs up to 13B parameters; especially it does not utilize GPT-4 or code execution. These findings offer a novel perspective on the role of outcome supervision in training verifiers for multi-step reasoning tasks and provide theoretical justification for its advantage in value estimation for planning.

We introduce StableLM 2 1.6B, the first in a new generation of our language model series. In this technical report, we present in detail the data and training procedure leading to the base and instruction-tuned versions of StableLM 2 1.6B. The weights for both models are available via Hugging Face for anyone to download and use. The report contains thorough evaluations of these models, including zero- and few-shot benchmarks, multilingual benchmarks, and the MT benchmark focusing on multi-turn dialogues. At the time of publishing this report, StableLM 2 1.6B was the state-of-the-art open model under 2B parameters by a significant margin. Given its appealing small size, we also provide throughput measurements on a number of edge devices. In addition, we open source several quantized checkpoints and provide their performance metrics compared to the original model.

Large Language Models (LLMs), particularly Code LLMs, have demonstrated impressive performance in code generation. Current research primarily focuses on the correctness of generated code, while efficiency remains less explored. Recent works have focused on modifying the initial version of the code to improve its efficiency. However, such refinements are limited by the algorithmic design and overall logic of the initial code, resulting in only incremental improvements. In contrast, when human developers write high-quality code, they typically begin by designing several potential solutions at the logical level, evaluating various algorithms and their complexities, and then proceeding to implement and optimize the solution. In this study, we introduce \tool: Large Language Model for Code Efficiency, a novel framework that enables LLMs to generate code that balances both efficiency and correctness. Specifically, \tool divides the efficiency optimization process into two domains: algorithmic exploration in the logic domain and implementation optimization in the code domain. The correctness of the code is then guaranteed through a synthetic test case refinement process. This approach, which prioritizes efficiency before ensuring correctness, offers a new paradigm for efficient code generation. Experiments demonstrate that \tool consistently improves both efficiency and correctness, achieving new state-of-the-art performance in code efficiency benchmarks across various LLM backbones.

Complex reasoning tasks often rely on the ability to consistently and accurately apply simple rules across incremental steps, a foundational capability which we term "level-0" reasoning. To systematically evaluate this capability, we introduce L0-Bench, a language model benchmark for testing procedural correctness -- the ability to generate correct reasoning processes, complementing existing benchmarks that primarily focus on outcome correctness. Given synthetic Python functions with simple operations, L0-Bench grades models on their ability to generate step-by-step, error-free execution traces. The synthetic nature of L0-Bench enables systematic and scalable generation of test programs along various axes (e.g., number of trace steps). We evaluate a diverse array of recent closed-source and open-weight models on a baseline test set. All models exhibit degradation as the number of target trace steps increases, while larger models and reasoning-enhanced models better maintain correctness over multiple steps. Additionally, we use L0-Bench to explore test-time scaling along three dimensions: input context length, number of solutions for majority voting, and inference steps. Our results suggest substantial room to improve "level-0" reasoning and potential directions to build more reliable reasoning systems.

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.

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.

Interpretability research now offers a variety of techniques for identifying abstract internal mechanisms in neural networks. Can such techniques be used to predict how models will behave on out-of-distribution examples? In this work, we provide a positive answer to this question. Through a diverse set of language modeling tasks--including symbol manipulation, knowledge retrieval, and instruction following--we show that the most robust features for correctness prediction are those that play a distinctive causal role in the model's behavior. Specifically, we propose two methods that leverage causal mechanisms to predict the correctness of model outputs: counterfactual simulation (checking whether key causal variables are realized) and value probing (using the values of those variables to make predictions). Both achieve high AUC-ROC in distribution and outperform methods that rely on causal-agnostic features in out-of-distribution settings, where predicting model behaviors is more crucial. Our work thus highlights a novel and significant application for internal causal analysis of language models.

Software that contains machine learning algorithms is an integral part of automotive perception, for example, in driving automation systems. The development of such software, specifically the training and validation of the machine learning components, require large annotated datasets. An industry of data and annotation services has emerged to serve the development of such data-intensive automotive software components. Wide-spread difficulties to specify data and annotation needs challenge collaborations between OEMs (Original Equipment Manufacturers) and their suppliers of software components, data, and annotations. This paper investigates the reasons for these difficulties for practitioners in the Swedish automotive industry to arrive at clear specifications for data and annotations. The results from an interview study show that a lack of effective metrics for data quality aspects, ambiguities in the way of working, unclear definitions of annotation quality, and deficits in the business ecosystems are causes for the difficulty in deriving the specifications. We provide a list of recommendations that can mitigate challenges when deriving specifications and we propose future research opportunities to overcome these challenges. Our work contributes towards the on-going research on accountability of machine learning as applied to complex software systems, especially for high-stake applications such as automated driving.

Ensuring faithfulness to context in large language models (LLMs) and retrieval-augmented generation (RAG) systems is crucial for reliable deployment in real-world applications, as incorrect or unsupported information can erode user trust. Despite advancements on standard benchmarks, faithfulness hallucination-where models generate responses misaligned with the provided context-remains a significant challenge. In this work, we introduce FaithEval, a novel and comprehensive benchmark tailored to evaluate the faithfulness of LLMs in contextual scenarios across three diverse tasks: unanswerable, inconsistent, and counterfactual contexts. These tasks simulate real-world challenges where retrieval mechanisms may surface incomplete, contradictory, or fabricated information. FaithEval comprises 4.9K high-quality problems in total, validated through a rigorous four-stage context construction and validation framework, employing both LLM-based auto-evaluation and human validation. Our extensive study across a wide range of open-source and proprietary models reveals that even state-of-the-art models often struggle to remain faithful to the given context, and that larger models do not necessarily exhibit improved faithfulness.Project is available at: https://github.com/SalesforceAIResearch/FaithEval.

We introduce Stable Code, the first in our new-generation of code language models series, which serves as a general-purpose base code language model targeting code completion, reasoning, math, and other software engineering-based tasks. Additionally, we introduce an instruction variant named Stable Code Instruct that allows conversing with the model in a natural chat interface for performing question-answering and instruction-based tasks. In this technical report, we detail the data and training procedure leading to both models. Their weights are available via Hugging Face for anyone to download and use at https://huggingface.co/stabilityai/stable-code-3b and https://huggingface.co/stabilityai/stable-code-instruct-3b. This report contains thorough evaluations of the models, including multilingual programming benchmarks, and the MT benchmark focusing on multi-turn dialogues. At the time of its release, Stable Code is the state-of-the-art open model under 3B parameters and even performs comparably to larger models of sizes 7 billion and 15 billion parameters on the popular Multi-PL benchmark. Stable Code Instruct also exhibits state-of-the-art performance on the MT-Bench coding tasks and on Multi-PL completion compared to other instruction tuned models. Given its appealing small size, we also provide throughput measurements on a number of edge devices. In addition, we open source several quantized checkpoints and provide their performance metrics compared to the original model.

We present FIMO, an innovative dataset comprising formal mathematical problem statements sourced from the International Mathematical Olympiad (IMO) Shortlisted Problems. Designed to facilitate advanced automated theorem proving at the IMO level, FIMO is currently tailored for the Lean formal language. It comprises 149 formal problem statements, accompanied by both informal problem descriptions and their corresponding LaTeX-based informal proofs. Through initial experiments involving GPT-4, our findings underscore the existing limitations in current methodologies, indicating a substantial journey ahead before achieving satisfactory IMO-level automated theorem proving outcomes.

Large language models (LLMs) now write code in settings where misreading a single word can break safety or cost money, yet we still expect them to overlook stray typos. To probe where useful robustness ends and harmful insensitivity begins, we compile 50 LeetCode problems and craft three minimal prompt perturbations that should vary in importance: (i) progressive underspecification deleting 10 % of words per step; (ii) lexical flip swapping a pivotal quantifier ("max" to "min"); and (iii) jargon inflation replacing a common noun with an obscure technical synonym. Six frontier models, including three "reasoning-tuned" versions, solve each mutated prompt, and their Python outputs are checked against the original test suites to reveal whether they reused the baseline solution or adapted. Among 11 853 generations we observe a sharp double asymmetry. Models remain correct in 85 % of cases even after 90 % of the prompt is missing, showing over-robustness to underspecification, yet only 54 % react to a single quantifier flip that reverses the task, with reasoning-tuned variants even less sensitive than their bases. Jargon edits lie in between, passing through 56 %. Current LLMs thus blur the line between harmless noise and meaning - changing edits, often treating both as ignorable. Masking salient anchors such as function names can force re - evaluation. We advocate evaluation and training protocols that reward differential sensitivity: stay steady under benign noise but adapt - or refuse - when semantics truly change.

Question answering (QA) can only make progress if we know if an answer is correct, but for many of the most challenging and interesting QA examples, current answer correctness (AC) metrics do not align with human judgments, particularly verbose, free form answers from large language models (LLM). There are two challenges: a lack of data and that models are too big. LLM based scorers correlate better with humans, but this expensive task has only been tested on limited QA datasets. We rectify these issues by providing clear guidelines for evaluating machine QA adopted from human QA contests. We also introduce Precise ANswer correctness Determination and Adjudication (PANDA), a small, efficient, deterministic AC classifier (812 KB) that more accurately evaluates answer correctness.

Ensuring that Large Language Models (LLMs) generate summaries faithful to a given source document is essential for real-world applications. While prior research has explored LLM faithfulness, existing benchmarks suffer from annotation ambiguity, primarily due to the ill-defined boundary of permissible external knowledge in generated outputs. For instance, common sense is often incorporated into responses and labeled as "faithful", yet the acceptable extent of such knowledge remains unspecified, leading to inconsistent annotations. To address this issue, we propose a novel faithfulness annotation framework, which introduces an intermediate category, Out-Dependent, to classify cases where external knowledge is required for verification. Using this framework, we construct VeriGray (Verification with the Gray Zone) -- a new unfaithfulness detection benchmark in summarization. Statistics reveal that even SOTA LLMs, such as GPT-5, exhibit hallucinations (sim 6% of sentences) in summarization tasks. Moreover, a substantial proportion (sim 8% on average of models) of generated sentences fall into the Out-Dependent category, underscoring the importance of resolving annotation ambiguity in unfaithfulness detection benchmarks. Experiments demonstrate that our benchmark poses significant challenges to multiple baseline methods, indicating considerable room for future improvement.

Large language models (LLMs) have demonstrated impressive capabilities in code generation, achieving high scores on benchmarks such as HumanEval and MBPP. However, these benchmarks primarily assess functional correctness and neglect broader dimensions of code quality, including security, reliability, readability, and maintainability. In this work, we systematically evaluate the ability of LLMs to generate high-quality code across multiple dimensions using the PythonSecurityEval benchmark. We introduce an iterative static analysis-driven prompting algorithm that leverages Bandit and Pylint to identify and resolve code quality issues. Our experiments with GPT-4o show substantial improvements: security issues reduced from >40% to 13%, readability violations from >80% to 11%, and reliability warnings from >50% to 11% within ten iterations. These results demonstrate that LLMs, when guided by static analysis feedback, can significantly enhance code quality beyond functional correctness.

The recent successful paradigm of solving logical reasoning problems with tool-augmented large language models (LLMs) leverages translation of natural language (NL) statements into First-Order Logic~(FOL) and external theorem provers. However, the correctness of FOL statements, comprising operators and text, often go unverified due to the lack of a reliable evaluation metric for comparing generated and ground-truth FOLs. In this paper, we conduct a comprehensive study on the sensitivity of existing NL-, FOL-, and graph-based metrics to capture differences between a sampled FOL and its corresponding ground-truth. We then measure the alignment between a metric-based ranking of FOL outputs and a strong LLM as-a-judge. To do this, we first apply operator and text-based perturbations to ground-truth FOL statements to assess metric sensitivity. We then evaluate metric robustness by comparing the metrics against LLMs judgment. Our empirical findings highlight a clear oversensitivity in the n-gram metric BLEU for text perturbations. The operator perturbation affects the semantic graph metric Smatch++ for structural changes, and the FOL metric for specific operator changes. We observe a closer alignment between BertScore and LLM judgement, proving the importance of semantic evaluation. Additionally, we show that combining metrics enhances both robustness and sensitivity compared to using individual metrics.

This paper presents a quantitative program verification infrastructure for discrete probabilistic programs. Our infrastructure can be viewed as the probabilistic analogue of Boogie: its central components are an intermediate verification language (IVL) together with a real-valued logic. Our IVL provides a programming-language-style for expressing verification conditions whose validity implies the correctness of a program under investigation. As our focus is on verifying quantitative properties such as bounds on expected outcomes, expected run-times, or termination probabilities, off-the-shelf IVLs based on Boolean first-order logic do not suffice. Instead, a paradigm shift from the standard Boolean to a real-valued domain is required. Our IVL features quantitative generalizations of standard verification constructs such as assume- and assert-statements. Verification conditions are generated by a weakest-precondition-style semantics, based on our real-valued logic. We show that our verification infrastructure supports natural encodings of numerous verification techniques from the literature. With our SMT-based implementation, we automatically verify a variety of benchmarks. To the best of our knowledge, this establishes the first deductive verification infrastructure for expectation-based reasoning about probabilistic programs.

The critique capacity of Large Language Models (LLMs) is essential for reasoning abilities, which can provide necessary suggestions (e.g., detailed analysis and constructive feedback). Therefore, how to evaluate the critique capacity of LLMs has drawn great attention and several critique benchmarks have been proposed. However, existing critique benchmarks usually have the following limitations: (1). Focusing on diverse reasoning tasks in general domains and insufficient evaluation on code tasks (e.g., only covering code generation task), where the difficulty of queries is relatively easy (e.g., the code queries of CriticBench are from Humaneval and MBPP). (2). Lacking comprehensive evaluation from different dimensions. To address these limitations, we introduce a holistic code critique benchmark for LLMs called CodeCriticBench. Specifically, our CodeCriticBench includes two mainstream code tasks (i.e., code generation and code QA) with different difficulties. Besides, the evaluation protocols include basic critique evaluation and advanced critique evaluation for different characteristics, where fine-grained evaluation checklists are well-designed for advanced settings. Finally, we conduct extensive experimental results of existing LLMs, which show the effectiveness of CodeCriticBench.

Large Language Models (LLMs) can correct their self-generated responses, but a decline in accuracy after self-correction is also witnessed. To have a deeper understanding of self-correction, we endeavor to decompose, evaluate, and analyze the self-correction behaviors of LLMs. By enumerating and analyzing answer correctness before and after self-correction, we decompose the self-correction capability into confidence (being confident to correct answers) and critique (turning wrong answers to correct) capabilities, and propose two metrics from a probabilistic perspective to measure these 2 capabilities, along with another metric for overall self-correction capability evaluation. Based on our decomposition and evaluation metrics, we conduct extensive experiments and draw some empirical conclusions. For example, we find different models can exhibit distinct behaviors: some models are confident while others are more critical. We also find the trade-off between the two capabilities (i.e. improving one can lead to a decline in the other) when manipulating model self-correction behavior by prompts or in-context learning. Further, we find a simple yet efficient strategy to improve self-correction capability by transforming Supervision Fine-Tuning (SFT) data format, and our strategy outperforms vanilla SFT in both capabilities and achieves much higher accuracy after self-correction. Our code will be publicly available on GitHub.

Aligning large language models (LLMs) with deployment-specific requirements is critical but inherently imperfect. Despite extensive training, models remain susceptible to misalignment and adversarial inputs such as jailbreaks. Content moderation filters are commonly used as external safeguards, though they typically focus narrowly on safety. We introduce SGM (Specification-Guided Moderation), a flexible framework for training moderation filters grounded in user-defined specifications that go beyond standard safety concerns. SGM automates training data generation without relying on human-written examples, enabling scalable support for diverse, application-specific alignment goals. SGM-trained filters perform on par with state-of-the-art safety filters built on curated datasets, while supporting fine-grained and user-defined alignment control.

The ISO 26262 standard from 2016 represents the state of the art for a safety-guided development of safety-critical electric/electronic vehicle systems. These vehicle systems include advanced driver assistance systems and vehicle guidance systems. The development process proposed in the ISO 26262 standard is based upon multiple V-models, and defines activities and work products for each process step. In many of these process steps, scenario based approaches can be applied to achieve the defined work products for the development of automated driving functions. To accomplish the work products of different process steps, scenarios have to focus on various aspects like a human understandable notation or a description via time-space variables. This leads to contradictory requirements regarding the level of detail and way of notation for the representation of scenarios. In this paper, the authors present requirements for the representation of scenarios in different process steps defined by the ISO 26262 standard, propose a consistent terminology based on prior publications for the identified levels of abstraction, and demonstrate how scenarios can be systematically evolved along the phases of the development process outlined in the ISO 26262 standard.

Large Language Models (LLMs) present an intriguing avenue for exploration in the field of formal theorem proving. Nevertheless, their full potential, particularly concerning the mitigation of hallucinations and refinement through prover error messages, remains an area that has yet to be thoroughly investigated. To enhance the effectiveness of LLMs in the field, we introduce the Lyra, a new framework that employs two distinct correction mechanisms: Tool Correction (TC) and Conjecture Correction (CC). To implement Tool Correction in the post-processing of formal proofs, we leverage prior knowledge to utilize predefined prover tools (e.g., Sledgehammer) for guiding the replacement of incorrect tools. Tool Correction significantly contributes to mitigating hallucinations, thereby improving the overall accuracy of the proof. In addition, we introduce Conjecture Correction, an error feedback mechanism designed to interact with prover to refine formal proof conjectures with prover error messages. Compared to the previous refinement framework, the proposed Conjecture Correction refines generation with instruction but does not collect paired (generation, error & refinement) prompts. Our method has achieved state-of-the-art (SOTA) performance on both miniF2F validation (48.0% -> 55.3%) and test (45.5% -> 51.2%). We also present 3 IMO problems solved by Lyra. We believe Tool Correction (post-process for hallucination mitigation) and Conjecture Correction (subgoal adjustment from interaction with environment) could provide a promising avenue for future research in this field.

Program synthesis has been long studied with recent approaches focused on directly using the power of Large Language Models (LLMs) to generate code. Programming benchmarks, with curated synthesis problems and test-cases, are used to measure the performance of various LLMs on code synthesis. However, these test-cases can be limited in both quantity and quality for fully assessing the functional correctness of the generated code. Such limitation in the existing benchmarks begs the following question: In the era of LLMs, is the code generated really correct? To answer this, we propose EvalPlus -- a code synthesis evaluation framework to rigorously benchmark the functional correctness of LLM-synthesized code. EvalPlus augments a given evaluation dataset with large amounts of test-cases newly produced by an automatic test input generator, powered by both LLM- and mutation-based strategies. While EvalPlus is general, we extend the test-cases of the popular HumanEval benchmark by 80x to build HumanEval+. Our extensive evaluation across 26 popular LLMs (e.g., GPT-4 and ChatGPT) demonstrates that HumanEval+ is able to catch significant amounts of previously undetected wrong code synthesized by LLMs, reducing the pass@k by up-to 19.3-28.9%. We also surprisingly found that test insufficiency can lead to mis-ranking. For example, both WizardCoder-CodeLlama and Phind-CodeLlama now outperform ChatGPT on HumanEval+, while none of them could on HumanEval. Our work not only indicates that prior popular code synthesis evaluation results do not accurately reflect the true performance of LLMs for code synthesis, but also opens up a new direction to improve such programming benchmarks through automated testing. We have open-sourced our tools, enhanced datasets as well as all LLM-generated code at https://github.com/evalplus/evalplus to facilitate and accelerate future LLM-for-code research.

In the absence of abundant reliable annotations for challenging tasks and contexts, how can we expand the frontier of LLM capabilities with potentially wrong answers? We focus on two research questions: (1) Can LLMs generate reliable preferences among wrong options? And if so, (2) Would alignment with such wrong-over-wrong preferences be helpful? We employ methods based on self-consistency, token probabilities, and LLM-as-a-judge to elicit wrong-over-wrong preferences, and fine-tune language models with preference optimization approaches using these synthesized preferences. Extensive experiments with seven LLMs and eight datasets demonstrate that (1) LLMs do have preliminary capability in distinguishing various shades of wrong, achieving up to 20.9% higher performance than random guess; (2) Alignment with wrong-over-wrong preferences helps LLMs to produce less wrong and sometimes even outright correct answers, while overall improving model calibration.

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.

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.

Commit messages are a valuable resource in comprehension of software evolution, since they provide a record of changes such as feature additions and bug repairs. Unfortunately, programmers often neglect to write good commit messages. Different techniques have been proposed to help programmers by automatically writing these messages. These techniques are effective at describing what changed, but are often verbose and lack context for understanding the rationale behind a change. In contrast, humans write messages that are short and summarize the high level rationale. In this paper, we adapt Neural Machine Translation (NMT) to automatically "translate" diffs into commit messages. We trained an NMT algorithm using a corpus of diffs and human-written commit messages from the top 1k Github projects. We designed a filter to help ensure that we only trained the algorithm on higher-quality commit messages. Our evaluation uncovered a pattern in which the messages we generate tend to be either very high or very low quality. Therefore, we created a quality-assurance filter to detect cases in which we are unable to produce good messages, and return a warning instead.

While there are numerous benchmarks comparing the performance of modern language models (LMs), end-task evaluations often conflate notions of *factual accuracy* ("truth") and *reasoning ability* ("rationality", or "honesty" in the sense of correctly reporting implications of beliefs). Our goal is a dataset that clearly distinguishes these two notions. Our approach is to leverage and extend a collection of human-annotated *entailment trees*, engineered to express both good and bad chains of reasoning, and using a mixture of true and false facts, in particular including counterfactual examples, to avoid belief bias (also known as the "content effect"). The resulting dataset, called BaRDa, contains 3000 entailments (1787 valid, 1213 invalid), using 6681 true and 2319 false statements. Testing on four GPT-series models, GPT3(curie)/GPT3(davinici)/3.5/4, we find factual accuracy (truth) scores of 74.1/80.6/82.6/87.1 and reasoning accuracy scores of 63.1/78.0/71.8/79.2. This shows the clear progression of models towards improved factual accuracy and entailment reasoning, and the dataset provides a new benchmark that more cleanly separates and quantifies these two notions.

The strive to make AI applications "safe" has led to the development of safety-measures as the main or even sole normative requirement of their permissible use. Similar can be attested to the latest version of chatbots, such as chatGPT. In this view, if they are "safe", they are supposed to be permissible to deploy. This approach, which we call "safety-normativity", is rather limited in solving the emerging issues that chatGPT and other chatbots have caused thus far. In answering this limitation, in this paper we argue for limiting chatbots in the range of topics they can chat about according to the normative concept of appropriateness. We argue that rather than looking for "safety" in a chatbot's utterances to determine what they may and may not say, we ought to assess those utterances according to three forms of appropriateness: technical-discursive, social, and moral. We then spell out what requirements for chatbots follow from these forms of appropriateness to avoid the limits of previous accounts: positionality, acceptability, and value alignment (PAVA). With these in mind, we may be able to determine what a chatbot may and may not say. Lastly, one initial suggestion is to use challenge sets, specifically designed for appropriateness, as a validation method.

Verifiers play a crucial role in large language model (LLM) reasoning, needed by post-training techniques such as reinforcement learning. However, reliable verifiers are hard to get for difficult coding problems, because a well-disguised wrong solution may only be detected by carefully human-written edge cases that are difficult to synthesize. To address this issue, we propose HARDTESTGEN, a pipeline for high-quality test synthesis using LLMs. With this pipeline, we curate a comprehensive competitive programming dataset HARDTESTS with 47k problems and synthetic high-quality tests. Compared with existing tests, HARDTESTGEN tests demonstrate precision that is 11.3 percentage points higher and recall that is 17.5 percentage points higher when evaluating LLM-generated code. For harder problems, the improvement in precision can be as large as 40 points. HARDTESTS also proves to be more effective for model training, measured by downstream code generation performance. We will open-source our dataset and synthesis pipeline at https://leililab.github.io/HardTests/.

Large Language Models (LLMs) changed the way we design and interact with software systems. Their ability to process and extract information from text has drastically improved productivity in a number of routine tasks. Developers that want to include these models in their software stack, however, face a dreadful challenge: debugging LLMs' inconsistent behavior across minor variations of the prompt. We therefore introduce two metrics for classification tasks, namely sensitivity and consistency, which are complementary to task performance. First, sensitivity measures changes of predictions across rephrasings of the prompt, and does not require access to ground truth labels. Instead, consistency measures how predictions vary across rephrasings for elements of the same class. We perform an empirical comparison of these metrics on text classification tasks, using them as guideline for understanding failure modes of the LLM. Our hope is that sensitivity and consistency will be helpful to guide prompt engineering and obtain LLMs that balance robustness with performance.

Large Language Models are trained on vast amounts of text from the internet, which contains both factual and misleading information about the world. Can language models discern truth from falsehood in this contradicting data? Expanding on the view that LLMs can model different agents producing the corpora, we hypothesize that they can cluster truthful text by modeling a truthful persona: a group of agents that are likely to produce truthful text and share similar features. For example, trustworthy sources like Wikipedia and Science usually use formal writing styles and make consistent claims. By modeling this persona, LLMs can generalize truthfulness beyond the specific contexts in which each agent generated the training text. For example, the model can infer that the agent "Wikipedia" will behave truthfully on topics that were only generated by "Science" because they share a persona. We first show evidence for the persona hypothesis via two observations: (1) we can probe whether a model's answer will be truthful before it is generated; (2) finetuning a model on a set of facts improves its truthfulness on unseen topics. Next, using arithmetics as a synthetic environment, we show that language models can separate true and false statements, and generalize truthfulness across agents; but only if agents in the training data share a truthful generative process that enables the creation of a truthful persona. Overall, our findings suggest that models can exploit hierarchical structures in the data to learn abstract concepts like truthfulness.

Generative search engines directly generate responses to user queries, along with in-line citations. A prerequisite trait of a trustworthy generative search engine is verifiability, i.e., systems should cite comprehensively (high citation recall; all statements are fully supported by citations) and accurately (high citation precision; every cite supports its associated statement). We conduct human evaluation to audit four popular generative search engines -- Bing Chat, NeevaAI, perplexity.ai, and YouChat -- across a diverse set of queries from a variety of sources (e.g., historical Google user queries, dynamically-collected open-ended questions on Reddit, etc.). We find that responses from existing generative search engines are fluent and appear informative, but frequently contain unsupported statements and inaccurate citations: on average, a mere 51.5% of generated sentences are fully supported by citations and only 74.5% of citations support their associated sentence. We believe that these results are concerningly low for systems that may serve as a primary tool for information-seeking users, especially given their facade of trustworthiness. We hope that our results further motivate the development of trustworthy generative search engines and help researchers and users better understand the shortcomings of existing commercial systems.

An abundance of datasets and availability of reliable evaluation metrics have resulted in strong progress in factoid question answering (QA). This progress, however, does not easily transfer to the task of long-form QA, where the goal is to answer questions that require in-depth explanations. The hurdles include (i) a lack of high-quality data, and (ii) the absence of a well-defined notion of the answer's quality. In this work, we address these problems by (i) releasing a novel dataset and a task that we call ASQA (Answer Summaries for Questions which are Ambiguous); and (ii) proposing a reliable metric for measuring performance on ASQA. Our task focuses on factoid questions that are ambiguous, that is, have different correct answers depending on interpretation. Answers to ambiguous questions should synthesize factual information from multiple sources into a long-form summary that resolves the ambiguity. In contrast to existing long-form QA tasks (such as ELI5), ASQA admits a clear notion of correctness: a user faced with a good summary should be able to answer different interpretations of the original ambiguous question. We use this notion of correctness to define an automated metric of performance for ASQA. Our analysis demonstrates an agreement between this metric and human judgments, and reveals a considerable gap between human performance and strong baselines.

For humans to trust the fluent generations of large language models (LLMs), they must be able to verify their correctness against trusted, external sources. Recent efforts aim to increase verifiability through citations of retrieved documents or post-hoc provenance. However, such citations are prone to mistakes that further complicate their verifiability. To address these limitations, we tackle the verifiability goal with a different philosophy: we trivialize the verification process by developing models that quote verbatim statements from trusted sources in pre-training data. We propose Quote-Tuning, which demonstrates the feasibility of aligning LLMs to leverage memorized information and quote from pre-training data. Quote-Tuning quantifies quoting against large corpora with efficient membership inference tools, and uses the amount of quotes as an implicit reward signal to construct a synthetic preference dataset for quoting, without any human annotation. Next, the target model is aligned to quote using preference optimization algorithms. Experimental results show that Quote-Tuning significantly increases the percentage of LLM generation quoted verbatim from high-quality pre-training documents by 55% to 130% relative to untuned models while maintaining response quality. Further experiments demonstrate that Quote-Tuning generalizes quoting to out-of-domain data, is applicable in different tasks, and provides additional benefits to truthfulness. Quote-Tuning not only serves as a hassle-free method to increase quoting but also opens up avenues for improving LLM trustworthiness through better verifiability.

The growing demand for Domain-Specific Architecture (DSA) has driven the development of Agile Hardware Development Methodology (AHDM). Hardware Construction Language (HCL) like Chisel offers high-level abstraction features, making it an ideal language for HCL-Based AHDM. While Large Language Models (LLMs) excel in code generation tasks, they still face challenges with Chisel generation, particularly regarding syntax correctness and design variability. Recent reasoning models have significantly enhanced code generation capabilities through test-time scaling techniques. However, we found that reasoning models without domain adaptation cannot bring substantial benefits to Chisel code generation tasks. This paper presents ChiseLLM, a solution comprising data processing and transformation, prompt-guided reasoning trace synthesis, and domain-adapted model training. We constructed high-quality datasets from public RTL code resources and guided the model to adopt structured thinking patterns through prompt enhancement methods. Experiments demonstrate that our ChiseLLM-7B and ChiseLLM-32B models improved syntax correctness by 18.85% and 26.32% respectively over base models, while increasing variability design ability by 47.58% compared to baseline reasoning models. Our datasets and models are publicly available, providing high-performance, cost-effective models for HCL-Based AHDM, and offering an effective baseline for future research. Github repository: https://github.com/observerw/ChiseLLM

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.

Self-correction of large language models (LLMs) emerges as a critical component for enhancing their reasoning performance. Although various self-correction methods have been proposed, a comprehensive evaluation of these methods remains largely unexplored, and the question of whether LLMs can truly correct themselves is a matter of significant interest and concern. In this study, we introduce CorrectBench, a benchmark developed to evaluate the effectiveness of self-correction strategies, including intrinsic, external, and fine-tuned approaches, across three tasks: commonsense reasoning, mathematical reasoning, and code generation. Our findings reveal that: 1) Self-correction methods can improve accuracy, especially for complex reasoning tasks; 2) Mixing different self-correction strategies yields further improvements, though it reduces efficiency; 3) Reasoning LLMs (e.g., DeepSeek-R1) have limited optimization under additional self-correction methods and have high time costs. Interestingly, a comparatively simple chain-of-thought (CoT) baseline demonstrates competitive accuracy and efficiency. These results underscore the potential of self-correction to enhance LLM's reasoning performance while highlighting the ongoing challenge of improving their efficiency. Consequently, we advocate for further research focused on optimizing the balance between reasoning capabilities and operational efficiency. Project Page: https://correctbench.github.io/

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.

Large Language Models (LLMs) are increasingly used by software engineers for code generation. However, limitations of LLMs such as irrelevant or incorrect code have highlighted the need for prompt programming (or prompt engineering) where engineers apply specific prompt techniques (e.g., chain-of-thought or input-output examples) to improve the generated code. Despite this, the impact of different prompt techniques -- and their combinations -- on code generation remains underexplored. In this study, we introduce CodePromptEval, a dataset of 7072 prompts designed to evaluate five prompt techniques (few-shot, persona, chain-of-thought, function signature, list of packages) and their effect on the correctness, similarity, and quality of complete functions generated by three LLMs (GPT-4o, Llama3, and Mistral). Our findings show that while certain prompt techniques significantly influence the generated code, combining multiple techniques does not necessarily improve the outcome. Additionally, we observed a trade-off between correctness and quality when using prompt techniques. Our dataset and replication package enable future research on improving LLM-generated code and evaluating new prompt techniques.

The reliance on translated or adapted datasets from English or multilingual resources introduces challenges regarding linguistic and cultural suitability. This study addresses the need for robust and culturally appropriate benchmarks by evaluating the quality of 17 commonly used Turkish benchmark datasets. Using a comprehensive framework that assesses six criteria, both human and LLM-judge annotators provide detailed evaluations to identify dataset strengths and shortcomings. Our results reveal that 70% of the benchmark datasets fail to meet our heuristic quality standards. The correctness of the usage of technical terms is the strongest criterion, but 85% of the criteria are not satisfied in the examined datasets. Although LLM judges demonstrate potential, they are less effective than human annotators, particularly in understanding cultural common sense knowledge and interpreting fluent, unambiguous text. GPT-4o has stronger labeling capabilities for grammatical and technical tasks, while Llama3.3-70B excels at correctness and cultural knowledge evaluation. Our findings emphasize the urgent need for more rigorous quality control in creating and adapting datasets for low-resource languages.

In the realm of formal theorem proving, the Coq proof assistant stands out for its rigorous approach to verifying mathematical assertions and software correctness. Despite the advances in artificial intelligence and machine learning, the specialized nature of Coq syntax and semantics poses unique challenges for Large Language Models (LLMs). Addressing this gap, we present a comprehensive dataset specifically designed to enhance LLMs' proficiency in interpreting and generating Coq code. This dataset, derived from a collection of over 10,000 Coq source files, encompasses a wide array of propositions, proofs, and definitions, enriched with metadata including source references and licensing information. Our primary aim is to facilitate the development of LLMs capable of generating syntactically correct and semantically meaningful Coq constructs, thereby advancing the frontier of automated theorem proving. Initial experiments with this dataset have showcased its significant potential; models trained on this data exhibited enhanced accuracy in Coq code generation. Notably, a particular experiment revealed that a fine-tuned LLM was capable of generating 141 valid proofs for a basic lemma, highlighting the dataset's utility in facilitating the discovery of diverse and valid proof strategies. This paper discusses the dataset's composition, the methodology behind its creation, and the implications of our findings for the future of machine learning in formal verification. The dataset is accessible for further research and exploration: https://huggingface.co/datasets/florath/coq-facts-props-proofs-gen0-v1

Signal Temporal Logic (STL) is a powerful formal language for specifying real-time specifications of Cyber-Physical Systems (CPS). Transforming specifications written in natural language into STL formulas automatically has attracted increasing attention. Existing rule-based methods depend heavily on rigid pattern matching and domain-specific knowledge, limiting their generalizability and scalability. Recently, Supervised Fine-Tuning (SFT) of large language models (LLMs) has been successfully applied to transform natural language into STL. However, the lack of fine-grained supervision on atomic proposition correctness, semantic fidelity, and formula readability often leads SFT-based methods to produce formulas misaligned with the intended meaning. To address these issues, we propose RESTL, a reinforcement learning (RL)-based framework for the transformation from natural language to STL. RESTL introduces multiple independently trained reward models that provide fine-grained, multi-faceted feedback from four perspectives, i.e., atomic proposition consistency, semantic alignment, formula succinctness, and symbol matching. These reward models are trained with a curriculum learning strategy to improve their feedback accuracy, and their outputs are aggregated into a unified signal that guides the optimization of the STL generator via Proximal Policy Optimization (PPO). Experimental results demonstrate that RESTL significantly outperforms state-of-the-art methods in both automatic metrics and human evaluations.

We present foundation language models developed to power Apple Intelligence features, including a ~3 billion parameter model designed to run efficiently on devices and a large server-based language model designed for Private Cloud Compute. These models are designed to perform a wide range of tasks efficiently, accurately, and responsibly. This report describes the model architecture, the data used to train the model, the training process, how the models are optimized for inference, and the evaluation results. We highlight our focus on Responsible AI and how the principles are applied throughout the model development.

We present a benchmark dataset for evaluating method-level code generation task. The benchmark contains a dataset of 175 samples for automated evaluation and a dataset of 161 samples for manual evaluation. We also present a new metric for automatically evaluating the correctness of the generated code, and a set of criteria to manually evaluating the overall quality of the generated code.

Translating human-written mathematical theorems and proofs from natural language (NL) into formal languages (FLs) like Lean 4 has long been a significant challenge for AI. Most state-of-the-art methods address this separately, first translating theorems and then generating proofs, creating a fundamental disconnect vis-a-vis true proof auto-formalization. This two-step process and its limitations were evident even in AlphaProof's silver-medal performance at the 2024 IMO, where problem statements needed manual translation before automated proof synthesis. We present ProofBridge, a unified framework for automatically translating entire NL theorems and proofs into Lean 4. At its core is a joint embedding model that aligns NL and FL (NL-FL) theorem-proof pairs in a shared semantic space, enabling cross-modal retrieval of semantically relevant FL examples to guide translation. Our training ensures that NL-FL theorems (and their proofs) are mapped close together in this space if and only if the NL-FL pairs are semantically equivalent. ProofBridge integrates retrieval-augmented fine-tuning with iterative proof repair, leveraging Lean's type checker and semantic equivalence feedback to ensure both syntactic correctness and semantic fidelity. Experiments show substantial improvements in proof auto-formalization over strong baselines (including GPT-5, Gemini-2.5, Kimina-Prover, DeepSeek-Prover), with our retrieval-augmented approach yielding significant gains in semantic correctness (SC, via proving bi-directional equivalence) and type correctness (TC, via type-checking theorem+proof) across pass@k metrics on miniF2F-Test-PF, a dataset we curated. In particular, ProofBridge improves cross-modal retrieval quality by up to 3.28x Recall@1 over all-MiniLM-L6-v2, and achieves +31.14% SC and +1.64% TC (pass@32) compared to the baseline Kimina-Prover-RL-1.7B.

Recent development of large language models (LLMs) for code like CodeX and CodeT5+ demonstrates tremendous promise in achieving code intelligence. Their ability of synthesizing code that completes a program for performing a pre-defined task has been intensively tested and verified on benchmark datasets including HumanEval and MBPP. Yet, evaluation of these LLMs from more perspectives (than just program synthesis) is also anticipated, considering their broad scope of applications in software engineering. In this paper, we explore the ability of LLMs for testing programs/code. By performing thorough analyses of recent LLMs for code in program testing, we show a series of intriguing properties of these models and demonstrate how program testing ability of LLMs can be improved. Following recent work which utilizes generated test cases to enhance program synthesis, we further leverage our findings in improving the quality of the synthesized programs and show +11.77% and +4.22% higher code pass rates on HumanEval+ comparing with the GPT-3.5-turbo baseline and the recent state-of-the-art, respectively.

Language Models [LMs] are now playing an increasingly large role in information generation and synthesis; the representation of scientific knowledge in these systems needs to be highly accurate. A prime challenge is hallucination; that is, generating apparently plausible but actually false information, including invented citations and nonexistent research papers. This kind of inaccuracy is dangerous in all the domains that require high levels of factual correctness, such as academia and education. This work presents a pipeline for evaluating the frequency with which language models hallucinate in generating responses in the scientific literature. We propose ArxEval, an evaluation pipeline with two tasks using ArXiv as a repository: Jumbled Titles and Mixed Titles. Our evaluation includes fifteen widely used language models and provides comparative insights into their reliability in handling scientific literature.

Formally verifying properties of software code has been a highly desirable task, especially with the emergence of LLM-generated code. In the same vein, they provide an interesting avenue for the exploration of formal verification and mechanistic interpretability. Since the introduction of code-specific models, despite their successes in generating code in Lean4 and Isabelle, the task of generalized theorem proving still remains far from being fully solved and will be a benchmark for reasoning capability in LLMs. In this work, we introduce a framework that generates whole proofs in a formal language to be used within systems that utilize the power of built-in tactics and off-the-shelf automated theorem provers. Our framework includes 3 components: generating natural language statements of the code to be verified, an LLM that generates formal proofs for the given statement, and a module employing heuristics for building the final proof. To train the LLM, we employ a 2-stage fine-tuning process, where we first use SFT-based training to enable the model to generate syntactically correct Isabelle code and then RL-based training that encourages the model to generate proofs verified by a theorem prover. We validate our framework using the miniF2F-test benchmark and the Isabelle proof assistant and design a use case to verify the correctness of the AWS S3 bucket access policy code. We also curate a dataset based on the FVEL\textnormal{ER} dataset for future training tasks.

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.

This paper presents FoFo, a pioneering benchmark for evaluating large language models' (LLMs) ability to follow complex, domain-specific formats, a crucial yet underexamined capability for their application as AI agents. Despite LLMs' advancements, existing benchmarks fail to assess their format-following proficiency adequately. FoFo fills this gap with a diverse range of real-world formats and instructions, developed through an AI-Human collaborative method. Our evaluation across both open-source (e.g., Llama 2, WizardLM) and closed-source (e.g., GPT-4, PALM2, Gemini) LLMs highlights three key findings: open-source models significantly lag behind closed-source ones in format adherence; LLMs' format-following performance is independent of their content generation quality; and LLMs' format proficiency varies across different domains. These insights suggest the need for specialized tuning for format-following skills and highlight FoFo's role in guiding the selection of domain-specific AI agents. FoFo is released here at https://github.com/SalesforceAIResearch/FoFo.

Autoformalization is the process of automatically translating from natural language mathematics to formal specifications and proofs. A successful autoformalization system could advance the fields of formal verification, program synthesis, and artificial intelligence. While the long-term goal of autoformalization seemed elusive for a long time, we show large language models provide new prospects towards this goal. We make the surprising observation that LLMs can correctly translate a significant portion (25.3%) of mathematical competition problems perfectly to formal specifications in Isabelle/HOL. We demonstrate the usefulness of this process by improving a previously introduced neural theorem prover via training on these autoformalized theorems. Our methodology results in a new state-of-the-art result on the MiniF2F theorem proving benchmark, improving the proof rate from 29.6% to 35.2%.

Evaluating large language models (LLMs) is crucial for both assessing their capabilities and identifying safety or robustness issues prior to deployment. Reliably measuring abstract and complex phenomena such as 'safety' and 'robustness' requires strong construct validity, that is, having measures that represent what matters to the phenomenon. With a team of 29 expert reviewers, we conduct a systematic review of 445 LLM benchmarks from leading conferences in natural language processing and machine learning. Across the reviewed articles, we find patterns related to the measured phenomena, tasks, and scoring metrics which undermine the validity of the resulting claims. To address these shortcomings, we provide eight key recommendations and detailed actionable guidance to researchers and practitioners in developing LLM benchmarks.

The Bernays-Sch\"onfinkel first-order logic fragment over simple linear real arithmetic constraints BS(SLR) is known to be decidable. We prove that BS(SLR) clause sets with both universally and existentially quantified verification conditions (conjectures) can be translated into BS(SLR) clause sets over a finite set of first-order constants. For the Horn case, we provide a Datalog hammer preserving validity and satisfiability. A toolchain from the BS(LRA) prover SPASS-SPL to the Datalog reasoner VLog establishes an effective way of deciding verification conditions in the Horn fragment. This is exemplified by the verification of supervisor code for a lane change assistant in a car and of an electronic control unit for a supercharged combustion engine.

In this paper, we introduce the Instruction Following Score (IFS), a metric that detects language models' ability to follow instructions. The metric has a dual purpose. First, IFS can be used to distinguish between base and instruct models. We benchmark publicly available base and instruct models, and show that the ratio of well formatted responses to partial and full sentences can be an effective measure between those two model classes. Secondly, the metric can be used as an early stopping criteria for instruct tuning. We compute IFS for Supervised Fine-Tuning (SFT) of 7B and 13B LLaMA models, showing that models learn to follow instructions relatively early in the training process, and the further finetuning can result in changes in the underlying base model semantics. As an example of semantics change we show the objectivity of model predictions, as defined by an auxiliary metric ObjecQA. We show that in this particular case, semantic changes are the steepest when the IFS tends to plateau. We hope that decomposing instruct tuning into IFS and semantic factors starts a new trend in better controllable instruct tuning and opens possibilities for designing minimal instruct interfaces querying foundation models.

Large language models that use retrieval augmented generation have the potential to unlock valuable knowledge for researchers, policymakers, and the public by making long and technical climate-related documents more accessible. While this approach can help alleviate factual hallucinations by relying on retrieved passages as additional context, its effectiveness depends on whether the model's output remains faithful to these passages. To address this, we explore the automatic assessment of faithfulness of different models in this setting. We then focus on ClimateGPT, a large language model specialised in climate science, to examine which factors in its instruction fine-tuning impact the model's faithfulness. By excluding unfaithful subsets of the model's training data, we develop ClimateGPT Faithful+, which achieves an improvement in faithfulness from 30% to 57% in supported atomic claims according to our automatic metric.

We introduce SimpleQA Verified, a 1,000-prompt benchmark for evaluating Large Language Model (LLM) short-form factuality based on OpenAI's SimpleQA. It addresses critical limitations in OpenAI's benchmark, including noisy and incorrect labels, topical biases, and question redundancy. SimpleQA Verified was created through a rigorous multi-stage filtering process involving de-duplication, topic balancing, and source reconciliation to produce a more reliable and challenging evaluation set, alongside improvements in the autorater prompt. On this new benchmark, Gemini 2.5 Pro achieves a state-of-the-art F1-score of 55.6, outperforming other frontier models, including GPT-5. This work provides the research community with a higher-fidelity tool to track genuine progress in parametric model factuality and to mitigate hallucinations. The benchmark dataset, evaluation code, and leaderboard are available at: https://www.kaggle.com/benchmarks/deepmind/simpleqa-verified.

Recent approaches in domain-specific named entity recognition (NER), such as biomedical NER, have shown remarkable advances. However, they still lack of faithfulness, producing erroneous predictions. We assume that knowledge of entities can be useful in verifying the correctness of the predictions. Despite the usefulness of knowledge, resolving such errors with knowledge is nontrivial, since the knowledge itself does not directly indicate the ground-truth label. To this end, we propose VerifiNER, a post-hoc verification framework that identifies errors from existing NER methods using knowledge and revises them into more faithful predictions. Our framework leverages the reasoning abilities of large language models to adequately ground on knowledge and the contextual information in the verification process. We validate effectiveness of VerifiNER through extensive experiments on biomedical datasets. The results suggest that VerifiNER can successfully verify errors from existing models as a model-agnostic approach. Further analyses on out-of-domain and low-resource settings show the usefulness of VerifiNER on real-world applications.

Previous works on Large Language Models (LLMs) have mainly focused on evaluating their helpfulness or harmlessness. However, honesty, another crucial alignment criterion, has received relatively less attention. Dishonest behaviors in LLMs, such as spreading misinformation and defrauding users, eroding user trust, and causing real-world harm, present severe risks that intensify as these models approach superintelligence levels. Enhancing honesty in LLMs addresses critical deficiencies and helps uncover latent capabilities that are not readily expressed. This underscores the urgent need for reliable methods and benchmarks to effectively ensure and evaluate the honesty of LLMs. In this paper, we introduce BeHonest, a pioneering benchmark specifically designed to assess honesty in LLMs comprehensively. BeHonest evaluates three essential aspects of honesty: awareness of knowledge boundaries, avoidance of deceit, and consistency in responses. Building on this foundation, we designed 10 scenarios to evaluate and analyze 9 popular LLMs on the market, including both closed-source and open-source models from different model families with varied model sizes. Our findings indicate that there is still significant room for improvement in the honesty of LLMs. We also encourage the AI community to prioritize honesty alignment in LLMs. Our benchmark and code can be found at: https://github.com/GAIR-NLP/BeHonest.

This paper introduces v0.5 of the AI Safety Benchmark, which has been created by the MLCommons AI Safety Working Group. The AI Safety Benchmark has been designed to assess the safety risks of AI systems that use chat-tuned language models. We introduce a principled approach to specifying and constructing the benchmark, which for v0.5 covers only a single use case (an adult chatting to a general-purpose assistant in English), and a limited set of personas (i.e., typical users, malicious users, and vulnerable users). We created a new taxonomy of 13 hazard categories, of which 7 have tests in the v0.5 benchmark. We plan to release version 1.0 of the AI Safety Benchmark by the end of 2024. The v1.0 benchmark will provide meaningful insights into the safety of AI systems. However, the v0.5 benchmark should not be used to assess the safety of AI systems. We have sought to fully document the limitations, flaws, and challenges of v0.5. This release of v0.5 of the AI Safety Benchmark includes (1) a principled approach to specifying and constructing the benchmark, which comprises use cases, types of systems under test (SUTs), language and context, personas, tests, and test items; (2) a taxonomy of 13 hazard categories with definitions and subcategories; (3) tests for seven of the hazard categories, each comprising a unique set of test items, i.e., prompts. There are 43,090 test items in total, which we created with templates; (4) a grading system for AI systems against the benchmark; (5) an openly available platform, and downloadable tool, called ModelBench that can be used to evaluate the safety of AI systems on the benchmark; (6) an example evaluation report which benchmarks the performance of over a dozen openly available chat-tuned language models; (7) a test specification for the benchmark.

Recent years have seen the remarkable capabilities of large language models (LLMs) for code generation. Different from existing work that evaluate the correctness of the code generated by LLMs, we propose to further evaluate its efficiency. More efficient code can lead to higher performance and execution efficiency of programs and software completed by LLM-assisted programming. First, we evaluate the efficiency of the code generated by LLMs on two benchmarks, HumanEval and MBPP. Then, we choose a set of programming problems from the online judge platform LeetCode to conduct a more difficult evaluation. Finally, we explore several prompts that would enable LLMs to generate more efficient code.

When deploying large language models (LLMs), it is important to ensure that these models are not only capable, but also reliable. Many benchmarks have been created to track LLMs' growing capabilities, however there has been no similar focus on measuring their reliability. To understand the potential ramifications of this gap, we investigate how well current benchmarks quantify model reliability. We find that pervasive label errors can compromise these evaluations, obscuring lingering model failures and hiding unreliable behavior. Motivated by this gap in the evaluation of reliability, we then propose the concept of so-called platinum benchmarks, i.e., benchmarks carefully curated to minimize label errors and ambiguity. As a first attempt at constructing such benchmarks, we revise examples from fifteen existing popular benchmarks. We evaluate a wide range of models on these platinum benchmarks and find that, indeed, frontier LLMs still exhibit failures on simple tasks such as elementary-level math word problems. Analyzing these failures further reveals previously unidentified patterns of problems on which frontier models consistently struggle. We provide code at https://github.com/MadryLab/platinum-benchmarks

While large language models (LLMs) have proven to be effective on a large variety of tasks, they are also known to hallucinate information. To measure whether an LLM prefers factually consistent continuations of its input, we propose a new benchmark called FIB(Factual Inconsistency Benchmark) that focuses on the task of summarization. Specifically, our benchmark involves comparing the scores an LLM assigns to a factually consistent versus a factually inconsistent summary for an input news article. For factually consistent summaries, we use human-written reference summaries that we manually verify as factually consistent. To generate summaries that are factually inconsistent, we generate summaries from a suite of summarization models that we have manually annotated as factually inconsistent. A model's factual consistency is then measured according to its accuracy, i.e.\ the proportion of documents where it assigns a higher score to the factually consistent summary. To validate the usefulness of FIB, we evaluate 23 large language models ranging from 1B to 176B parameters from six different model families including BLOOM and OPT. We find that existing LLMs generally assign a higher score to factually consistent summaries than to factually inconsistent summaries. However, if the factually inconsistent summaries occur verbatim in the document, then LLMs assign a higher score to these factually inconsistent summaries than factually consistent summaries. We validate design choices in our benchmark including the scoring method and source of distractor summaries. Our code and benchmark data can be found at https://github.com/r-three/fib.

Uncertainty Quantification (UQ) in Language Models (LMs) is crucial for improving their safety and reliability. Evaluations often use performance metrics like AUROC to assess how well UQ methods (e.g., negative sequence probabilities) correlate with task correctness functions (e.g., ROUGE-L). In this paper, we show that commonly used correctness functions bias UQ evaluations by inflating the performance of certain UQ methods. We evaluate 7 correctness functions -- from lexical-based and embedding-based metrics to LLM-as-a-judge approaches -- across 4 datasets x 4 models x 6 UQ methods. Our analysis reveals that length biases in the errors of these correctness functions distort UQ assessments by interacting with length biases in UQ methods. We identify LLM-as-a-judge approaches as among the least length-biased choices and hence a potential solution to mitigate these biases.

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.

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.

Existing informal language-based (e.g., human language) Large Language Models (LLMs) trained with Reinforcement Learning (RL) face a significant challenge: their verification processes, which provide crucial training signals, are neither reliable nor scalable. In fact, the prevalent large proprietary models could hardly generate verifiable programs. A promising yet largely uncharted alternative is formal language-based reasoning. Grounding LLMs in rigorous formal systems where generative models operate in formal language spaces (e.g., Dafny) enables the automatic and mathematically provable verification of their reasoning processes and outcomes. This capability is pivotal for achieving large-scale, reliable formal software verification. It is a common practice to employ human-annotated chain-of-thought and other human priors to induce the reasoning and coding capabilities of LLMs. Unfortunately, it becomes unacceptably all-consuming to provide such priors for supervising complex programming tasks. In this work, we systematically explore ways to reduce human priors with the formal language, Dafny, as the main environment for our pilot study. Our pipeline mainly relies on introducing an automatic and scalable data curation pipeline, and careful RL designs integrated with feedback from the formal language verifier. We introduce DafnyComp, a benchmark of compositional formal programs with auto-formalized specifications for specification reasoning. Our supervised fine-tuning (SFT) stage enables even small models (e.g., 0.5B) to generate syntactically valid and verifiable Dafny code, surpassing proprietary models. RL with regularization further improves performance, achieving stronger generalization to out-of-domain tasks and outperforming all strong baselines on the challenging DafnyComp benchmark.

We present Llemma, a large language model for mathematics. We continue pretraining Code Llama on the Proof-Pile-2, a mixture of scientific papers, web data containing mathematics, and mathematical code, yielding Llemma. On the MATH benchmark Llemma outperforms all known open base models, as well as the unreleased Minerva model suite on an equi-parameter basis. Moreover, Llemma is capable of tool use and formal theorem proving without any further finetuning. We openly release all artifacts, including 7 billion and 34 billion parameter models, the Proof-Pile-2, and code to replicate our experiments.

In this paper, we propose DuaShepherd, a novel reward modeling framework that integrates two complementary reward signals, correctness and potential, to enhance the mathematical reasoning capabilities of Large Language Models (LLMs). While correctness-based signals emphasize identification of stepwise errors, potential-based signals focus on the likelihood of reaching the correct final answer. We developed an automated pipeline for constructing large-scale reward modeling dataset with both signals. A unified, multi-head architecture was explored to train the two reward models in a multi-task setup, demonstrating benefits from learning both correctness and potential in parallel. By combining these two signals into a compound probability, our model achieves consistent performance improvements across multiple benchmarks. Empirical evaluations on MATH500 and ProcessBench confirm that this combined reward significantly outperforms models trained on either reward type alone, achieving state-of-the-art performance under comparable resource constraints.

Automating hardware design could obviate a significant amount of human error from the engineering process and lead to fewer errors. Verilog is a popular hardware description language to model and design digital systems, thus generating Verilog code is a critical first step. Emerging large language models (LLMs) are able to write high-quality code in other programming languages. In this paper, we characterize the ability of LLMs to generate useful Verilog. For this, we fine-tune pre-trained LLMs on Verilog datasets collected from GitHub and Verilog textbooks. We construct an evaluation framework comprising test-benches for functional analysis and a flow to test the syntax of Verilog code generated in response to problems of varying difficulty. Our findings show that across our problem scenarios, the fine-tuning results in LLMs more capable of producing syntactically correct code (25.9% overall). Further, when analyzing functional correctness, a fine-tuned open-source CodeGen LLM can outperform the state-of-the-art commercial Codex LLM (6.5% overall). Training/evaluation scripts and LLM checkpoints are available: https://github.com/shailja-thakur/VGen.