Daily Papers

In this paper, we present the current progress of the project Verif.ai, an open-source scientific generative question-answering system with referenced and verified answers. The components of the system are (1) an information retrieval system combining semantic and lexical search techniques over scientific papers (PubMed), (2) a fine-tuned generative model (Mistral 7B) taking top answers and generating answers with references to the papers from which the claim was derived, and (3) a verification engine that cross-checks the generated claim and the abstract or paper from which the claim was derived, verifying whether there may have been any hallucinations in generating the claim. We are reinforcing the generative model by providing the abstract in context, but in addition, an independent set of methods and models are verifying the answer and checking for hallucinations. Therefore, we believe that by using our method, we can make scientists more productive, while building trust in the use of generative language models in scientific environments, where hallucinations and misinformation cannot be tolerated.

Reinforcement Learning with Verifiable Rewards (RLVR) has recently emerged as a powerful paradigm for post-training large language models (LLMs), achieving state-of-the-art performance on tasks with structured, verifiable answers. Applying RLVR to Multimodal LLMs (MLLMs) presents significant opportunities but is complicated by the broader, heterogeneous nature of vision-language tasks that demand nuanced visual, logical, and spatial capabilities. As such, training MLLMs using RLVR on multiple datasets could be beneficial but creates challenges with conflicting objectives from interaction among diverse datasets, highlighting the need for optimal dataset mixture strategies to improve generalization and reasoning. We introduce a systematic post-training framework for Multimodal LLM RLVR, featuring a rigorous data mixture problem formulation and benchmark implementation. Specifically, (1) We developed a multimodal RLVR framework for multi-dataset post-training by curating a dataset that contains different verifiable vision-language problems and enabling multi-domain online RL learning with different verifiable rewards; (2) We proposed a data mixture strategy that learns to predict the RL fine-tuning outcome from the data mixture distribution, and consequently optimizes the best mixture. Comprehensive experiments showcase that multi-domain RLVR training, when combined with mixture prediction strategies, can significantly boost MLLM general reasoning capacities. Our best mixture improves the post-trained model's accuracy on out-of-distribution benchmarks by an average of 5.24% compared to the same model post-trained with uniform data mixture, and by a total of 20.74% compared to the pre-finetuning baseline.

Fine-tuning language models~(LMs) on human-generated data remains a prevalent practice. However, the performance of such models is often limited by the quantity and diversity of high-quality human data. In this paper, we explore whether we can go beyond human data on tasks where we have access to scalar feedback, for example, on math problems where one can verify correctness. To do so, we investigate a simple self-training method based on expectation-maximization, which we call ReST^{EM}, where we (1) generate samples from the model and filter them using binary feedback, (2) fine-tune the model on these samples, and (3) repeat this process a few times. Testing on advanced MATH reasoning and APPS coding benchmarks using PaLM-2 models, we find that ReST^{EM} scales favorably with model size and significantly surpasses fine-tuning only on human data. Overall, our findings suggest self-training with feedback can substantially reduce dependence on human-generated data.

Despite recent progress in large-scale reinforcement learning (RL) for reasoning, the training recipe for building high-performing reasoning models remains elusive. Key implementation details of frontier models, such as DeepSeek-R1, including data curation strategies and RL training recipe, are often omitted. Moreover, recent research indicates distillation remains more effective than RL for smaller models. In this work, we demonstrate that large-scale RL can significantly enhance the reasoning capabilities of strong, small- and mid-sized models, achieving results that surpass those of state-of-the-art distillation-based models. We systematically study the RL training process through extensive ablations and propose a simple yet effective approach: first training on math-only prompts, then on code-only prompts. Notably, we find that math-only RL not only significantly enhances the performance of strong distilled models on math benchmarks (e.g., +14.6% / +17.2% on AIME 2025 for the 7B / 14B models), but also code reasoning tasks (e.g., +6.8% / +5.8% on LiveCodeBench for the 7B / 14B models). In addition, extended code-only RL iterations further improve performance on code benchmarks with minimal or no degradation in math results. We develop a robust data curation pipeline to collect challenging prompts with high-quality, verifiable answers and test cases to enable verification-based RL across both domains. Finally, we identify key experimental insights, including curriculum learning with progressively increasing response lengths and the stabilizing effect of on-policy parameter updates. We find that RL not only elicits the foundational reasoning capabilities acquired during pretraining and supervised fine-tuning (e.g., distillation), but also pushes the limits of the model's reasoning ability, enabling it to solve problems that were previously unsolvable.

Reinforcement learning (RL) has recently demonstrated strong potential in enhancing the reasoning capabilities of large language models (LLMs). Particularly, the "Zero" reinforcement learning introduced by Deepseek-R1-Zero, enables direct RL training of base LLMs without relying on an intermediate supervised fine-tuning stage. Despite these advancements, current works for LLM reasoning mainly focus on mathematical and coding domains, largely due to data abundance and the ease of answer verification. This limits the applicability and generalization of such models to broader domains, where questions often have diverse answer representations, and data is more scarce. In this paper, we propose General-Reasoner, a novel training paradigm designed to enhance LLM reasoning capabilities across diverse domains. Our key contributions include: (1) constructing a large-scale, high-quality dataset of questions with verifiable answers curated by web crawling, covering a wide range of disciplines; and (2) developing a generative model-based answer verifier, which replaces traditional rule-based verification with the capability of chain-of-thought and context-awareness. We train a series of models and evaluate them on a wide range of datasets covering wide domains like physics, chemistry, finance, electronics etc. Our comprehensive evaluation across these 12 benchmarks (e.g. MMLU-Pro, GPQA, SuperGPQA, TheoremQA, BBEH and MATH AMC) demonstrates that General-Reasoner outperforms existing baseline methods, achieving robust and generalizable reasoning performance while maintaining superior effectiveness in mathematical reasoning tasks.

Reinforcement Learning with Verifiable Rewards (RLVR) has proven effective for training large language models (LLMs) on complex reasoning tasks, such as mathematical problem solving. A prerequisite for the scalability of RLVR is a high-quality problem set with precise and verifiable answers. However, the scarcity of well-crafted human-labeled math problems and limited-verification answers in existing distillation-oriented synthetic datasets limit their effectiveness in RL. Additionally, most problem synthesis strategies indiscriminately expand the problem set without considering the model's capabilities, leading to low efficiency in generating useful questions. To mitigate this issue, we introduce a Self-aware Weakness-driven problem Synthesis framework (SwS) that systematically identifies model deficiencies and leverages them for problem augmentation. Specifically, we define weaknesses as questions that the model consistently fails to learn through its iterative sampling during RL training. We then extract the core concepts from these failure cases and synthesize new problems to strengthen the model's weak areas in subsequent augmented training, enabling it to focus on and gradually overcome its weaknesses. Without relying on external knowledge distillation, our framework enables robust generalization byempowering the model to self-identify and address its weaknesses in RL, yielding average performance gains of 10.0% and 7.7% on 7B and 32B models across eight mainstream reasoning benchmarks.

While Multimodal Large Language Models (MLLMs) have achieved impressive progress in vision-language understanding, they still struggle with complex multi-step reasoning, often producing logically inconsistent or partially correct solutions. A key limitation lies in the lack of fine-grained supervision over intermediate reasoning steps. To address this, we propose MM-PRM, a process reward model trained within a fully automated, scalable framework. We first build MM-Policy, a strong multimodal model trained on diverse mathematical reasoning data. Then, we construct MM-K12, a curated dataset of 10,000 multimodal math problems with verifiable answers, which serves as seed data. Leveraging a Monte Carlo Tree Search (MCTS)-based pipeline, we generate over 700k step-level annotations without human labeling. The resulting PRM is used to score candidate reasoning paths in the Best-of-N inference setup and achieves significant improvements across both in-domain (MM-K12 test set) and out-of-domain (OlympiadBench, MathVista, etc.) benchmarks. Further analysis confirms the effectiveness of soft labels, smaller learning rates, and path diversity in optimizing PRM performance. MM-PRM demonstrates that process supervision is a powerful tool for enhancing the logical robustness of multimodal reasoning systems. We release all our codes and data at https://github.com/ModalMinds/MM-PRM.

Effective evaluation of multi-hop tool use is critical for analyzing the understanding, reasoning, and function-calling capabilities of large language models (LLMs). However, progress has been hindered by a lack of reliable evaluation datasets. To address this, we present ToolHop, a dataset comprising 995 user queries and 3,912 associated tools, specifically designed for rigorous evaluation of multi-hop tool use. ToolHop ensures diverse queries, meaningful interdependencies, locally executable tools, detailed feedback, and verifiable answers through a novel query-driven data construction approach that includes tool creation, document refinement, and code generation. We evaluate 14 LLMs across five model families (i.e., LLaMA3.1, Qwen2.5, Gemini1.5, Claude3.5, and GPT), uncovering significant challenges in handling multi-hop tool-use scenarios. The leading model, GPT-4o, achieves an accuracy of 49.04%, underscoring substantial room for improvement. Further analysis reveals variations in tool-use strategies for various families, offering actionable insights to guide the development of more effective approaches. Code and data can be found in https://huggingface.co/bytedance-research/ToolHop.

Increasing interest in reasoning models has led math to become a prominent testing ground for algorithmic and methodological improvements. However, existing open math datasets either contain a small collection of high-quality, human-written problems or a large corpus of machine-generated problems of uncertain quality, forcing researchers to choose between quality and quantity. In this work, we present Big-Math, a dataset of over 250,000 high-quality math questions with verifiable answers, purposefully made for reinforcement learning (RL). To create Big-Math, we rigorously filter, clean, and curate openly available datasets, extracting questions that satisfy our three desiderata: (1) problems with uniquely verifiable solutions, (2) problems that are open-ended, (3) and problems with a closed-form solution. To ensure the quality of Big-Math, we manually verify each step in our filtering process. Based on the findings from our filtering process, we introduce 47,000 new questions with verified answers, Big-Math-Reformulated: closed-ended questions (i.e. multiple choice questions) that have been reformulated as open-ended questions through a systematic reformulation algorithm. Compared to the most commonly used existing open-source datasets for math reasoning, GSM8k and MATH, Big-Math is an order of magnitude larger, while our rigorous filtering ensures that we maintain the questions most suitable for RL. We also provide a rigorous analysis of the dataset, finding that Big-Math contains a high degree of diversity across problem domains, and incorporates a wide range of problem difficulties, enabling a wide range of downstream uses for models of varying capabilities and training requirements. By bridging the gap between data quality and quantity, Big-Math establish a robust foundation for advancing reasoning in LLMs.

Recent breakthroughs in large language models (LLMs) have effectively improved their reasoning abilities, particularly on mathematical and logical problems that have verifiable answers, through techniques such as supervised finetuning (SFT) and reinforcement learning (RL). Prior research indicates that RL effectively internalizes search strategies, enabling long chain-of-thought (CoT) reasoning, with backtracking emerging naturally as a learned capability. However, the precise benefits of backtracking, specifically, how significantly it contributes to reasoning improvements and the optimal extent of its use, remain poorly understood. In this work, we systematically investigate the dynamics between SFT and RL on eight reasoning tasks: Countdown, Sudoku, Arc 1D, Geometry, Color Cube Rotation, List Functions, Zebra Puzzles, and Self Reference. Our findings highlight that short CoT sequences used in SFT as a warm-up do have moderate contribution to RL training, compared with cold-start RL; however such contribution diminishes when tasks become increasingly difficult. Motivated by this observation, we construct synthetic datasets varying systematically in the number of backtracking steps and conduct controlled experiments to isolate the influence of either the correctness (content) or the structure (i.e., backtrack frequency). We find that (1) longer CoT with backtracks generally induce better and more stable RL training, (2) more challenging problems with larger search space tend to need higher numbers of backtracks during the SFT stage. Additionally, we demonstrate through experiments on distilled data that RL training is largely unaffected by the correctness of long CoT sequences, suggesting that RL prioritizes structural patterns over content correctness. Collectively, our results offer practical insights into designing optimal training strategies to effectively scale reasoning in LLMs.

Large Language Models (LLMs) have fast become an essential tools to many conversational chatbots due to their ability to provide coherent answers for varied queries. Datasets used to train these LLMs are often a mix of generic and synthetic samples, thus lacking the verification needed to provide correct and verifiable answers for T.V. News. We collect and share a large collection of QA pairs extracted from transcripts of news recordings from various news-channels across the United States. Resultant QA pairs are then used to fine-tune an off-the-shelf LLM model. Our model surpasses base models of similar size on several open LLM benchmarks. We further integrate and propose a RAG method to improve contextualization of our answers and also point it to a verifiable news recording.

Large Language Models (LLMs) have shown strong reasoning capabilities, particularly when enhanced through Reinforcement Learning (RL). While prior work has successfully applied RL to mathematical reasoning -- where rules and correctness are well-defined -- generalizing these methods to broader reasoning domains remains challenging due to limited data, the lack of verifiable reward structures, and diverse task requirements. In this work, we propose NEMOTRON-CROSSTHINK, a framework that systematically incorporates multi-domain corpora, including both synthetic and real-world question-answer pairs, into RL training to improve generalization across diverse reasoning tasks. NEMOTRON-CROSSTHINK addresses key challenges by (1) incorporating data from varied sources spanning STEM, humanities, social sciences, etc.; (2) applying structured templates (e.g., multiple-choice and open-ended) to control answer-space complexity; (3) filtering for verifiable answers; and (4) optimizing data blending strategies that utilizes data from multiple sources effectively. Our approach enables scalable and verifiable reward modeling beyond mathematics and demonstrates improved accuracies on both math (MATH-500: +30.1%, AMC23:+27.5%) and non-math reasoning benchmarks (MMLU-PRO: +12.8%, GPQA-DIAMOND: +11.3%, AGIEVAL: +15.1%, SUPERGPQA: +3.8%). Moreover, NEMOTRON-CROSSTHINK exhibits significantly improved response efficiency -- using 28% fewer tokens for correct answers -- highlighting more focused and effective reasoning. Through NEMOTRON-CROSSTHINK, we demonstrate that integrating multi-domain, multi-format data in RL leads to more accurate, efficient, and generalizable LLMs.

Recent advancements in Chain of Thought (COT) generation have significantly improved the reasoning capabilities of Large Language Models (LLMs), with reinforcement learning (RL) emerging as an effective post-training approach. Multimodal Large Language Models (MLLMs) inherit this reasoning potential but remain underexplored in tasks requiring both perception and logical reasoning. To address this, we introduce SEED-Bench-R1, a benchmark designed to systematically evaluate post-training methods for MLLMs in video understanding. It includes intricate real-world videos and complex everyday planning tasks in the format of multiple-choice questions, requiring sophisticated perception and reasoning. SEED-Bench-R1 assesses generalization through a three-level hierarchy: in-distribution, cross-environment, and cross-environment-task scenarios, equipped with a large-scale training dataset with easily verifiable ground-truth answers. Using Qwen2-VL-Instruct-7B as a base model, we compare RL with supervised fine-tuning (SFT), demonstrating RL's data efficiency and superior performance on both in-distribution and out-of-distribution tasks, even outperforming SFT on general video understanding benchmarks like LongVideoBench. Our detailed analysis reveals that RL enhances visual perception but often produces less logically coherent reasoning chains. We identify key limitations such as inconsistent reasoning and overlooked visual cues, and suggest future improvements in base model reasoning, reward modeling, and RL robustness against noisy signals.

Reinforcement learning (RL) with verifiable rewards (RLVR) has shown promising results in mathematical reasoning and coding tasks where well-structured reference answers are available. However, its applicability to broader domains remains underexplored. In this work, we study the extension of RLVR to more diverse domains such as medicine, chemistry, psychology, and economics. We observe high agreement in binary judgments across different large language models (LLMs) when objective reference answers exist, which challenges the necessity of large-scale annotation for training domain-specific reward models. To address the limitations of binary rewards when handling unstructured reference answers, we further incorporate model-based soft scoring into RLVR to improve its flexibility. Our experiments show that a distilled generative reward model can serve as an effective cross-domain verifier, providing reliable reward signals for RL without requiring domain-specific annotations. By fine-tuning a base 7B model using various RL algorithms against our reward model, we obtain policies that outperform state-of-the-art open-source aligned LLMs such as Qwen2.5-72B-Instruct and DeepSeek-R1-Distill-Qwen-32B by a large margin, across domains in free-form answer settings. This also strengthens RLVR's robustness and scalability, highlighting its potential for real-world applications with noisy or weak labels.

Multi-step symbolic reasoning is critical for advancing downstream performance on financial tasks. Yet, benchmarks for systematically evaluating this capability are lacking. Existing datasets like FinQA and ConvFinQA supervise only final numerical answers, without assessing intermediate reasoning steps. To address this, we introduce FinChain, the first symbolic benchmark designed for verifiable Chain-of- Thought (CoT) financial reasoning. Spanning 54 topics across 12 financial domains, Fin- Chain offers five parameterized templates per topic, each varying in reasoning complexity and domain expertise required. Each dataset instance includes an executable Python trace, enabling automatic generation of extensive training data and easy adaptation to other domains. We also introduce ChainEval, a new metric for automatic evaluation of both final answers and intermediate reasoning. Benchmarking 30 LLMs on our dataset, we find that even state-of-the-art models have considerable room for improvement in multi-step financial reasoning. All templates and evaluation metrics for FinChain are available at https: //github.com/mbzuai-nlp/finchain.

Reinforcement learning with verifiable rewards (RLVR) has enabled large language models (LLMs) to achieve remarkable breakthroughs in reasoning tasks with objective ground-truth answers, such as mathematics and code generation. However, a significant gap remains for non-verifiable tasks, like creative writing and open-ended dialogue, where quality assessment is inherently subjective and lacks definitive references. Existing approaches for these domains often rely on scalar reward models trained with human preferences, which suffer from limited generalization and are prone to reward hacking, such as over-explanation and length bias. In this work, we propose a unified RLVR-based training paradigm that bridges the gap between non-verifiable tasks and verifiable rewards. We introduce a writing-principle-based pairwise Generative Reward Model (GenRM) and a novel Bootstrapped Relative Policy Optimization (BRPO) algorithm. The pairwise writing GenRM leverages self-principled critique to transform subjective assessments into reliable, verifiable rewards, while BRPO enables dynamic, reference-free pairwise comparison by leveraging a bootstrapped response as temporary reference from within group rollouts during RL training. Our approach empowers LLMs to develop robust writing capabilities without supervised fine-tuning, as demonstrated by Writing-Zero, which shows consistent improvement and strong resistance to reward hacking compared to scalar reward baselines. Furthermore, our method achieves competitive results on both in-house and open-source writing benchmarks. Our findings suggest the potential to unify rule-based, reference-based, and reference-free reward modeling under the RLVR framework, thus paving the way for a comprehensive and scalable RL training paradigm applicable across all language tasks.

Large Language Model (LLM)-based applications are graduating from research prototypes to products serving millions of users, influencing how people write and consume information. A prominent example is the appearance of Answer Engines: LLM-based generative search engines supplanting traditional search engines. Answer engines not only retrieve relevant sources to a user query but synthesize answer summaries that cite the sources. To understand these systems' limitations, we first conducted a study with 21 participants, evaluating interactions with answer vs. traditional search engines and identifying 16 answer engine limitations. From these insights, we propose 16 answer engine design recommendations, linked to 8 metrics. An automated evaluation implementing our metrics on three popular engines (You.com, Perplexity.ai, BingChat) quantifies common limitations (e.g., frequent hallucination, inaccurate citation) and unique features (e.g., variation in answer confidence), with results mirroring user study insights. We release our Answer Engine Evaluation benchmark (AEE) to facilitate transparent evaluation of LLM-based applications.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a promising paradigm for advancing the reasoning capabilities of Large Language Models (LLMs). However, a critical paradox clouds its efficacy: RLVR-tuned models often underperform their base models on the Pass@K metric for solution-finding, leading to the hypothesis that RLVR merely re-weights existing reasoning paths at the cost of reasoning diversity. In this work, we resolve this contradiction by identifying the source of the problem: the Pass@K metric itself is a flawed measure of reasoning, as it credits correct final answers that probably arise from inaccurate or incomplete chains of thought (CoTs). To address this, we introduce a more precise evaluation metric, CoT-Pass@K, which mandates that both the reasoning path and the final answer be correct. We provide a new theoretical foundation that formalizes how RLVR, unlike traditional RL, is uniquely structured to incentivize logical integrity. Our empirical results are supportive: using CoT-Pass@K, we observe that RLVR can incentivize the generalization of correct reasoning for all values of K. Furthermore, by analyzing the training dynamics, we find that this enhanced reasoning capability emerges early in the training process and smoothly generalizes. Our work provides a clear perspective on the role of RLVR, offers a more reliable method for its evaluation, and confirms its potential to genuinely advance machine reasoning.

Vision-language models (VLMs) trained via reinforcement learning with verifiable reward (RLVR) have shown notable progress in scaling test-time compute effectively. In this work, we investigate how synthesized RL data can further improve RLVR. To this end, we propose SynthRL-a scalable and guaranteed pipeline for automatic data scaling in reasoning-oriented RL training. SynthRL comprises three key stages: (1) selecting seed questions with appropriate distribution, (2) augmenting them into more challenging variants while preserving the original answers, and (3) a guaranteed verification stage that ensures near-perfect correctness and difficulty enhancement. Our empirical experiments demonstrate SynthRL's scalability and effectiveness. When applied to the MMK12 dataset, SynthRL synthesizes over 3.3K additional verifiable, challenging questions from approximately 8K seed samples. Models trained with our synthesized data achieve consistent gains across five out-of-domain visual math reasoning benchmarks, with a significant improvement over baseline models trained on seed data alone. Notably, detailed analysis reveals that the gains are more pronounced on the most challenging evaluation samples, highlighting SynthRL's effectiveness in eliciting deeper and more complex reasoning patterns.

As language models are adapted by a more sophisticated and diverse set of users, the importance of guaranteeing that they provide factually correct information supported by verifiable sources is critical across fields of study & professions. This is especially the case for high-stakes fields, such as medicine and law, where the risk of propagating false information is high and can lead to undesirable societal consequences. Previous work studying factuality and attribution has not focused on analyzing these characteristics of language model outputs in domain-specific scenarios. In this work, we present an evaluation study analyzing various axes of factuality and attribution provided in responses from a few systems, by bringing domain experts in the loop. Specifically, we first collect expert-curated questions from 484 participants across 32 fields of study, and then ask the same experts to evaluate generated responses to their own questions. We also ask experts to revise answers produced by language models, which leads to ExpertQA, a high-quality long-form QA dataset with 2177 questions spanning 32 fields, along with verified answers and attributions for claims in the answers.

Large multimodal models (LMMs) have shown impressive capabilities in a wide range of visual tasks. However, they often struggle with fine-grained visual reasoning, failing to identify domain-specific objectives and provide justifiable explanations for their predictions. To address this, we propose a novel visual rejection sampling framework to improve the cognition and explainability of LMMs using self-synthesized data. Specifically, visual fine-tuning requires images, queries, and target answers. Our approach begins by synthesizing interpretable answers that include human-verifiable visual features. These features are based on expert-defined concepts, carefully selected based on their alignment with the image content. After each round of fine-tuning, we apply a reward model-free filtering mechanism to select the highest-quality interpretable answers for the next round of tuning. This iterative process of data synthesis and fine-tuning progressively improves the model's ability to generate accurate and reasonable explanations. Experimental results demonstrate the effectiveness of our method in improving both the accuracy and explainability of specialized visual classification tasks.

We explore a method for improving the performance of large language models through self-reflection and reinforcement learning. By incentivizing the model to generate better self-reflections when it answers incorrectly, we demonstrate that a model's ability to solve complex, verifiable tasks can be enhanced even when generating synthetic data is infeasible and only binary feedback is available. Our framework operates in two stages: first, upon failing a given task, the model generates a self-reflective commentary analyzing its previous attempt; second, the model is given another attempt at the task with the self-reflection in context. If the subsequent attempt succeeds, the tokens generated during the self-reflection phase are rewarded. Our experimental results show substantial performance gains across a variety of model architectures, as high as 34.7% improvement at math equation writing and 18.1% improvement at function calling. Notably, smaller fine-tuned models (1.5 billion to 7 billion parameters) outperform models in the same family that are 10 times larger. Our novel paradigm is thus an exciting pathway to more useful and reliable language models that can self-improve on challenging tasks with limited external feedback.

While large language models (LLMs) have demonstrated exceptional capabilities in challenging tasks such as mathematical reasoning, existing methods to enhance reasoning ability predominantly rely on supervised fine-tuning (SFT) followed by reinforcement learning (RL) on reasoning-specific data after pre-training. However, these approaches critically depend on external supervisions--such as human labelled reasoning traces, verified golden answers, or pre-trained reward models--which limits scalability and practical applicability. In this work, we propose Entropy Minimized Policy Optimization (EMPO), which makes an early attempt at fully unsupervised LLM reasoning incentivization. EMPO does not require any supervised information for incentivizing reasoning capabilities (i.e., neither verifiable reasoning traces, problems with golden answers, nor additional pre-trained reward models). By continuously minimizing the predictive entropy of LLMs on unlabeled user queries in a latent semantic space, EMPO enables purely self-supervised evolution of reasoning capabilities with strong flexibility and practicality. Our experiments demonstrate competitive performance of EMPO on both mathematical reasoning and free-form commonsense reasoning tasks. Specifically, without any supervised signals, EMPO boosts the accuracy of Qwen2.5-Math-7B Base from 30.7\% to 48.1\% on mathematical benchmarks and improves truthfulness accuracy of Qwen2.5-7B Instruct from 87.16\% to 97.25\% on TruthfulQA.

While large language models (LLMs) can answer many questions correctly, they can also hallucinate and give wrong answers. Wikidata, with its over 12 billion facts, can be used to ground LLMs to improve their factuality. This paper presents WikiWebQuestions, a high-quality question answering benchmark for Wikidata. Ported over from WebQuestions for Freebase, it consists of real-world data with SPARQL annotation. This paper presents a few-shot sequence-to-sequence semantic parser for Wikidata. We modify SPARQL to use the unique domain and property names instead of their IDs. We train the parser to use either the results from an entity linker or mentions in the query. We fine-tune LLaMA by adding the few-shot training data to that used to fine-tune Alpaca. Our experimental results demonstrate the effectiveness of this methodology, establishing a strong baseline of 76% and 65% answer accuracy in the dev and test sets of WikiWebQuestions, respectively. By pairing our semantic parser with GPT-3, we combine verifiable results with qualified GPT-3 guesses to provide useful answers to 96% of the questions in dev. We also show that our method outperforms the state-of-the-art for the QALD-7 Wikidata dataset by 3.6% in F1 score.

Reinforcement learning with verifiable rewards (RLVR) has shown promise in enhancing the reasoning capabilities of large language models by learning directly from outcome-based rewards. Recent RLVR works that operate under the zero setting avoid supervision in labeling the reasoning process, but still depend on manually curated collections of questions and answers for training. The scarcity of high-quality, human-produced examples raises concerns about the long-term scalability of relying on human supervision, a challenge already evident in the domain of language model pretraining. Furthermore, in a hypothetical future where AI surpasses human intelligence, tasks provided by humans may offer limited learning potential for a superintelligent system. To address these concerns, we propose a new RLVR paradigm called Absolute Zero, in which a single model learns to propose tasks that maximize its own learning progress and improves reasoning by solving them, without relying on any external data. Under this paradigm, we introduce the Absolute Zero Reasoner (AZR), a system that self-evolves its training curriculum and reasoning ability by using a code executor to both validate proposed code reasoning tasks and verify answers, serving as an unified source of verifiable reward to guide open-ended yet grounded learning. Despite being trained entirely without external data, AZR achieves overall SOTA performance on coding and mathematical reasoning tasks, outperforming existing zero-setting models that rely on tens of thousands of in-domain human-curated examples. Furthermore, we demonstrate that AZR can be effectively applied across different model scales and is compatible with various model classes.

Reinforcement Fine-Tuning (RFT) in Large Reasoning Models like OpenAI o1 learns from feedback on its answers, which is especially useful in applications when fine-tuning data is scarce. Recent open-source work like DeepSeek-R1 demonstrates that reinforcement learning with verifiable reward is one key direction in reproducing o1. While the R1-style model has demonstrated success in language models, its application in multi-modal domains remains under-explored. This work introduces Visual Reinforcement Fine-Tuning (Visual-RFT), which further extends the application areas of RFT on visual tasks. Specifically, Visual-RFT first uses Large Vision-Language Models (LVLMs) to generate multiple responses containing reasoning tokens and final answers for each input, and then uses our proposed visual perception verifiable reward functions to update the model via the policy optimization algorithm such as Group Relative Policy Optimization (GRPO). We design different verifiable reward functions for different perception tasks, such as the Intersection over Union (IoU) reward for object detection. Experimental results on fine-grained image classification, few-shot object detection, reasoning grounding, as well as open-vocabulary object detection benchmarks show the competitive performance and advanced generalization ability of Visual-RFT compared with Supervised Fine-tuning (SFT). For example, Visual-RFT improves accuracy by 24.3% over the baseline in one-shot fine-grained image classification with around 100 samples. In few-shot object detection, Visual-RFT also exceeds the baseline by 21.9 on COCO's two-shot setting and 15.4 on LVIS. Our Visual-RFT represents a paradigm shift in fine-tuning LVLMs, offering a data-efficient, reward-driven approach that enhances reasoning and adaptability for domain-specific tasks.

We introduce TangoFlux, an efficient Text-to-Audio (TTA) generative model with 515M parameters, capable of generating up to 30 seconds of 44.1kHz audio in just 3.7 seconds on a single A40 GPU. A key challenge in aligning TTA models lies in the difficulty of creating preference pairs, as TTA lacks structured mechanisms like verifiable rewards or gold-standard answers available for Large Language Models (LLMs). To address this, we propose CLAP-Ranked Preference Optimization (CRPO), a novel framework that iteratively generates and optimizes preference data to enhance TTA alignment. We demonstrate that the audio preference dataset generated using CRPO outperforms existing alternatives. With this framework, TangoFlux achieves state-of-the-art performance across both objective and subjective benchmarks. We open source all code and models to support further research in TTA generation.

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.

The capacity for complex mathematical reasoning is a key benchmark for artificial intelligence. While reinforcement learning (RL) applied to LLMs shows promise, progress is significantly hindered by the lack of large-scale training data that is sufficiently challenging, possesses verifiable answer formats suitable for RL, and is free from contamination with evaluation benchmarks. To address these limitations, we introduce DeepMath-103K, a new, large-scale dataset comprising approximately 103K mathematical problems, specifically designed to train advanced reasoning models via RL. DeepMath-103K is curated through a rigorous pipeline involving source analysis, stringent decontamination against numerous benchmarks, and filtering for high difficulty (primarily Levels 5-9), significantly exceeding existing open resources in challenge. Each problem includes a verifiable final answer, enabling rule-based RL, and three distinct R1-generated solutions suitable for diverse training paradigms like supervised fine-tuning or distillation. Spanning a wide range of mathematical topics, DeepMath-103K promotes the development of generalizable reasoning. We demonstrate that models trained on DeepMath-103K achieve significant improvements on challenging mathematical benchmarks, validating its effectiveness. We release DeepMath-103K publicly to facilitate community progress in building more capable AI reasoning systems: https://github.com/zwhe99/DeepMath.

Verifiability is a core content policy of Wikipedia: claims that are likely to be challenged need to be backed by citations. There are millions of articles available online and thousands of new articles are released each month. For this reason, finding relevant sources is a difficult task: many claims do not have any references that support them. Furthermore, even existing citations might not support a given claim or become obsolete once the original source is updated or deleted. Hence, maintaining and improving the quality of Wikipedia references is an important challenge and there is a pressing need for better tools to assist humans in this effort. Here, we show that the process of improving references can be tackled with the help of artificial intelligence (AI). We develop a neural network based system, called Side, to identify Wikipedia citations that are unlikely to support their claims, and subsequently recommend better ones from the web. We train this model on existing Wikipedia references, therefore learning from the contributions and combined wisdom of thousands of Wikipedia editors. Using crowd-sourcing, we observe that for the top 10% most likely citations to be tagged as unverifiable by our system, humans prefer our system's suggested alternatives compared to the originally cited reference 70% of the time. To validate the applicability of our system, we built a demo to engage with the English-speaking Wikipedia community and find that Side's first citation recommendation collects over 60% more preferences than existing Wikipedia citations for the same top 10% most likely unverifiable claims according to Side. Our results indicate that an AI-based system could be used, in tandem with humans, to improve the verifiability of Wikipedia. More generally, we hope that our work can be used to assist fact checking efforts and increase the general trustworthiness of information online.

The recent paradigm shift towards training large language models (LLMs) using DeepSeek-R1-Zero-style reinforcement learning (RL) on verifiable rewards has led to impressive advancements in code and mathematical reasoning. However, this methodology is limited to tasks where rule-based answer verification is possible and does not naturally extend to real-world domains such as chemistry, healthcare, engineering, law, biology, business, and economics. Current practical workarounds use an additional LLM as a model-based verifier; however, this introduces issues such as reliance on a strong verifier LLM, susceptibility to reward hacking, and the practical burden of maintaining the verifier model in memory during training. To address this and extend DeepSeek-R1-Zero-style training to general reasoning domains, we propose a verifier-free method (VeriFree) that bypasses answer verification and instead uses RL to directly maximize the probability of generating the reference answer. We compare VeriFree with verifier-based methods and demonstrate that, in addition to its significant practical benefits and reduced compute requirements, VeriFree matches and even surpasses verifier-based methods on extensive evaluations across MMLU-Pro, GPQA, SuperGPQA, and math-related benchmarks. Moreover, we provide insights into this method from multiple perspectives: as an elegant integration of training both the policy and implicit verifier in a unified model, and as a variational optimization approach. Code is available at https://github.com/sail-sg/VeriFree.

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.

Large language models demonstrate remarkable reasoning capabilities but often produce unreliable or incorrect responses. Existing verification methods are typically model-specific or domain-restricted, requiring significant computational resources and lacking scalability across diverse reasoning tasks. To address these limitations, we propose VerifiAgent, a unified verification agent that integrates two levels of verification: meta-verification, which assesses completeness and consistency in model responses, and tool-based adaptive verification, where VerifiAgent autonomously selects appropriate verification tools based on the reasoning type, including mathematical, logical, or commonsense reasoning. This adaptive approach ensures both efficiency and robustness across different verification scenarios. Experimental results show that VerifiAgent outperforms baseline verification methods (e.g., deductive verifier, backward verifier) among all reasoning tasks. Additionally, it can further enhance reasoning accuracy by leveraging feedback from verification results. VerifiAgent can also be effectively applied to inference scaling, achieving better results with fewer generated samples and costs compared to existing process reward models in the mathematical reasoning domain. Code is available at https://github.com/Jiuzhouh/VerifiAgent

Reasoning models have achieved remarkable performance on tasks like math and logical reasoning thanks to their ability to search during reasoning. However, they still suffer from overthinking, often performing unnecessary reasoning steps even after reaching the correct answer. This raises the question: can models evaluate the correctness of their intermediate answers during reasoning? In this work, we study whether reasoning models encode information about answer correctness through probing the model's hidden states. The resulting probe can verify intermediate answers with high accuracy and produces highly calibrated scores. Additionally, we find models' hidden states encode correctness of future answers, enabling early prediction of the correctness before the intermediate answer is fully formulated. We then use the probe as a verifier to decide whether to exit reasoning at intermediate answers during inference, reducing the number of inference tokens by 24\% without compromising performance. These findings confirm that reasoning models do encode a notion of correctness yet fail to exploit it, revealing substantial untapped potential to enhance their efficiency.

The breakthrough of OpenAI o1 highlights the potential of enhancing reasoning to improve LLM. Yet, most research in reasoning has focused on mathematical tasks, leaving domains like medicine underexplored. The medical domain, though distinct from mathematics, also demands robust reasoning to provide reliable answers, given the high standards of healthcare. However, verifying medical reasoning is challenging, unlike those in mathematics. To address this, we propose verifiable medical problems with a medical verifier to check the correctness of model outputs. This verifiable nature enables advancements in medical reasoning through a two-stage approach: (1) using the verifier to guide the search for a complex reasoning trajectory for fine-tuning LLMs, (2) applying reinforcement learning (RL) with verifier-based rewards to enhance complex reasoning further. Finally, we introduce HuatuoGPT-o1, a medical LLM capable of complex reasoning, which outperforms general and medical-specific baselines using only 40K verifiable problems. Experiments show complex reasoning improves medical problem-solving and benefits more from RL. We hope our approach inspires advancements in reasoning across medical and other specialized domains.

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.

Machine reading comprehension (MRC) is an AI challenge that requires machine to determine the correct answers to questions based on a given passage. MRC systems must not only answer question when necessary but also distinguish when no answer is available according to the given passage and then tactfully abstain from answering. When unanswerable questions are involved in the MRC task, an essential verification module called verifier is especially required in addition to the encoder, though the latest practice on MRC modeling still most benefits from adopting well pre-trained language models as the encoder block by only focusing on the "reading". This paper devotes itself to exploring better verifier design for the MRC task with unanswerable questions. Inspired by how humans solve reading comprehension questions, we proposed a retrospective reader (Retro-Reader) that integrates two stages of reading and verification strategies: 1) sketchy reading that briefly investigates the overall interactions of passage and question, and yield an initial judgment; 2) intensive reading that verifies the answer and gives the final prediction. The proposed reader is evaluated on two benchmark MRC challenge datasets SQuAD2.0 and NewsQA, achieving new state-of-the-art results. Significance tests show that our model is significantly better than the strong ELECTRA and ALBERT baselines. A series of analysis is also conducted to interpret the effectiveness of the proposed reader.

As large language models (LLMs) evolve into tool-using agents, the ability to browse the web in real-time has become a critical yardstick for measuring their reasoning and retrieval competence. Existing benchmarks such as BrowseComp concentrate on English and overlook the linguistic, infrastructural, and censorship-related complexities of other major information ecosystems -- most notably Chinese. To address this gap, we introduce BrowseComp-ZH, a high-difficulty benchmark purpose-built to comprehensively evaluate LLM agents on the Chinese web. BrowseComp-ZH consists of 289 multi-hop questions spanning 11 diverse domains. Each question is reverse-engineered from a short, objective, and easily verifiable answer (e.g., a date, number, or proper noun). A two-stage quality control protocol is applied to strive for high question difficulty and answer uniqueness. We benchmark over 20 state-of-the-art language models and agentic search systems on our proposed BrowseComp-ZH. Despite their strong conversational and retrieval capabilities, most models struggle severely: a large number achieve accuracy rates below 10%, and only a handful exceed 20%. Even the best-performing system, OpenAI's DeepResearch, reaches just 42.9%. These results demonstrate the considerable difficulty of BrowseComp-ZH, where success demands not only effective retrieval strategies, but also sophisticated reasoning and information reconciliation -- capabilities that current models still struggle to master. Our dataset, construction guidelines, and benchmark results have been publicly released at https://github.com/PALIN2018/BrowseComp-ZH.

Verifying a question's validity before answering is crucial in real-world applications, where users may provide imperfect instructions. In this scenario, an ideal model should address the discrepancies in the query and convey them to the users rather than generating the best possible answer. Addressing this requirement, we introduce a new compositional visual question-answering dataset, VISREAS, that consists of answerable and unanswerable visual queries formulated by traversing and perturbing commonalities and differences among objects, attributes, and relations. VISREAS contains 2.07M semantically diverse queries generated automatically using Visual Genome scene graphs. The unique feature of this task, validating question answerability with respect to an image before answering, and the poor performance of state-of-the-art models inspired the design of a new modular baseline, LOGIC2VISION that reasons by producing and executing pseudocode without any external modules to generate the answer. LOGIC2VISION outperforms generative models in VISREAS (+4.82% over LLaVA-1.5; +12.23% over InstructBLIP) and achieves a significant gain in performance against the classification models.

Metrics like FactScore and VeriScore that evaluate long-form factuality operate by decomposing an input response into atomic claims and then individually verifying each claim. While effective and interpretable, these methods incur numerous LLM calls and can take upwards of 100 seconds to evaluate a single response, limiting their practicality in large-scale evaluation and training scenarios. To address this, we propose VeriFastScore, which leverages synthetic data to fine-tune Llama3.1 8B for simultaneously extracting and verifying all verifiable claims within a given text based on evidence from Google Search. We show that this task cannot be solved via few-shot prompting with closed LLMs due to its complexity: the model receives ~4K tokens of evidence on average and needs to concurrently decompose claims, judge their verifiability, and verify them against noisy evidence. However, our fine-tuned VeriFastScore model demonstrates strong correlation with the original VeriScore pipeline at both the example level (r=0.80) and system level (r=0.94) while achieving an overall speedup of 6.6x (9.9x excluding evidence retrieval) over VeriScore. To facilitate future factuality research, we publicly release our VeriFastScore model and synthetic datasets.

Despite significant advancements in the general capability of large language models (LLMs), they continue to struggle with consistent and accurate reasoning, especially in complex tasks such as mathematical and code reasoning. One key limitation is that LLMs are trained primarily on correct solutions, reducing their ability to detect and learn from errors, which hampers their ability to reliably verify and rank outputs. To address this, we scale up the inference-time computation by generating multiple reasoning paths and employing verifiers to assess and rank the generated outputs by correctness. To facilitate this, we introduce a comprehensive dataset consisting of correct and incorrect solutions for math and code tasks, generated by multiple LLMs. This diverse set of solutions enables verifiers to more effectively distinguish and rank correct answers from erroneous outputs. The training methods for building verifiers were selected based on an extensive comparison of existing approaches. Moreover, to leverage the unique strengths of different reasoning strategies, we propose a novel collaborative method integrating Chain-of-Thought (CoT) and Program-of-Thought (PoT) solutions for verification. CoT provides a clear, step-by-step reasoning process that enhances interpretability, while PoT, being executable, offers a precise and error-sensitive validation mechanism. By taking both of their strengths, our approach significantly improves the accuracy and reliability of reasoning verification. Our verifiers, Math-Rev and Code-Rev, demonstrate substantial performance gains to existing LLMs, achieving state-of-the-art results on benchmarks such as GSM8k and MATH and even outperforming GPT-4o with Qwen-72B-Instruct as the reasoner.

Large Language Models (LLMs) are revolutionizing information retrieval, with chatbots becoming an important source for answering user queries. As by their design, LLMs prioritize generating correct answers, the value of highly plausible yet incorrect answers (candidate answers) tends to be overlooked. However, such answers can still prove useful, for example, they can play a crucial role in tasks like Multiple-Choice Question Answering (MCQA) and QA Robustness Assessment (QARA). Existing QA datasets primarily focus on correct answers without explicit consideration of the plausibility of other candidate answers, limiting opportunity for more nuanced evaluations of models. To address this gap, we introduce PlausibleQA, a large-scale dataset comprising 10,000 questions and 100,000 candidate answers, each annotated with plausibility scores and justifications for their selection. Additionally, the dataset includes 900,000 justifications for pairwise comparisons between candidate answers, further refining plausibility assessments. We evaluate PlausibleQA through human assessments and empirical experiments, demonstrating its utility in MCQA and QARA analysis. Our findings show that plausibility-aware approaches are effective for MCQA distractor generation and QARA. We release PlausibleQA as a resource for advancing QA research and enhancing LLM performance in distinguishing plausible distractors from correct answers.

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

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

Language models (LMs) are widely used by an increasing number of users, underscoring the challenge of maintaining factuality across a broad range of topics. We first present VERIFY (Verification and Evidence RetrIeval for FactualitY evaluation), a pipeline to evaluate LMs' factuality in real-world user interactions. VERIFY considers the verifiability of LM-generated content and categorizes content units as supported, unsupported, or undecidable based on the retrieved evidence from the Web. Importantly, factuality judgment by VERIFY correlates better with human evaluations than existing methods. Using VERIFY, we identify "hallucination prompts" across diverse topics, i.e., those eliciting the highest rates of incorrect and inconclusive LM responses. These prompts form FactBench, a dataset of 1K prompts across 150 fine-grained topics. Our dataset captures emerging factuality challenges in real-world LM interactions and can be regularly updated with new prompts. We benchmark widely-used LMs from GPT, Gemini, and Llama3.1 family on FactBench, yielding the following key findings: (i) Proprietary models exhibit better factuality, with performance declining from Easy to Hard hallucination prompts. (ii) Llama3.1-405B-Instruct shows comparable or lower factual accuracy than Llama3.1-70B-Instruct across all evaluation methods due to its higher subjectivity that leads to more content labeled as undecidable. (iii) Gemini1.5-Pro shows a significantly higher refusal rate, with over-refusal in 25% of cases. Our code and data are publicly available at https://huggingface.co/spaces/launch/factbench.

Large reasoning models such as OpenAI o1 and DeepSeek-R1 have achieved remarkable performance in the domain of reasoning. A key component of their training is the incorporation of verifiable rewards within reinforcement learning (RL). However, existing reward benchmarks do not evaluate reference-based reward systems, leaving researchers with limited understanding of the accuracy of verifiers used in RL. In this paper, we introduce two benchmarks, VerifyBench and VerifyBench-Hard, designed to assess the performance of reference-based reward systems. These benchmarks are constructed through meticulous data collection and curation, followed by careful human annotation to ensure high quality. Current models still show considerable room for improvement on both VerifyBench and VerifyBench-Hard, especially smaller-scale models. Furthermore, we conduct a thorough and comprehensive analysis of evaluation results, offering insights for understanding and developing reference-based reward systems. Our proposed benchmarks serve as effective tools for guiding the development of verifier accuracy and the reasoning capabilities of models trained via RL in reasoning tasks.

Ensuring the verifiability of model answers is a fundamental challenge for retrieval-augmented generation (RAG) in the question answering (QA) domain. Recently, self-citation prompting was proposed to make large language models (LLMs) generate citations to supporting documents along with their answers. However, self-citing LLMs often struggle to match the required format, refer to non-existent sources, and fail to faithfully reflect LLMs' context usage throughout the generation. In this work, we present MIRAGE --Model Internals-based RAG Explanations -- a plug-and-play approach using model internals for faithful answer attribution in RAG applications. MIRAGE detects context-sensitive answer tokens and pairs them with retrieved documents contributing to their prediction via saliency methods. We evaluate our proposed approach on a multilingual extractive QA dataset, finding high agreement with human answer attribution. On open-ended QA, MIRAGE achieves citation quality and efficiency comparable to self-citation while also allowing for a finer-grained control of attribution parameters. Our qualitative evaluation highlights the faithfulness of MIRAGE's attributions and underscores the promising application of model internals for RAG answer attribution.

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

Recent Language Models (LMs) have shown impressive capabilities in generating texts with the knowledge internalized in parameters. Yet, LMs often generate the factually incorrect responses to the given queries, since their knowledge may be inaccurate, incomplete, and outdated. To address this problem, previous works propose to augment LMs with the knowledge retrieved from an external knowledge source. However, such approaches often show suboptimal text generation performance due to two reasons: 1) the model may fail to retrieve the knowledge relevant to the given query, or 2) the model may not faithfully reflect the retrieved knowledge in the generated text. To overcome these, we propose to verify the output and the knowledge of the knowledge-augmented LMs with a separate verifier, which is a small LM that is trained to detect those two types of errors through instruction-finetuning. Then, when the verifier recognizes an error, we can rectify it by either retrieving new knowledge or generating new text. Further, we use an ensemble of the outputs from different instructions with a single verifier to enhance the reliability of the verification processes. We validate the effectiveness of the proposed verification steps on multiple question answering benchmarks, whose results show that the proposed verifier effectively identifies retrieval and generation errors, allowing LMs to provide more factually correct outputs. Our code is available at https://github.com/JinheonBaek/KALMV.

Large Language Model (LLM) reasoning for complex tasks inherently involves a trade-off between solution accuracy and computational efficiency. The subsequent step of verification, while intended to improve performance, further complicates this landscape by introducing its own challenging trade-off: sophisticated Generative Reward Models (GenRMs) can be computationally prohibitive if naively integrated with LLMs at test-time, while simpler, faster methods may lack reliability. To overcome these challenges, we introduce FlexiVe, a novel generative verifier that flexibly balances computational resources between rapid, reliable fast thinking and meticulous slow thinking using a Flexible Allocation of Verification Budget strategy. We further propose the Solve-Detect-Verify pipeline, an efficient inference-time scaling framework that intelligently integrates FlexiVe, proactively identifying solution completion points to trigger targeted verification and provide focused solver feedback. Experiments show FlexiVe achieves superior accuracy in pinpointing errors within reasoning traces on ProcessBench. Furthermore, on challenging mathematical reasoning benchmarks (AIME 2024, AIME 2025, and CNMO), our full approach outperforms baselines like self-consistency in reasoning accuracy and inference efficiency. Our system offers a scalable and effective solution to enhance LLM reasoning at test time.

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.

Recent large language models often answer factual questions correctly. But users can't trust any given claim a model makes without fact-checking, because language models can hallucinate convincing nonsense. In this work we use reinforcement learning from human preferences (RLHP) to train "open-book" QA models that generate answers whilst also citing specific evidence for their claims, which aids in the appraisal of correctness. Supporting evidence is drawn from multiple documents found via a search engine, or from a single user-provided document. Our 280 billion parameter model, GopherCite, is able to produce answers with high quality supporting evidence and abstain from answering when unsure. We measure the performance of GopherCite by conducting human evaluation of answers to questions in a subset of the NaturalQuestions and ELI5 datasets. The model's response is found to be high-quality 80\% of the time on this Natural Questions subset, and 67\% of the time on the ELI5 subset. Abstaining from the third of questions for which it is most unsure improves performance to 90\% and 80\% respectively, approaching human baselines. However, analysis on the adversarial TruthfulQA dataset shows why citation is only one part of an overall strategy for safety and trustworthiness: not all claims supported by evidence are true.

Trustworthy verifiers are essential for the success of reinforcement learning with verifiable reward (RLVR), which is the core methodology behind various large reasoning models such as DeepSeek-R1. In complex domains like mathematical reasoning, rule-based verifiers have been widely adopted in previous works to train strong reasoning models. However, the reliability of these verifiers and their impact on the RL training process remain poorly understood. In this work, we take mathematical reasoning as a case study and conduct a comprehensive analysis of various verifiers in both static evaluation and RL training scenarios. First, we find that current open-source rule-based verifiers often fail to recognize equivalent answers presented in different formats across multiple commonly used mathematical datasets, resulting in non-negligible false negative rates. This limitation adversely affects RL training performance and becomes more pronounced as the policy model gets stronger. Subsequently, we investigate model-based verifiers as a potential solution to address these limitations. While the static evaluation shows that model-based verifiers achieve significantly higher verification accuracy, further analysis and RL training results imply that they are highly susceptible to hacking, where they misclassify certain patterns in responses as correct (i.e., false positives). This vulnerability is exploited during policy model optimization, leading to artificially inflated rewards. Our findings underscore the unique risks inherent to both rule-based and model-based verifiers, aiming to offer valuable insights to develop more robust reward systems in reinforcement learning.

Reasoning LLMs such as OpenAI o1, o3 and DeepSeek R1 have made significant progress in mathematics and coding, yet find challenging advanced tasks such as International Mathematical Olympiad (IMO) combinatorics problems, Abstraction and Reasoning Corpus (ARC) puzzles, and Humanity's Last Exam (HLE) questions. We use a diverse inference approach that combines multiple models and methods at test time. We find that verifying mathematics and code problems, and rejection sampling on other problems is simple and effective. We automatically verify correctness of solutions to IMO problems by Lean, and ARC puzzles by code, and find that best-of-N effectively answers HLE questions. Our approach increases answer accuracy on IMO combinatorics problems from 33.3% to 77.8%, accuracy on HLE questions from 8% to 37%, and solves 80% of ARC puzzles that 948 humans could not and 26.5% of ARC puzzles that o3 high compute does not. Test-time simulations, reinforcement learning, and meta-learning with inference feedback improve generalization by adapting agent graph representations and varying prompts, code, and datasets. Our approach is reliable, robust, and scalable, and in the spirit of reproducible research, we will make it publicly available upon publication.

Fact-checking requires retrieving evidence related to a claim under investigation. The task can be formulated as question generation based on a claim, followed by question answering. However, recent question generation approaches assume that the answer is known and typically contained in a passage given as input, whereas such passages are what is being sought when verifying a claim. In this paper, we present {\it Varifocal}, a method that generates questions based on different focal points within a given claim, i.e.\ different spans of the claim and its metadata, such as its source and date. Our method outperforms previous work on a fact-checking question generation dataset on a wide range of automatic evaluation metrics. These results are corroborated by our manual evaluation, which indicates that our method generates more relevant and informative questions. We further demonstrate the potential of focal points in generating sets of clarification questions for product descriptions.

Large language models (LLMs) have made significant advancements in various natural language processing tasks, including question answering (QA) tasks. While incorporating new information with the retrieval of relevant passages is a promising way to improve QA with LLMs, the existing methods often require additional fine-tuning which becomes infeasible with recent LLMs. Augmenting retrieved passages via prompting has the potential to address this limitation, but this direction has been limitedly explored. To this end, we design a simple yet effective framework to enhance open-domain QA (ODQA) with LLMs, based on the summarized retrieval (SuRe). SuRe helps LLMs predict more accurate answers for a given question, which are well-supported by the summarized retrieval that could be viewed as an explicit rationale extracted from the retrieved passages. Specifically, SuRe first constructs summaries of the retrieved passages for each of the multiple answer candidates. Then, SuRe confirms the most plausible answer from the candidate set by evaluating the validity and ranking of the generated summaries. Experimental results on diverse ODQA benchmarks demonstrate the superiority of SuRe, with improvements of up to 4.6% in exact match (EM) and 4.0% in F1 score over standard prompting approaches. SuRe also can be integrated with a broad range of retrieval methods and LLMs. Finally, the generated summaries from SuRe show additional advantages to measure the importance of retrieved passages and serve as more preferred rationales by models and humans.

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

Prompting language models to provide step-by-step answers (e.g., "Chain-of-Thought") is the prominent approach for complex reasoning tasks, where more accurate reasoning chains typically improve downstream task performance. Recent literature discusses automatic methods to verify reasoning steps to evaluate and improve their correctness. However, no fine-grained step-level datasets are available to enable thorough evaluation of such verification methods, hindering progress in this direction. We introduce Reveal: Reasoning Verification Evaluation, a new dataset to benchmark automatic verifiers of complex Chain-of-Thought reasoning in open-domain question answering settings. Reveal includes comprehensive labels for the relevance, attribution to evidence passages, and logical correctness of each reasoning step in a language model's answer, across a wide variety of datasets and state-of-the-art language models.

Large Language Models (LLMs) show great promise in complex reasoning, with Reinforcement Learning with Verifiable Rewards (RLVR) being a key enhancement strategy. However, a prevalent issue is ``superficial self-reflection'', where models fail to robustly verify their own outputs. We introduce RISE (Reinforcing Reasoning with Self-Verification), a novel online RL framework designed to tackle this. RISE explicitly and simultaneously trains an LLM to improve both its problem-solving and self-verification abilities within a single, integrated RL process. The core mechanism involves leveraging verifiable rewards from an outcome verifier to provide on-the-fly feedback for both solution generation and self-verification tasks. In each iteration, the model generates solutions, then critiques its own on-policy generated solutions, with both trajectories contributing to the policy update. Extensive experiments on diverse mathematical reasoning benchmarks show that RISE consistently improves model's problem-solving accuracy while concurrently fostering strong self-verification skills. Our analyses highlight the advantages of online verification and the benefits of increased verification compute. Additionally, RISE models exhibit more frequent and accurate self-verification behaviors during reasoning. These advantages reinforce RISE as a flexible and effective path towards developing more robust and self-aware reasoners.

One way to increase confidence in the outputs of Large Language Models (LLMs) is to support them with reasoning that is clear and easy to check -- a property we call legibility. We study legibility in the context of solving grade-school math problems and show that optimizing chain-of-thought solutions only for answer correctness can make them less legible. To mitigate the loss in legibility, we propose a training algorithm inspired by Prover-Verifier Game from Anil et al. (2021). Our algorithm iteratively trains small verifiers to predict solution correctness, "helpful" provers to produce correct solutions that the verifier accepts, and "sneaky" provers to produce incorrect solutions that fool the verifier. We find that the helpful prover's accuracy and the verifier's robustness to adversarial attacks increase over the course of training. Furthermore, we show that legibility training transfers to time-constrained humans tasked with verifying solution correctness. Over course of LLM training human accuracy increases when checking the helpful prover's solutions, and decreases when checking the sneaky prover's solutions. Hence, training for checkability by small verifiers is a plausible technique for increasing output legibility. Our results suggest legibility training against small verifiers as a practical avenue for increasing legibility of large LLMs to humans, and thus could help with alignment of superhuman models.

This paper provides a systematic analysis of the opportunities, challenges, and potential solutions of harnessing Large Language Models (LLMs) such as GPT-4 to dig out vulnerabilities within smart contracts based on our ongoing research. For the task of smart contract vulnerability detection, achieving practical usability hinges on identifying as many true vulnerabilities as possible while minimizing the number of false positives. Nonetheless, our empirical study reveals contradictory yet interesting findings: generating more answers with higher randomness largely boosts the likelihood of producing a correct answer but inevitably leads to a higher number of false positives. To mitigate this tension, we propose an adversarial framework dubbed GPTLens that breaks the conventional one-stage detection into two synergistic stages - generation and discrimination, for progressive detection and refinement, wherein the LLM plays dual roles, i.e., auditor and critic, respectively. The goal of auditor is to yield a broad spectrum of vulnerabilities with the hope of encompassing the correct answer, whereas the goal of critic that evaluates the validity of identified vulnerabilities is to minimize the number of false positives. Experimental results and illustrative examples demonstrate that auditor and critic work together harmoniously to yield pronounced improvements over the conventional one-stage detection. GPTLens is intuitive, strategic, and entirely LLM-driven without relying on specialist expertise in smart contracts, showcasing its methodical generality and potential to detect a broad spectrum of vulnerabilities. Our code is available at: https://github.com/git-disl/GPTLens.

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.

Existing question answering (QA) datasets are no longer challenging to most powerful Large Language Models (LLMs). Traditional QA benchmarks like TriviaQA, NaturalQuestions, ELI5 and HotpotQA mainly study ``known unknowns'' with clear indications of both what information is missing, and how to find it to answer the question. Hence, good performance on these benchmarks provides a false sense of security. A yet unmet need of the NLP community is a bank of non-factoid, multi-perspective questions involving a great deal of unclear information needs, i.e. ``unknown uknowns''. We claim we can find such questions in search engine logs, which is surprising because most question-intent queries are indeed factoid. We present Researchy Questions, a dataset of search engine queries tediously filtered to be non-factoid, ``decompositional'' and multi-perspective. We show that users spend a lot of ``effort'' on these questions in terms of signals like clicks and session length, and that they are also challenging for GPT-4. We also show that ``slow thinking'' answering techniques, like decomposition into sub-questions shows benefit over answering directly. We release sim 100k Researchy Questions, along with the Clueweb22 URLs that were clicked.

State-of-the-art language models can match human performance on many tasks, but they still struggle to robustly perform multi-step mathematical reasoning. To diagnose the failures of current models and support research, we introduce GSM8K, a dataset of 8.5K high quality linguistically diverse grade school math word problems. We find that even the largest transformer models fail to achieve high test performance, despite the conceptual simplicity of this problem distribution. To increase performance, we propose training verifiers to judge the correctness of model completions. At test time, we generate many candidate solutions and select the one ranked highest by the verifier. We demonstrate that verification significantly improves performance on GSM8K, and we provide strong empirical evidence that verification scales more effectively with increased data than a finetuning baseline.

Common self-improvement approaches for large language models (LLMs), such as STaR (Zelikman et al., 2022), iteratively fine-tune LLMs on self-generated solutions to improve their problem-solving ability. However, these approaches discard the large amounts of incorrect solutions generated during this process, potentially neglecting valuable information in such solutions. To address this shortcoming, we propose V-STaR that utilizes both the correct and incorrect solutions generated during the self-improvement process to train a verifier using DPO that judges correctness of model-generated solutions. This verifier is used at inference time to select one solution among many candidate solutions. Running V-STaR for multiple iterations results in progressively better reasoners and verifiers, delivering a 4% to 17% test accuracy improvement over existing self-improvement and verification approaches on common code generation and math reasoning benchmarks with LLaMA2 models.

We contribute the largest publicly available dataset of naturally occurring factual claims for the purpose of automatic claim verification. It is collected from 26 fact checking websites in English, paired with textual sources and rich metadata, and labelled for veracity by human expert journalists. We present an in-depth analysis of the dataset, highlighting characteristics and challenges. Further, we present results for automatic veracity prediction, both with established baselines and with a novel method for joint ranking of evidence pages and predicting veracity that outperforms all baselines. Significant performance increases are achieved by encoding evidence, and by modelling metadata. Our best-performing model achieves a Macro F1 of 49.2%, showing that this is a challenging testbed for claim veracity prediction.

We present IBR, an Iterative Backward Reasoning model to solve the proof generation tasks on rule-based Question Answering (QA), where models are required to reason over a series of textual rules and facts to find out the related proof path and derive the final answer. We handle the limitations of existed works in two folds: 1) enhance the interpretability of reasoning procedures with detailed tracking, by predicting nodes and edges in the proof path iteratively backward from the question; 2) promote the efficiency and accuracy via reasoning on the elaborate representations of nodes and history paths, without any intermediate texts that may introduce external noise during proof generation. There are three main modules in IBR, QA and proof strategy prediction to obtain the answer and offer guidance for the following procedure; parent node prediction to determine a node in the existing proof that a new child node will link to; child node prediction to find out which new node will be added to the proof. Experiments on both synthetic and paraphrased datasets demonstrate that IBR has better in-domain performance as well as cross-domain transferability than several strong baselines. Our code and models are available at https://github.com/find-knowledge/IBR .

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

We present the Verifee Dataset: a novel dataset of news articles with fine-grained trustworthiness annotations. We develop a detailed methodology that assesses the texts based on their parameters encompassing editorial transparency, journalist conventions, and objective reporting while penalizing manipulative techniques. We bring aboard a diverse set of researchers from social, media, and computer sciences to overcome barriers and limited framing of this interdisciplinary problem. We collect over 10,000 unique articles from almost 60 Czech online news sources. These are categorized into one of the 4 classes across the credibility spectrum we propose, raging from entirely trustworthy articles all the way to the manipulative ones. We produce detailed statistics and study trends emerging throughout the set. Lastly, we fine-tune multiple popular sequence-to-sequence language models using our dataset on the trustworthiness classification task and report the best testing F-1 score of 0.52. We open-source the dataset, annotation methodology, and annotators' instructions in full length at https://verifee.ai/research to enable easy build-up work. We believe similar methods can help prevent disinformation and educate in the realm of media literacy.

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

The recent LLMs like GPT-4 and PaLM-2 have made tremendous progress in solving fundamental math problems like GSM8K by achieving over 90\% accuracy. However, their capabilities to solve more challenging math problems which require domain-specific knowledge (i.e. theorem) have yet to be investigated. In this paper, we introduce TheoremQA, the first theorem-driven question-answering dataset designed to evaluate AI models' capabilities to apply theorems to solve challenging science problems. \dataset is curated by domain experts containing 800 high-quality questions covering 350 theoremse.g. Taylor's theorem, Lagrange's theorem, Huffman coding, Quantum Theorem, Elasticity Theorem, etc from Math, Physics, EE\&CS, and Finance. We evaluate a wide spectrum of 16 large language and code models with different prompting strategies like Chain-of-Thoughts and Program-of-Thoughts. We found that GPT-4's capabilities to solve these problems are unparalleled, achieving an accuracy of 51\% with Program-of-Thoughts Prompting. All the existing open-sourced models are below 15\%, barely surpassing the random-guess baseline. Given the diversity and broad coverage of \dataset, we believe it can be used as a better benchmark to evaluate LLMs' capabilities to solve challenging science problems. The data and code are released in https://github.com/wenhuchen/TheoremQA.

We introduce a benchmark to evaluate the capability of AI to solve problems in theoretical physics, focusing on high-energy theory and cosmology. The first iteration of our benchmark consists of 57 problems of varying difficulty, from undergraduate to research level. These problems are novel in the sense that they do not come from public problem collections. We evaluate our data set on various open and closed language models, including o3-mini, o1, DeepSeek-R1, GPT-4o and versions of Llama and Qwen. While we find impressive progress in model performance with the most recent models, our research-level difficulty problems are mostly unsolved. We address challenges of auto-verifiability and grading, and discuss common failure modes. While currently state-of-the art models are still of limited use for researchers, our results show that AI assisted theoretical physics research may become possible in the near future. We discuss the main obstacles towards this goal and possible strategies to overcome them. The public problems and solutions, results for various models, and updates to the data set and score distribution, are available on the website of the dataset tpbench.org.

This paper introduces a new suite of question answering datasets for Norwegian; NorOpenBookQA, NorCommonSenseQA, NorTruthfulQA, and NRK-Quiz-QA. The data covers a wide range of skills and knowledge domains, including world knowledge, commonsense reasoning, truthfulness, and knowledge about Norway. Covering both of the written standards of Norwegian - Bokm{\aa}l and Nynorsk - our datasets comprise over 10k question-answer pairs, created by native speakers. We detail our dataset creation approach and present the results of evaluating 11 language models (LMs) in zero- and few-shot regimes. Most LMs perform better in Bokm{\aa}l than Nynorsk, struggle most with commonsense reasoning, and are often untruthful in generating answers to questions. All our datasets and annotation materials are publicly available.

Vision-Language Models (VLMs) often generate plausible but incorrect responses to visual queries. However, reliably quantifying the effect of such hallucinations in free-form responses to open-ended queries is challenging as it requires visually verifying each claim within the response. We propose Programmatic VLM Evaluation (PROVE), a new benchmarking paradigm for evaluating VLM responses to open-ended queries. To construct PROVE, we provide a large language model (LLM) with a high-fidelity scene-graph representation constructed from a hyper-detailed image caption, and prompt it to generate diverse question-answer (QA) pairs, as well as programs that can be executed over the scene graph object to verify each QA pair. We thus construct a benchmark of 10.5k challenging but visually grounded QA pairs. Next, to evaluate free-form model responses to queries in PROVE, we propose a programmatic evaluation strategy that measures both the helpfulness and truthfulness of a response within a unified scene graph-based framework. We benchmark the helpfulness-truthfulness trade-offs of a range of VLMs on PROVE, finding that very few are in-fact able to achieve a good balance between the two. Project page: https://prove-explorer.netlify.app/.

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.

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}.

Scaling automated formal verification to real-world projects requires resolving cross-module dependencies and global contexts, which are challenges overlooked by existing function-centric methods. We introduce RagVerus, a framework that synergizes retrieval-augmented generation with context-aware prompting to automate proof synthesis for multi-module repositories, achieving a 27% relative improvement on our novel RepoVBench benchmark -- the first repository-level dataset for Verus with 383 proof completion tasks. RagVerus triples proof pass rates on existing benchmarks under constrained language model budgets, demonstrating a scalable and sample-efficient verification.

This article proposes a new approach for assessing the quality of answers in political question-and-answer sessions. We measure the quality of an answer based on how easily and accurately it can be recognized in a random set of candidate answers given the question's text. This measure reflects the answer's relevance and depth of engagement with the question. Like semantic search, we can implement this approach by training a language model on the corpus of observed questions and answers without additional human-labeled data. We showcase and validate our methodology within the context of the Question Period in the Canadian House of Commons. Our analysis reveals that while some answers have a weak semantic connection to questions, hinting at some evasion or obfuscation, they are generally at least moderately relevant, far exceeding what we would expect from random replies. We also find a meaningful correlation between answer quality and the party affiliation of the members of Parliament asking the questions.

The progress of AI is bottlenecked by the quality of evaluation, and powerful LLM-as-a-Judge models have proved to be a core solution. Improved judgment ability is enabled by stronger chain-of-thought reasoning, motivating the need to find the best recipes for training such models to think. In this work we introduce J1, a reinforcement learning approach to training such models. Our method converts both verifiable and non-verifiable prompts to judgment tasks with verifiable rewards that incentivize thinking and mitigate judgment bias. In particular, our approach outperforms all other existing 8B or 70B models when trained at those sizes, including models distilled from DeepSeek-R1. J1 also outperforms o1-mini, and even R1 on some benchmarks, despite training a smaller model. We provide analysis and ablations comparing Pairwise-J1 vs Pointwise-J1 models, offline vs online training recipes, reward strategies, seed prompts, and variations in thought length and content. We find that our models make better judgments by learning to outline evaluation criteria, comparing against self-generated reference answers, and re-evaluating the correctness of model responses.

Mathematical reasoning lies at the heart of artificial intelligence, underpinning applications in education, program verification, and research-level mathematical discovery. Mathematical competitions, in particular, present two challenging problem types: theorem proving, which requires rigorous proofs of stated conclusions, and answer construction, which involves hypothesizing and formally verifying mathematical objects. Large Language Models (LLMs) effectively generate creative candidate answers but struggle with formal verification, while symbolic provers ensure rigor but cannot efficiently handle creative conjecture generation. We introduce the Enumerate-Conjecture-Prove (ECP) framework, a modular neuro-symbolic method integrating LLM-based enumeration and pattern-driven conjecturing with formal theorem proving. We present ConstructiveBench, a dataset of 3,431 answer-construction problems in various math competitions with verified Lean formalizations. On the ConstructiveBench dataset, ECP improves the accuracy of answer construction from a Chain-of-Thought (CoT) baseline of 14.54% to 45.06% with the gpt-4.1-mini model. Moreover, combined with ECP's constructed answers, the state-of-the-art DeepSeek-Prover-V2-7B model generates correct proofs for 858 of the 3,431 constructive problems in Lean, achieving 25.01% accuracy compared to 9.86% for symbolic-only baselines. Our code and dataset are publicly available at https://github.com/JackSun200312/ECP.

How do reasoning models verify their own answers? We study this question by training a model using DeepSeek R1's recipe on the CountDown task. We leverage the fact that preference tuning leads to mode collapse, yielding a model that always produces highly structured chain-of-thought sequences. With this setup, we do top-down and bottom-up analyses to reverse-engineer how the model verifies its outputs. Top-down, we find Gated Linear Unit (GLU) weights encoding verification-related tokens, such as ``success'' or ``incorrect''. Bottom-up, we find that ``previous-token heads'' are mainly responsible for self-verification in our setup. Our analyses meet in the middle: drawing inspiration from inter-layer communication channels, we use the identified GLU weights to localize as few as three attention heads that can disable self-verification, pointing to a necessary component of a potentially larger verification circuit. Finally, we verify that similar verification components exist in our base model and a general reasoning DeepSeek-R1 model.

Fact verification is essential for ensuring the reliability of LLM applications. In this study, we evaluate 12 pre-trained LLMs and one specialized fact-verifier, including frontier LLMs and open-weight reasoning LLMs, using a collection of examples from 14 fact-checking benchmarks. We share three findings intended to guide future development of more robust fact verifiers. First, we highlight the importance of addressing annotation errors and ambiguity in datasets, demonstrating that approximately 16\% of ambiguous or incorrectly labeled data substantially influences model rankings. Neglecting this issue may result in misleading conclusions during comparative evaluations, and we suggest using a systematic pipeline utilizing LLM-as-a-judge to help identify these issues at scale. Second, we discover that frontier LLMs with few-shot in-context examples, often overlooked in previous works, achieve top-tier performance. We therefore recommend future studies include comparisons with these simple yet highly effective baselines. Lastly, despite their effectiveness, frontier LLMs incur substantial costs, motivating the development of small, fine-tuned fact verifiers. We show that these small models still have room for improvement, particularly on instances that require complex reasoning. Encouragingly, we demonstrate that augmenting training with synthetic multi-hop reasoning data significantly enhances their capabilities in such instances. We release our code, model, and dataset at https://github.com/just1nseo/verifying-the-verifiers

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

As post-training techniques evolve, large language models (LLMs) are increasingly augmented with structured multi-step reasoning abilities, often optimized through reinforcement learning. These reasoning-enhanced models outperform standard LLMs on complex tasks and now underpin many commercial LLM APIs. However, to protect proprietary behavior and reduce verbosity, providers typically conceal the reasoning traces while returning only the final answer. This opacity introduces a critical transparency gap: users are billed for invisible reasoning tokens, which often account for the majority of the cost, yet have no means to verify their authenticity. This opens the door to token count inflation, where providers may overreport token usage or inject synthetic, low-effort tokens to inflate charges. To address this issue, we propose CoIn, a verification framework that audits both the quantity and semantic validity of hidden tokens. CoIn constructs a verifiable hash tree from token embedding fingerprints to check token counts, and uses embedding-based relevance matching to detect fabricated reasoning content. Experiments demonstrate that CoIn, when deployed as a trusted third-party auditor, can effectively detect token count inflation with a success rate reaching up to 94.7%, showing the strong ability to restore billing transparency in opaque LLM services. The dataset and code are available at https://github.com/CASE-Lab-UMD/LLM-Auditing-CoIn.

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

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

Machine learning models are increasingly used in societal applications, yet legal and privacy concerns demand that they very often be kept confidential. Consequently, there is a growing distrust about the fairness properties of these models in the minds of consumers, who are often at the receiving end of model predictions. To this end, we propose \name -- a system that uses Zero-Knowledge Proofs (a cryptographic primitive) to publicly verify the fairness of a model, while maintaining confidentiality. We also propose a fairness certification algorithm for fully-connected neural networks which is befitting to ZKPs and is used in this system. We implement \name in Gnark and demonstrate empirically that our system is practically feasible. Code is available at https://github.com/infinite-pursuits/FairProof.

We consider the problem of how a trusted, but computationally bounded agent (a 'verifier') can learn to interact with one or more powerful but untrusted agents ('provers') in order to solve a given task. More specifically, we study the case in which agents are represented using neural networks and refer to solutions of this problem as neural interactive proofs. First we introduce a unifying framework based on prover-verifier games, which generalises previously proposed interaction protocols. We then describe several new protocols for generating neural interactive proofs, and provide a theoretical comparison of both new and existing approaches. Finally, we support this theory with experiments in two domains: a toy graph isomorphism problem that illustrates the key ideas, and a code validation task using large language models. In so doing, we aim to create a foundation for future work on neural interactive proofs and their application in building safer AI 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.

Existing datasets for automated fact-checking have substantial limitations, such as relying on artificial claims, lacking annotations for evidence and intermediate reasoning, or including evidence published after the claim. In this paper we introduce AVeriTeC, a new dataset of 4,568 real-world claims covering fact-checks by 50 different organizations. Each claim is annotated with question-answer pairs supported by evidence available online, as well as textual justifications explaining how the evidence combines to produce a verdict. Through a multi-round annotation process, we avoid common pitfalls including context dependence, evidence insufficiency, and temporal leakage, and reach a substantial inter-annotator agreement of kappa=0.619 on verdicts. We develop a baseline as well as an evaluation scheme for verifying claims through several question-answering steps against the open web.

Recent advances in automated theorem proving (ATP) through LLMs have highlighted the potential of formal reasoning with Lean 4 codes. However, ATP has not yet be revolutionized by the recent posttraining scaling as demonstrated by Open AI O1/O3 and Deepseek R1. In this work, we investigate the entire posttraining of ATP, aiming to align it with breakthroughs in reasoning models in natural languages.To begin, we continual train current ATP models with a hybrid dataset, which consists of numerous statement-proof pairs, and additional data aimed at incorporating cognitive behaviors that emulate human reasoning and hypothesis refinement. Next, we explore reinforcement learning with the use of outcome reward returned by Lean 4 compiler. Through our designed continual training and reinforcement learning processes, we have successfully improved existing formal provers, including both DeepSeek-Prover-v1.5 and Goedel-Prover, achieving state-of-the-art performance in the field of whole-proof generation. For example, we achieve a 59.8% pass rate (pass@32) on MiniF2F. This is an on-going project and we will progressively update our findings, release our data and training details.

Code verification has recently found great success as a critical component in training large scale reasoning models for coding. Synthetic techniques such as self-generated test cases and reward models provide a way to enhance code capabilities beyond predefined tests. Building on these advancements, we propose new benchmarks designed to systematically evaluate the impact of synthetic verification methods on assessing solution correctness. We introduce HE-R, HE-R+, MBPP-R, and MBPP-R+, which transform existing coding benchmarks into scoring and ranking datasets to evaluate the effectiveness of synthetic verifiers. Using these benchmarks, we analyze synthetic verification methods in standard, reasoning-based, and reward-based LLMs. Our results show that recent reasoning models significantly improve test case generation and that scaling test cases enhances verification accuracy.

Proof assistants like Lean have revolutionized mathematical proof verification, ensuring high accuracy and reliability. Although large language models (LLMs) show promise in mathematical reasoning, their advancement in formal theorem proving is hindered by a lack of training data. To address this issue, we introduce an approach to generate extensive Lean 4 proof data derived from high-school and undergraduate-level mathematical competition problems. This approach involves translating natural language problems into formal statements, filtering out low-quality statements, and generating proofs to create synthetic data. After fine-tuning the DeepSeekMath 7B model on this synthetic dataset, which comprises 8 million formal statements with proofs, our model achieved whole-proof generation accuracies of 46.3% with 64 samples and 52% cumulatively on the Lean 4 miniF2F test, surpassing the baseline GPT-4 at 23.0% with 64 samples and a tree search reinforcement learning method at 41.0%. Additionally, our model successfully proved 5 out of 148 problems in the Lean 4 Formalized International Mathematical Olympiad (FIMO) benchmark, while GPT-4 failed to prove any. These results demonstrate the potential of leveraging large-scale synthetic data to enhance theorem-proving capabilities in LLMs. Both the synthetic dataset and the model will be made available to facilitate further research in this promising field.

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.

With the release of the o1 model by OpenAI, reasoning models adopting slow thinking strategies have gradually emerged. As the responses generated by such models often include complex reasoning, intermediate steps, and self-reflection, existing evaluation methods are often inadequate. They struggle to determine whether the LLM output is truly equivalent to the reference answer, and also have difficulty identifying and extracting the final answer from long, complex responses. To address this issue, we propose xVerify, an efficient answer verifier for reasoning model evaluations. xVerify demonstrates strong capability in equivalence judgment, enabling it to effectively determine whether the answers produced by reasoning models are equivalent to reference answers across various types of objective questions. To train and evaluate xVerify, we construct the VAR dataset by collecting question-answer pairs generated by multiple LLMs across various datasets, leveraging multiple reasoning models and challenging evaluation sets designed specifically for reasoning model assessment. A multi-round annotation process is employed to ensure label accuracy. Based on the VAR dataset, we train multiple xVerify models of different scales. In evaluation experiments conducted on both the test set and generalization set, all xVerify models achieve overall F1 scores and accuracy exceeding 95\%. Notably, the smallest variant, xVerify-0.5B-I, outperforms all evaluation methods except GPT-4o, while xVerify-3B-Ib surpasses GPT-4o in overall performance. These results validate the effectiveness and generalizability of xVerify.

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.

Automatic fact verification has received significant attention recently. Contemporary automatic fact-checking systems focus on estimating truthfulness using numerical scores which are not human-interpretable. A human fact-checker generally follows several logical steps to verify a verisimilitude claim and conclude whether its truthful or a mere masquerade. Popular fact-checking websites follow a common structure for fact categorization such as half true, half false, false, pants on fire, etc. Therefore, it is necessary to have an aspect-based (delineating which part(s) are true and which are false) explainable system that can assist human fact-checkers in asking relevant questions related to a fact, which can then be validated separately to reach a final verdict. In this paper, we propose a 5W framework (who, what, when, where, and why) for question-answer-based fact explainability. To that end, we present a semi-automatically generated dataset called FACTIFY-5WQA, which consists of 391, 041 facts along with relevant 5W QAs - underscoring our major contribution to this paper. A semantic role labeling system has been utilized to locate 5Ws, which generates QA pairs for claims using a masked language model. Finally, we report a baseline QA system to automatically locate those answers from evidence documents, which can serve as a baseline for future research in the field. Lastly, we propose a robust fact verification system that takes paraphrased claims and automatically validates them. The dataset and the baseline model are available at https: //github.com/ankuranii/acl-5W-QA

The standard paradigm for solving coding tasks via large language models (LLMs) is to generate-then-rank programs, where the latter step uses a verifier in the ranking process. The growing consensus is that a comprehensive verifier (e.g., a full test suite) should be prioritized over an outcome reward model (ORM) whenever possible, with little consideration given to the trade-offs involved. We aim to challenge this assumption by systematically exploring the tradeoff between speed and accuracy. We find that ORMs play a crucial role in scaling verification through trading accuracy for speed, even when a comprehensive verifier is available. Their value becomes especially apparent when used in a generate-prune-then-rank approach, where a faster but less accurate verifier removes incorrect solutions prior to ranking -- leading to a system that is 11.65x faster while only being 8.33% less accurate than the full test suite. We analyze the generate-prune-then-rank approach and show that it works by filtering out incorrect but highly ranked solutions. These findings enable the design of scalable and accurate program ranking systems.

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.

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

A key component of fact verification is thevevidence retrieval, often from multiple documents. Recent approaches use dense representations and condition the retrieval of each document on the previously retrieved ones. The latter step is performed over all the documents in the collection, requiring storing their dense representations in an index, thus incurring a high memory footprint. An alternative paradigm is retrieve-and-rerank, where documents are retrieved using methods such as BM25, their sentences are reranked, and further documents are retrieved conditioned on these sentences, reducing the memory requirements. However, such approaches can be brittle as they rely on heuristics and assume hyperlinks between documents. We propose a novel retrieve-and-rerank method for multi-hop retrieval, that consists of a retriever that jointly scores documents in the knowledge source and sentences from previously retrieved documents using an autoregressive formulation and is guided by a proof system based on natural logic that dynamically terminates the retrieval process if the evidence is deemed sufficient. This method is competitive with current state-of-the-art methods on FEVER, HoVer and FEVEROUS-S, while using 5 to 10 times less memory than competing systems. Evaluation on an adversarial dataset indicates improved stability of our approach compared to commonly deployed threshold-based methods. Finally, the proof system helps humans predict model decisions correctly more often than using the evidence alone.

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

We present WeaverBird, an intelligent dialogue system designed specifically for the finance domain. Our system harnesses a large language model of GPT architecture that has been tuned using extensive corpora of finance-related text. As a result, our system possesses the capability to understand complex financial queries, such as "How should I manage my investments during inflation?", and provide informed responses. Furthermore, our system incorporates a local knowledge base and a search engine to retrieve relevant information. The final responses are conditioned on the search results and include proper citations to the sources, thus enjoying an enhanced credibility. Through a range of finance-related questions, we have demonstrated the superior performance of our system compared to other models. To experience our system firsthand, users can interact with our live demo at https://weaverbird.ttic.edu, as well as watch our 2-min video illustration at https://www.youtube.com/watch?v=fyV2qQkX6Tc.

Large language models (LLMs) showcase impressive reasoning capabilities when coupled with Chain-of-Thought (CoT) prompting. However, the robustness of this approach warrants further investigation. In this paper, we introduce a novel scenario termed preemptive answers, where the LLM obtains an answer before engaging in reasoning. This situation can arise inadvertently or induced by malicious users by prompt injection attacks. Experiments reveal that preemptive answers significantly impair the model's reasoning capability across various CoT methods and a broad spectrum of datasets. To bolster the robustness of reasoning, we propose two measures aimed at mitigating this issue to some extent.

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

From a first-principles perspective, it may seem odd that the strongest results in foundation model fine-tuning (FT) are achieved via a relatively complex, two-stage training procedure. Specifically, one first trains a reward model (RM) on some dataset (e.g. human preferences) before using it to provide online feedback as part of a downstream reinforcement learning (RL) procedure, rather than directly optimizing the policy parameters on the dataset via offline maximum likelihood estimation. In fact, from an information-theoretic perspective, we can only lose information via passing through a reward model and cannot create any new information via on-policy sampling. To explain this discrepancy, we scrutinize several hypotheses on the value of RL in FT through both theoretical and empirical lenses. Of the hypotheses considered, we find the most support for the explanation that on problems with a generation-verification gap, the combination of the ease of learning the relatively simple RM (verifier) from the preference data, coupled with the ability of the downstream RL procedure to then filter its search space to the subset of policies (generators) that are optimal for relatively simple verifiers is what leads to the superior performance of online FT.

Recently, with the chain of thought (CoT) prompting, large language models (LLMs), e.g., GPT-3, have shown strong reasoning ability in several natural language processing tasks such as arithmetic, commonsense, and logical reasoning. However, LLMs with CoT require multi-step prompting and multi-token prediction, which is highly sensitive to individual mistakes and vulnerable to error accumulation. The above issues make the LLMs need the ability to verify the answers. In fact, after inferring conclusions in some thinking decision tasks, people often check them by re-verifying steps to avoid some mistakes. In this paper, we propose and prove that LLMs also have similar self-verification abilities. We take the conclusion obtained by CoT as one of the conditions for solving the original problem. By taking turns masking the original conditions and predicting their results, we calculate an explainable answer verification score based on whether the re-predicted conditions are correct. Experimental results demonstrate that the proposed method can improve the reasoning performance on various arithmetic, commonsense, and logical reasoning datasets. Our code is publicly available at: https://github.com/WENGSYX/Self-Verification.

One of the most widely used methods to evaluate LLMs are Multiple Choice Question (MCQ) tests. MCQ benchmarks enable the testing of LLM knowledge on almost any topic at scale as the results can be processed automatically. To help the LLM answer, a few examples called few shots can be included in the prompt. Moreover, the LLM can be asked to answer the question directly with the selected option or to first provide the reasoning and then the selected answer, which is known as chain of thought. In addition to checking whether the selected answer is correct, the evaluation can look at the LLM-estimated probability of its response as an indication of the confidence of the LLM in the response. In this paper, we study how the LLM confidence in its answer depends on whether the model has been asked to answer directly or to provide the reasoning before answering. The results of the evaluation of questions on a wide range of topics in seven different models show that LLMs are more confident in their answers when they provide reasoning before the answer. This occurs regardless of whether the selected answer is correct. Our hypothesis is that this behavior is due to the reasoning that modifies the probability of the selected answer, as the LLM predicts the answer based on the input question and the reasoning that supports the selection made. Therefore, LLM estimated probabilities seem to have intrinsic limitations that should be understood in order to use them in evaluation procedures. Interestingly, the same behavior has been observed in humans, for whom explaining an answer increases confidence in its correctness.

Large language models (LLMs) present an opportunity to scale high-quality personalized education to all. A promising approach towards this means is to build dialog tutoring models that scaffold students' problem-solving. However, even though existing LLMs perform well in solving reasoning questions, they struggle to precisely detect student's errors and tailor their feedback to these errors. Inspired by real-world teaching practice where teachers identify student errors and customize their response based on them, we focus on verifying student solutions and show how grounding to such verification improves the overall quality of tutor response generation. We collect a dataset of 1K stepwise math reasoning chains with the first error step annotated by teachers. We show empirically that finding the mistake in a student solution is challenging for current models. We propose and evaluate several verifiers for detecting these errors. Using both automatic and human evaluation we show that the student solution verifiers steer the generation model towards highly targeted responses to student errors which are more often correct with less hallucinations compared to existing baselines.

This work presents a framework for assessing whether large language models (LLMs) encode more factual knowledge in their parameters than what they express in their outputs. While a few studies hint at this possibility, none has clearly defined or demonstrated this phenomenon. We first propose a formal definition of knowledge, quantifying it for a given question as the fraction of correct-incorrect answer pairs where the correct one is ranked higher. This gives rise to external and internal knowledge, depending on the information used to score individual answer candidates: either the model's observable token-level probabilities or its intermediate computations. Hidden knowledge arises when internal knowledge exceeds external knowledge. We then present a case study, applying this framework to three popular open-weights LLMs in a closed-book QA setup. Our results indicate that: (1) LLMs consistently encode more factual knowledge internally than what they express externally, with an average gap of 40%. (2) Surprisingly, some knowledge is so deeply hidden that a model can internally know an answer perfectly, yet fail to generate it even once, despite large-scale repeated sampling of 1,000 answers. This reveals fundamental limitations in the generation capabilities of LLMs, which (3) puts a practical constraint on scaling test-time compute via repeated answer sampling in closed-book QA: significant performance improvements remain inaccessible because some answers are practically never sampled, yet if they were, we would be guaranteed to rank them first.

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

Existing datasets that contain boolean questions, such as BoolQ and TYDI QA , provide the user with a YES/NO response to the question. However, a one word response is not sufficient for an explainable system. We promote explainability by releasing a new set of annotations marking the evidence in existing TyDi QA and BoolQ datasets. We show that our annotations can be used to train a model that extracts improved evidence spans compared to models that rely on existing resources. We confirm our findings with a user study which shows that our extracted evidence spans enhance the user experience. We also provide further insight into the challenges of answering boolean questions, such as passages containing conflicting YES and NO answers, and varying degrees of relevance of the predicted evidence.

As large language models (LLMs) grow larger and more sophisticated, assessing their "reasoning" capabilities in natural language grows more challenging. Recent question answering (QA) benchmarks that attempt to assess reasoning are often limited by a narrow scope of covered situations and subject matters. We introduce WikiWhy, a QA dataset built around a novel auxiliary task: explaining why an answer is true in natural language. WikiWhy contains over 9,000 "why" question-answer-rationale triples, grounded on Wikipedia facts across a diverse set of topics. Each rationale is a set of supporting statements connecting the question to the answer. WikiWhy serves as a benchmark for the reasoning capabilities of LLMs because it demands rigorous explicit rationales for each answer to demonstrate the acquisition of implicit commonsense knowledge, which is unlikely to be easily memorized. GPT-3 baselines achieve only 38.7% human-evaluated correctness in the end-to-end answer & explain condition, leaving significant room for future improvements.

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.

Identifying how much a model {p}_{theta}(Y|X) knows about the stochastic real-world process p(Y|X) it was trained on is important to ensure it avoids producing incorrect or "hallucinated" answers or taking unsafe actions. But this is difficult for generative models because probabilistic predictions do not distinguish between per-response noise (aleatoric uncertainty) and lack of knowledge about the process (epistemic uncertainty), and existing epistemic uncertainty quantification techniques tend to be overconfident when the model underfits. We propose a general strategy for teaching a model to both approximate p(Y|X) and also estimate the remaining gaps between {p}_{theta}(Y|X) and p(Y|X): train it to predict pairs of independent responses drawn from the true conditional distribution, allow it to "cheat" by observing one response while predicting the other, then measure how much it cheats. Remarkably, we prove that being good at cheating (i.e. cheating whenever it improves your prediction) is equivalent to being second-order calibrated, a principled extension of ordinary calibration that allows us to construct provably-correct frequentist confidence intervals for p(Y|X) and detect incorrect responses with high probability. We demonstrate empirically that our approach accurately estimates how much models don't know across ambiguous image classification, (synthetic) language modeling, and partially-observable navigation tasks, outperforming existing techniques.

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

Robustness of reasoning remains a significant challenge for large language models, and addressing it is essential for the practical applicability of AI-driven reasoning systems. We introduce Semantic Self-Verification (SSV), a novel approach that addresses the key challenge in combining language models with the rigor of logical solvers: to accurately formulate the reasoning problem from natural language to the formal language of the solver. SSV uses a consistency-based approach to produce strong abstract formalizations of problems using concrete instantiations that are generated by the model and verified by the solver. In addition to significantly advancing the overall reasoning accuracy over the state-of-the-art, a key novelty that this approach presents is a feature of verification that has near-perfect precision over a significant coverage of cases, as we demonstrate on open reasoning benchmarks. We propose such *near-certain reasoning* as a new approach to reduce the need for manual verification in many cases, taking us closer to more dependable and autonomous AI reasoning systems.

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.

Machine learning models are often used to decide who will receive a loan, a job interview, or a public benefit. Standard techniques to build these models use features about people but overlook their actionability. In turn, models can assign predictions that are fixed, meaning that consumers who are denied loans, interviews, or benefits may be permanently locked out from access to credit, employment, or assistance. In this work, we introduce a formal testing procedure to flag models that assign fixed predictions that we call recourse verification. We develop machinery to reliably determine if a given model can provide recourse to its decision subjects from a set of user-specified actionability constraints. We demonstrate how our tools can ensure recourse and adversarial robustness in real-world datasets and use them to study the infeasibility of recourse in real-world lending datasets. Our results highlight how models can inadvertently assign fixed predictions that permanently bar access, and we provide tools to design algorithms that account for actionability when developing models.

The rapid advancement of ML models in critical sectors such as healthcare, finance, and security has intensified the need for robust data security, model integrity, and reliable outputs. Large multimodal foundational models, while crucial for complex tasks, present challenges in scalability, reliability, and potential misuse. Decentralized systems offer a solution by distributing workload and mitigating central points of failure, but they introduce risks of unauthorized access to sensitive data across nodes. We address these challenges with a comprehensive framework designed for responsible AI development. Our approach incorporates: 1) Zero-knowledge proofs for secure model verification, enhancing trust without compromising privacy. 2) Consensus-based verification checks to ensure consistent outputs across nodes, mitigating hallucinations and maintaining model integrity. 3) Split Learning techniques that segment models across different nodes, preserving data privacy by preventing full data access at any point. 4) Hardware-based security through trusted execution environments (TEEs) to protect data and computations. This framework aims to enhance security and privacy and improve the reliability and fairness of multimodal AI systems. Promoting efficient resource utilization contributes to more sustainable AI development. Our state-of-the-art proofs and principles demonstrate the framework's effectiveness in responsibly democratizing artificial intelligence, offering a promising approach for building secure and private foundational models.

Reinforcement learning from verifiable rewards (RLVR) has recently gained attention for its ability to elicit self-evolved reasoning capabilitie from base language models without explicit reasoning supervisions, as demonstrated by DeepSeek-R1. While prior work on RLVR has primarily focused on mathematical and coding domains, its applicability to other tasks and domains remains unexplored. In this work, we investigate whether medical reasoning can emerge from RLVR. We introduce Med-RLVR as an initial study of RLVR in the medical domain leveraging medical multiple-choice question answering (MCQA) data as verifiable labels. Our results demonstrate that RLVR is not only effective for math and coding but also extends successfully to medical question answering. Notably, Med-RLVR achieves performance comparable to traditional supervised fine-tuning (SFT) on in-distribution tasks while significantly improving out-of-distribution generalization, with an 8-point accuracy gain. Further analysis of training dynamics reveals that, with no explicit reasoning supervision, reasoning emerges from the 3B-parameter base model. These findings underscore the potential of RLVR in domains beyond math and coding, opening new avenues for its application in knowledge-intensive fields such as medicine.

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

How to design reinforcement learning (RL) tasks that effectively unleash the reasoning capability of large language models (LLMs) remains an open question. Existing RL tasks (e.g., math, programming, and constructing reasoning tasks) suffer from three key limitations: (1) Scalability. They rely heavily on human annotation or expensive LLM synthesis to generate sufficient training data. (2) Verifiability. LLMs' outputs are hard to verify automatically and reliably. (3) Controllable Difficulty. Most tasks lack fine-grained difficulty control, making it hard to train LLMs to develop reasoning ability from easy to hard. To address these limitations, we propose Saturn, a SAT-based RL framework that uses Boolean Satisfiability (SAT) problems to train and evaluate LLM reasoning. Saturn enables scalable task construction, rule-based verification, and precise difficulty control. Saturn designs a curriculum learning pipeline that continuously improves LLMs' reasoning capability by constructing SAT tasks of increasing difficulty and training LLMs from easy to hard. To ensure stable training, we design a principled mechanism to control difficulty transitions. We introduce Saturn-2.6k, a dataset of 2,660 SAT problems with varying difficulty. It supports the evaluation of how LLM reasoning changes with problem difficulty. We apply Saturn to DeepSeek-R1-Distill-Qwen and obtain Saturn-1.5B and Saturn-7B. We achieve several notable results: (1) On SAT problems, Saturn-1.5B and Saturn-7B achieve average pass@3 improvements of +14.0 and +28.1, respectively. (2) On math and programming tasks, Saturn-1.5B and Saturn-7B improve average scores by +4.9 and +1.8 on benchmarks (e.g., AIME, LiveCodeBench). (3) Compared to the state-of-the-art (SOTA) approach in constructing RL tasks, Saturn achieves further improvements of +8.8%. We release the source code, data, and models to support future research.

Current research on the Decompose-Then-Verify paradigm for evaluating the factuality of long-form text typically treats decomposition and verification in isolation, overlooking their interactions and potential misalignment. We find that existing decomposition policies, typically hand-crafted demonstrations, do not align well with downstream verifiers in terms of atomicity -- a novel metric quantifying information density -- leading to suboptimal verification results. We formulate finding the optimal decomposition policy for optimal verification as a bilevel optimization problem. To approximate a solution for this strongly NP-hard problem, we propose dynamic decomposition, a reinforcement learning framework that leverages verifier feedback to learn a policy for dynamically decomposing claims to verifier-preferred atomicity. Experimental results show that dynamic decomposition outperforms existing decomposition policies, improving verification confidence by 0.07 and accuracy by 0.12 (on a 0-1 scale) on average across varying verifiers, datasets, and atomcities of input claims.

Digital identity is unsolved: after many years of research there is still no trusted communication over the Internet. To provide identity within the context of mutual distrust, this paper presents a blockchain-based digital identity solution. Without depending upon a single trusted third party, the proposed solution achieves passport-level legally valid identity. This solution for making identities Self-Sovereign, builds on a generic provable claim model for which attestations of truth from third parties need to be collected. The claim model is then shown to be both blockchain structure and proof method agnostic. Four different implementations in support of these two claim model properties are shown to offer sub-second performance for claim creation and claim verification. Through the properties of Self-Sovereign Identity, legally valid status and acceptable performance, our solution is considered to be fit for adoption by the general public.

We present GPQA, a challenging dataset of 448 multiple-choice questions written by domain experts in biology, physics, and chemistry. We ensure that the questions are high-quality and extremely difficult: experts who have or are pursuing PhDs in the corresponding domains reach 65% accuracy (74% when discounting clear mistakes the experts identified in retrospect), while highly skilled non-expert validators only reach 34% accuracy, despite spending on average over 30 minutes with unrestricted access to the web (i.e., the questions are "Google-proof"). The questions are also difficult for state-of-the-art AI systems, with our strongest GPT-4 based baseline achieving 39% accuracy. If we are to use future AI systems to help us answer very hard questions, for example, when developing new scientific knowledge, we need to develop scalable oversight methods that enable humans to supervise their outputs, which may be difficult even if the supervisors are themselves skilled and knowledgeable. The difficulty of GPQA both for skilled non-experts and frontier AI systems should enable realistic scalable oversight experiments, which we hope can help devise ways for human experts to reliably get truthful information from AI systems that surpass human capabilities.

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

Large language models (LLMs) have proven to be very capable, but access to the best models currently rely on inference providers which introduces trust challenges -- how can we be sure that the provider is using the model configuration they claim? We propose TOPLOC, a novel method for verifiable inference that addresses this problem. TOPLOC leverages a compact locality sensitive hashing mechanism for intermediate activations which can detect unauthorized modifications to models, prompts, or precision with 100% accuracy, achieving no false positives or negatives in our empirical evaluations. Our approach is robust across diverse hardware configurations, GPU types, and algebraic reorderings, which allows for validation speeds significantly faster than the original inference. By introducing a polynomial encoding scheme, TOPLOC minimizes memory overhead of the generated commits by 1000times, requiring only 258 bytes of storage per 32 new tokens compared to the 262KB requirement of storing the token embeddings directly for Llama-3.1-8B-Instruct. Our method empowers users to verify LLM inference computations efficiently, fostering greater trust and transparency in open ecosystems and lays a foundation for decentralized and verifiable AI services.

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

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.

Large language models (LLMs) now achieve near-human performance on standard math word problem benchmarks (e.g., GSM8K), yet their true reasoning ability remains disputed. A key concern is that models often produce confident, yet unfounded, answers to unanswerable problems. We introduce TreeCut, a synthetic dataset that systematically generates infinite unanswerable math word problems and their answerable counterparts, by representing each question as a tree and removing chosen necessary conditions. Experiments show TreeCut effectively induce hallucinations in large language models, including GPT-4o and o3-mini, with rates of 64% and 44% in their respective worst-case scenarios under zero-shot setting. Further analysis highlights that deeper or more complex trees, composite item names, and removing necessary condition near the middle of a path all increase the likelihood of hallucinations, underscoring the persistent challenges LLMs face in identifying unanswerable math problems. The dataset generation code and sample data are available at https://github.com/j-bagel/treecut-math.

As Large Language Models (LLMs) become more pervasive across various users and scenarios, identifying potential issues when using these models becomes essential. Examples of such issues include: bias, inconsistencies, and hallucination. Although auditing the LLM for these problems is often warranted, such a process is neither easy nor accessible for most. An effective method is to probe the LLM using different versions of the same question. This could expose inconsistencies in its knowledge or operation, indicating potential for bias or hallucination. However, to operationalize this auditing method at scale, we need an approach to create those probes reliably and automatically. In this paper we propose the LLMAuditor framework which is an automatic, and scalable solution, where one uses a different LLM along with human-in-the-loop (HIL). This approach offers verifiability and transparency, while avoiding circular reliance on the same LLM, and increasing scientific rigor and generalizability. Specifically, LLMAuditor includes two phases of verification using humans: standardized evaluation criteria to verify responses, and a structured prompt template to generate desired probes. A case study using questions from the TruthfulQA dataset demonstrates that we can generate a reliable set of probes from one LLM that can be used to audit inconsistencies in a different LLM. This process is enhanced by our structured prompt template with HIL, which not only boosts the reliability of our approach in auditing but also yields the delivery of less hallucinated results. The novelty of our research stems from the development of a comprehensive, general-purpose framework that includes a HIL verified prompt template for auditing responses generated by LLMs.

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

Watermarking has emerged as a promising way to detect LLM-generated text, by augmenting LLM generations with later detectable signals. Recent work has proposed multiple families of watermarking schemes, several of which focus on preserving the LLM distribution. This distribution-preservation property is motivated by the fact that it is a tractable proxy for retaining LLM capabilities, as well as the inherently implied undetectability of the watermark by downstream users. Yet, despite much discourse around undetectability, no prior work has investigated the practical detectability of any of the current watermarking schemes in a realistic black-box setting. In this work we tackle this for the first time, developing rigorous statistical tests to detect the presence, and estimate parameters, of all three popular watermarking scheme families, using only a limited number of black-box queries. We experimentally confirm the effectiveness of our methods on a range of schemes and a diverse set of open-source models. Further, we validate the feasibility of our tests on real-world APIs. Our findings indicate that current watermarking schemes are more detectable than previously believed.

Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achieve over 90\% accuracy on popular benchmarks like MMLU, limiting informed measurement of state-of-the-art LLM capabilities. In response, we introduce Humanity's Last Exam (HLE), a multi-modal benchmark at the frontier of human knowledge, designed to be the final closed-ended academic benchmark of its kind with broad subject coverage. HLE consists of 3,000 questions across dozens of subjects, including mathematics, humanities, and the natural sciences. HLE is developed globally by subject-matter experts and consists of multiple-choice and short-answer questions suitable for automated grading. Each question has a known solution that is unambiguous and easily verifiable, but cannot be quickly answered via internet retrieval. State-of-the-art LLMs demonstrate low accuracy and calibration on HLE, highlighting a significant gap between current LLM capabilities and the expert human frontier on closed-ended academic questions. To inform research and policymaking upon a clear understanding of model capabilities, we publicly release HLE at https://lastexam.ai.

While Large Language Models (LLMs) demonstrate impressive performance in mathematics, existing math benchmarks come with significant limitations. Many focus on problems with fixed ground-truth answers, and are often saturated due to problem simplicity or the viability of guessing or memorization. Crucially, they capture only a narrow subset of relevant math problems. To address this research gap, we introduce \mc, a new benchmark of 126 challenging problems sourced from various math competitions, which targets constructive proofs, a widely encountered problem type requiring the construction of mathematical objects with specific properties. These proofs are particularly suitable for LLM evaluation, as solution correctness can be easily verified. Our automated verifiers also enable MathConstruct to generate problem variations, used to evaluate robustness. State-of-the-art LLMs solve only 54% of MathConstruct problems, highlighting its complexity and importance for LLM evaluation.

Reinforcement learning with verifiable rewards (RLVR) has become a key technique for enhancing large language models (LLMs), with verification engineering playing a central role. However, best practices for RL in instruction following remain underexplored. In this work, we explore the verification challenge in RL for instruction following and propose VerIF, a verification method that combines rule-based code verification with LLM-based verification from a large reasoning model (e.g., QwQ-32B). To support this approach, we construct a high-quality instruction-following dataset, VerInstruct, containing approximately 22,000 instances with associated verification signals. We apply RL training with VerIF to two models, achieving significant improvements across several representative instruction-following benchmarks. The trained models reach state-of-the-art performance among models of comparable size and generalize well to unseen constraints. We further observe that their general capabilities remain unaffected, suggesting that RL with VerIF can be integrated into existing RL recipes to enhance overall model performance. We have released our datasets, codes, and models to facilitate future research at https://github.com/THU-KEG/VerIF.

Large language models (LLMs) have shown remarkable reasoning capabilities given chain-of-thought prompts (examples with intermediate reasoning steps). Existing benchmarks measure reasoning ability indirectly, by evaluating accuracy on downstream tasks such as mathematical reasoning. However, it is unclear how these models obtain the answers and whether they rely on simple heuristics rather than the generated chain-of-thought. To enable systematic exploration of the reasoning ability of LLMs, we present a new synthetic question-answering dataset called PrOntoQA, where each example is generated from a synthetic world model represented in first-order logic. This allows us to parse the generated chain-of-thought into symbolic proofs for formal analysis. Our analysis on InstructGPT and GPT-3 shows that LLMs are quite capable of making correct individual deduction steps, and so are generally capable of reasoning, even in fictional contexts. However, they have difficulty with proof planning: When multiple valid deduction steps are available, they are not able to systematically explore the different options.

Recent studies have shown that reinforcement learning with verifiable rewards (RLVR) enhances overall accuracy but fails to improve capability, while distillation can improve both. In this paper, we investigate the mechanisms behind these phenomena. First, we demonstrate that RLVR does not improve capability because it focuses on improving the accuracy of the less-difficult questions to the detriment of the accuracy of the most difficult questions, thereby leading to no improvement in capability. Second, we find that RLVR does not merely increase the success probability for the less difficult questions, but in our small model settings produces quality responses that were absent in its output distribution before training. In addition, we show these responses are neither noticeably longer nor feature more reflection-related keywords, underscoring the need for more reliable indicators of response quality. Third, we show that while distillation reliably improves accuracy by learning strong reasoning patterns, it only improves capability when new knowledge is introduced. Moreover, when distilling only with reasoning patterns and no new knowledge, the accuracy of the less-difficult questions improves to the detriment of the most difficult questions, similar to RLVR. Together, these findings offer a clearer understanding of how RLVR and distillation shape reasoning behavior in language models.

Teaching Visual Question Answering (VQA) models to abstain from unanswerable questions is indispensable for building a trustworthy AI system. Existing studies, though have explored various aspects of VQA, yet marginally ignored this particular attribute. This paper aims to bridge the research gap by contributing a comprehensive dataset, called UNK-VQA. The dataset is specifically designed to address the challenge of questions that can be unanswerable. To this end, we first augment the existing data via deliberate perturbations on either the image or question. In specific, we carefully ensure that the question-image semantics remain close to the original unperturbed distribution. By means of this, the identification of unanswerable questions becomes challenging, setting our dataset apart from others that involve mere image replacement. We then extensively evaluate the zero- and few-shot performance of several emerging multi-modal large models and discover significant limitations of them when applied to our dataset. Additionally, we also propose a straightforward method to tackle these unanswerable questions. This dataset, we believe, will serve as a valuable benchmark for enhancing the abstention capability of VQA models, thereby leading to increased trustworthiness of AI systems.

We describe a Question Answering (QA) dataset that contains complex questions with conditional answers, i.e. the answers are only applicable when certain conditions apply. We call this dataset ConditionalQA. In addition to conditional answers, the dataset also features: (1) long context documents with information that is related in logically complex ways; (2) multi-hop questions that require compositional logical reasoning; (3) a combination of extractive questions, yes/no questions, questions with multiple answers, and not-answerable questions; (4) questions asked without knowing the answers. We show that ConditionalQA is challenging for many of the existing QA models, especially in selecting answer conditions. We believe that this dataset will motivate further research in answering complex questions over long documents. Data and leaderboard are publicly available at https://github.com/haitian-sun/ConditionalQA.

Large language models (LLMs) have demonstrated impressive performance on several tasks and are increasingly deployed in real-world applications. However, especially in high-stakes settings, it becomes vital to know when the output of an LLM may be unreliable. Depending on whether an answer is trustworthy, a system can then choose to route the question to another expert, or otherwise fall back on a safe default behavior. In this work, we study the extent to which LLMs can reliably indicate confidence in their answers, and how this notion of confidence can translate into downstream accuracy gains. We propose Self-REF, a lightweight training strategy to teach LLMs to express confidence in whether their answers are correct in a reliable manner. Self-REF introduces confidence tokens into the LLM, from which a confidence score can be extracted. Compared to conventional approaches such as verbalizing confidence and examining token probabilities, we demonstrate empirically that confidence tokens show significant improvements in downstream routing and rejection learning tasks.

Large Language Models (LLMs) have exploded a new heatwave of AI, for their ability to engage end-users in human-level conversations with detailed and articulate answers across many knowledge domains. In response to their fast adoption in many industrial applications, this survey concerns their safety and trustworthiness. First, we review known vulnerabilities of the LLMs, categorising them into inherent issues, intended attacks, and unintended bugs. Then, we consider if and how the Verification and Validation (V&V) techniques, which have been widely developed for traditional software and deep learning models such as convolutional neural networks, can be integrated and further extended throughout the lifecycle of the LLMs to provide rigorous analysis to the safety and trustworthiness of LLMs and their applications. Specifically, we consider four complementary techniques: falsification and evaluation, verification, runtime monitoring, and ethical use. Considering the fast development of LLMs, this survey does not intend to be complete (although it includes 300 references), especially when it comes to the applications of LLMs in various domains, but rather a collection of organised literature reviews and discussions to support the quick understanding of the safety and trustworthiness issues from the perspective of V&V.

Circuits based on sum-product structure have become a ubiquitous representation to compactly encode knowledge, from Boolean functions to probability distributions. By imposing constraints on the structure of such circuits, certain inference queries become tractable, such as model counting and most probable configuration. Recent works have explored analyzing probabilistic and causal inference queries as compositions of basic operators to derive tractability conditions. In this paper, we take an algebraic perspective for compositional inference, and show that a large class of queries - including marginal MAP, probabilistic answer set programming inference, and causal backdoor adjustment - correspond to a combination of basic operators over semirings: aggregation, product, and elementwise mapping. Using this framework, we uncover simple and general sufficient conditions for tractable composition of these operators, in terms of circuit properties (e.g., marginal determinism, compatibility) and conditions on the elementwise mappings. Applying our analysis, we derive novel tractability conditions for many such compositional queries. Our results unify tractability conditions for existing problems on circuits, while providing a blueprint for analysing novel compositional inference queries.

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

We show that reinforcement learning with verifiable rewards (RLVR) can elicit strong mathematical reasoning in certain models even with spurious rewards that have little, no, or even negative correlation with the correct answer. For example, RLVR improves MATH-500 performance for Qwen2.5-Math-7B in absolute points by 21.4% (random reward), 13.8% (format reward), 24.1% (incorrect label), 26.0% (1-shot RL), and 27.1% (majority voting) -- nearly matching the 29.1% gained with ground truth rewards. However, the spurious rewards that work for Qwen often fail to yield gains with other model families like Llama3 or OLMo2. In particular, we find code reasoning -- thinking in code without actual code execution -- to be a distinctive Qwen2.5-Math behavior that becomes significantly more frequent after RLVR, from 65% to over 90%, even with spurious rewards. Overall, we hypothesize that, given the lack of useful reward signal, RLVR must somehow be surfacing useful reasoning representations learned during pretraining, although the exact mechanism remains a topic for future work. We suggest that future RLVR research should possibly be validated on diverse models rather than a single de facto choice, as we show that it is easy to get significant performance gains on Qwen models even with completely spurious reward signals.

We present SimpleQA, a benchmark that evaluates the ability of language models to answer short, fact-seeking questions. We prioritized two properties in designing this eval. First, SimpleQA is challenging, as it is adversarially collected against GPT-4 responses. Second, responses are easy to grade, because questions are created such that there exists only a single, indisputable answer. Each answer in SimpleQA is graded as either correct, incorrect, or not attempted. A model with ideal behavior would get as many questions correct as possible while not attempting the questions for which it is not confident it knows the correct answer. SimpleQA is a simple, targeted evaluation for whether models "know what they know," and our hope is that this benchmark will remain relevant for the next few generations of frontier models. SimpleQA can be found at https://github.com/openai/simple-evals.

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.

Modern Question Answering (QA) and Reasoning approaches based on Large Language Models (LLMs) commonly use prompting techniques, such as Chain-of-Thought (CoT), assuming the resulting generation will have a more granular exploration and reasoning over the question space and scope. However, such methods struggle with generating outputs that are faithful to the intermediate chain of reasoning produced by the model. On the other end of the spectrum, neuro-symbolic methods such as Faithful CoT (F-CoT) propose to combine LLMs with external symbolic solvers. While such approaches boast a high degree of faithfulness, they usually require a model trained for code generation and struggle with tasks that are ambiguous or hard to formalise strictly. We introduce Faithful Logic-Aided Reasoning and Exploration (\ours), a novel interpretable approach for traversing the problem space using task decompositions. We use the LLM to plan a solution, soft-formalise the query into facts and predicates using a logic programming code and simulate that code execution using an exhaustive multi-hop search over the defined space. Our method allows us to compute the faithfulness of the reasoning process w.r.t. the generated code and analyse the steps of the multi-hop search without relying on external solvers. Our methods achieve SOTA results on 7 out of 9 diverse reasoning benchmarks. We also show that model faithfulness positively correlates with overall performance and further demonstrate that {\ours} allows pinpointing the decisive factors sufficient for and leading to the correct answer with optimal reasoning during the multi-hop search.

Generation of plausible yet incorrect factual information, termed hallucination, is an unsolved issue in large language models. We study the ability of language models to deliberate on the responses they give in order to correct their mistakes. We develop the Chain-of-Verification (CoVe) method whereby the model first (i) drafts an initial response; then (ii) plans verification questions to fact-check its draft; (iii) answers those questions independently so the answers are not biased by other responses; and (iv) generates its final verified response. In experiments, we show CoVe decreases hallucinations across a variety of tasks, from list-based questions from Wikidata, closed book MultiSpanQA and longform text generation.

Ambiguous questions are a challenge for Question Answering models, as they require answers that cover multiple interpretations of the original query. To this end, these models are required to generate long-form answers that often combine conflicting pieces of information. Although recent advances in the field have shown strong capabilities in generating fluent responses, certain research questions remain unanswered. Does model/data scaling improve the answers' quality? Do automated metrics align with human judgment? To what extent do these models ground their answers in evidence? In this study, we aim to thoroughly investigate these aspects, and provide valuable insights into the limitations of the current approaches. To aid in reproducibility and further extension of our work, we open-source our code at https://github.com/din0s/ambig_lfqa.

Claim verification is essential in combating misinformation, and large language models (LLMs) have recently emerged in this area as powerful tools for assessing the veracity of claims using external knowledge. Existing LLM-based methods for claim verification typically adopt a Decompose-Then-Verify paradigm, which involves decomposing complex claims into several independent sub-claims and verifying each sub-claim separately. However, this paradigm often introduces errors during the claim decomposition process. To mitigate these errors, we propose to develop the Chain-of-Thought (CoT)-Verify paradigm, which leverages LLM reasoning methods to generate CoT-verification paths for the original complex claim without requiring decompositions into sub-claims and separate verification stages. The CoT-Verify paradigm allows us to propose a natural fine-tuning method called Reasoning-CV to enhance the verification capabilities in LLMs. Reasoning-CV includes a supervised fine-tuning (SFT) stage and a self-improvement direct preference optimization (DPO) stage. Utilizing only an 8B pre-trained LLM, Reasoning-CV demonstrates superior knowledge-assisted claim verification performances compared to existing Decompose-Then-Verify methods, as well as powerful black-box LLMs such as GPT-4o+CoT and o1-preview. Our code is available.

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.

For Large Language Models (LLMs) to be reliably deployed in both everyday and high-stakes domains, knowing when not to answer is equally critical as answering correctly. Real-world user queries, which can be underspecified, ill-posed, or fundamentally unanswerable, require LLMs to reason about uncertainty and selectively abstain -- i.e., refuse to answer definitively. However, abstention remains understudied, without a systematic evaluation framework for modern LLMs. In this work, we introduce AbstentionBench, a large-scale benchmark for holistically evaluating abstention across 20 diverse datasets, including questions with unknown answers, underspecification, false premises, subjective interpretations, and outdated information. Evaluating 20 frontier LLMs reveals abstention is an unsolved problem, and one where scaling models is of little use. While recent reasoning LLMs have shown impressive results in complex problem solving, surprisingly, we find that reasoning fine-tuning degrades abstention (by 24% on average), even for math and science domains on which reasoning models are explicitly trained. We find that while a carefully crafted system prompt can boost abstention in practice, it does not resolve models' fundamental inability to reason about uncertainty. We release AbstentionBench to foster research into advancing LLM reliability.

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

A promising approach for improving reasoning in large language models is to use process reward models (PRMs). PRMs provide feedback at each step of a multi-step reasoning trace, potentially improving credit assignment over outcome reward models (ORMs) that only provide feedback at the final step. However, collecting dense, per-step human labels is not scalable, and training PRMs from automatically-labeled data has thus far led to limited gains. To improve a base policy by running search against a PRM or using it as dense rewards for reinforcement learning (RL), we ask: "How should we design process rewards?". Our key insight is that, to be effective, the process reward for a step should measure progress: a change in the likelihood of producing a correct response in the future, before and after taking the step, corresponding to the notion of step-level advantages in RL. Crucially, this progress should be measured under a prover policy distinct from the base policy. We theoretically characterize the set of good provers and our results show that optimizing process rewards from such provers improves exploration during test-time search and online RL. In fact, our characterization shows that weak prover policies can substantially improve a stronger base policy, which we also observe empirically. We validate our claims by training process advantage verifiers (PAVs) to predict progress under such provers, and show that compared to ORMs, test-time search against PAVs is >8% more accurate, and 1.5-5times more compute-efficient. Online RL with dense rewards from PAVs enables one of the first results with 5-6times gain in sample efficiency, and >6% gain in accuracy, over ORMs.

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

This paper investigates the capabilities of Large Language Models (LLMs) in the context of understanding their own knowledge and measuring their uncertainty. We argue this is an important feature for mitigating hallucinations. Specifically, we focus on addressing known-unknown questions, characterized by high uncertainty due to the absence of definitive answers. To facilitate our study, we collect a dataset with new Known-Unknown Questions (KUQ) and propose a novel categorization scheme to elucidate the sources of uncertainty. Subsequently, we assess the LLMs' ability to differentiate between known and unknown questions and classify them accordingly. Moreover, we evaluate the quality of their answers in an Open-Ended QA setting. To quantify the uncertainty expressed in the answers, we create a semantic evaluation method that measures the model's accuracy in expressing uncertainty between known vs unknown questions.

Recent advances such as OpenAI-o1 and DeepSeek R1 have demonstrated the potential of Reinforcement Learning (RL) to enhance reasoning abilities in Large Language Models (LLMs). While open-source replication efforts have primarily focused on mathematical and coding domains, methods and resources for developing general reasoning capabilities remain underexplored. This gap is partly due to the challenge of collecting diverse and verifiable reasoning data suitable for RL. We hypothesize that logical reasoning is critical for developing general reasoning capabilities, as logic forms a fundamental building block of reasoning. In this work, we present SynLogic, a data synthesis framework and dataset that generates diverse logical reasoning data at scale, encompassing 35 diverse logical reasoning tasks. The SynLogic approach enables controlled synthesis of data with adjustable difficulty and quantity. Importantly, all examples can be verified by simple rules, making them ideally suited for RL with verifiable rewards. In our experiments, we validate the effectiveness of RL training on the SynLogic dataset based on 7B and 32B models. SynLogic leads to state-of-the-art logical reasoning performance among open-source datasets, surpassing DeepSeek-R1-Distill-Qwen-32B by 6 points on BBEH. Furthermore, mixing SynLogic data with mathematical and coding tasks improves the training efficiency of these domains and significantly enhances reasoning generalization. Notably, our mixed training model outperforms DeepSeek-R1-Zero-Qwen-32B across multiple benchmarks. These findings position SynLogic as a valuable resource for advancing the broader reasoning capabilities of LLMs. We open-source both the data synthesis pipeline and the SynLogic dataset at https://github.com/MiniMax-AI/SynLogic.

We introduce FAITHSCORE (Faithfulness to Atomic Image Facts Score), a reference-free and fine-grained evaluation metric that measures the faithfulness of the generated free-form answers from large vision-language models (LVLMs). The FAITHSCORE evaluation first identifies sub-sentences containing descriptive statements that need to be verified, then extracts a comprehensive list of atomic facts from these sub-sentences, and finally conducts consistency verification between fine-grained atomic facts and the input image. Meta-evaluation demonstrates that our metric highly correlates with human judgments of faithfulness. We collect two benchmark datasets (i.e. LLaVA-1k and MSCOCO-Cap) for evaluating LVLMs instruction-following hallucinations. We measure hallucinations in state-of-the-art LVLMs with FAITHSCORE on the datasets. Results reveal that current systems are prone to generate hallucinated content unfaithful to the image, which leaves room for future improvements. Further, we find that current LVLMs despite doing well on color and counting, still struggle with long answers, relations, and multiple objects.

It is important that consumers and regulators can verify the provenance of large neural models to evaluate their capabilities and risks. We introduce the concept of a "Proof-of-Training-Data": any protocol that allows a model trainer to convince a Verifier of the training data that produced a set of model weights. Such protocols could verify the amount and kind of data and compute used to train the model, including whether it was trained on specific harmful or beneficial data sources. We explore efficient verification strategies for Proof-of-Training-Data that are compatible with most current large-model training procedures. These include a method for the model-trainer to verifiably pre-commit to a random seed used in training, and a method that exploits models' tendency to temporarily overfit to training data in order to detect whether a given data-point was included in training. We show experimentally that our verification procedures can catch a wide variety of attacks, including all known attacks from the Proof-of-Learning literature.

Despite substantial advances in scaling test-time compute, an ongoing debate in the community is how it should be scaled up to enable continued and efficient improvements with scaling. There are largely two approaches: first, distilling successful search or thinking traces; and second, using verification (e.g., 0/1 outcome rewards, reward models, or verifiers) to guide reinforcement learning (RL) and search algorithms. In this paper, we prove that finetuning LLMs with verifier-based (VB) methods based on RL or search is far superior to verifier-free (VF) approaches based on distilling or cloning search traces, given a fixed amount of compute/data budget. Further, we show that as we scale test-time compute (measured as the output token length) and training data, suboptimality of VF methods scales poorly compared to VB when the base pre-trained LLM presents a heterogeneous distribution over correct solution traces (e.g., different lengths, styles, etc.) and admits a non-sharp distribution over rewards on traces sampled from it. We formalize this condition using anti-concentration [Erdos, 1945]. This implies a stronger result that VB methods scale better asymptotically, with the performance gap between VB and VF methods widening as test-time budget grows. We corroborate our theory empirically on both didactic and math reasoning problems with 3/8/32B-sized pre-trained LLMs, where we find verification is crucial for scaling test-time compute.

Since the proliferation of LLMs, there have been concerns about their misuse for harmful content creation and spreading. Recent studies justify such fears, providing evidence of LLM vulnerabilities and high potential of their misuse. Humans are no longer able to distinguish between high-quality machine-generated and authentic human-written texts. Therefore, it is crucial to develop automated means to accurately detect machine-generated content. It would enable to identify such content in online information space, thus providing an additional information about its credibility. This work addresses the problem by proposing a robust fine-tuning process of LLMs for the detection task, making the detectors more robust against obfuscation and more generalizable to out-of-distribution data.

Reinforcement learning (RL) has recently emerged as a compelling approach for enhancing the reasoning capabilities of large language models (LLMs), where an LLM generator serves as a policy guided by a verifier (reward model). However, current RL post-training methods for LLMs typically use verifiers that are fixed (rule-based or frozen pretrained) or trained discriminatively via supervised fine-tuning (SFT). Such designs are susceptible to reward hacking and generalize poorly beyond their training distributions. To overcome these limitations, we propose Tango, a novel framework that uses RL to concurrently train both an LLM generator and a verifier in an interleaved manner. A central innovation of Tango is its generative, process-level LLM verifier, which is trained via RL and co-evolves with the generator. Importantly, the verifier is trained solely based on outcome-level verification correctness rewards without requiring explicit process-level annotations. This generative RL-trained verifier exhibits improved robustness and superior generalization compared to deterministic or SFT-trained verifiers, fostering effective mutual reinforcement with the generator. Extensive experiments demonstrate that both components of Tango achieve state-of-the-art results among 7B/8B-scale models: the generator attains best-in-class performance across five competition-level math benchmarks and four challenging out-of-domain reasoning tasks, while the verifier leads on the ProcessBench dataset. Remarkably, both components exhibit particularly substantial improvements on the most difficult mathematical reasoning problems. Code is at: https://github.com/kaiwenzha/rl-tango.

Recent advances such as DeepSeek R1-Zero highlight the effectiveness of incentive training, a reinforcement learning paradigm that computes rewards solely based on the final answer part of a language model's output, thereby encouraging the generation of intermediate reasoning steps. However, these methods fundamentally rely on external verifiers, which limits their applicability to domains like mathematics and coding where such verifiers are readily available. Although reward models can serve as verifiers, they require high-quality annotated data and are costly to train. In this work, we propose NOVER, NO-VERifier Reinforcement Learning, a general reinforcement learning framework that requires only standard supervised fine-tuning data with no need for an external verifier. NOVER enables incentive training across a wide range of text-to-text tasks and outperforms the model of the same size distilled from large reasoning models such as DeepSeek R1 671B by 7.7 percent. Moreover, the flexibility of NOVER enables new possibilities for optimizing large language models, such as inverse incentive training.

Readers of academic research papers often read with the goal of answering specific questions. Question Answering systems that can answer those questions can make consumption of the content much more efficient. However, building such tools requires data that reflect the difficulty of the task arising from complex reasoning about claims made in multiple parts of a paper. In contrast, existing information-seeking question answering datasets usually contain questions about generic factoid-type information. We therefore present QASPER, a dataset of 5,049 questions over 1,585 Natural Language Processing papers. Each question is written by an NLP practitioner who read only the title and abstract of the corresponding paper, and the question seeks information present in the full text. The questions are then answered by a separate set of NLP practitioners who also provide supporting evidence to answers. We find that existing models that do well on other QA tasks do not perform well on answering these questions, underperforming humans by at least 27 F1 points when answering them from entire papers, motivating further research in document-grounded, information-seeking QA, which our dataset is designed to facilitate.

This paper investigates the mathematical reasoning capabilities of large language models (LLMs) using 50 newly constructed high-school-level word problems. Unlike prior studies that focus solely on answer correctness, we rigorously analyze both final answers and solution steps to identify reasoning failures. Evaluating eight state-of-the-art models - including Mixtral, Llama, Gemini, GPT-4o, and OpenAI's o1 variants - we find that while newer models (e.g., o3-mini, deepseek-r1) achieve higher accuracy, all models exhibit errors in spatial reasoning, strategic planning, and arithmetic, sometimes producing correct answers through flawed logic. Common failure modes include unwarranted assumptions, over-reliance on numerical patterns, and difficulty translating physical intuition into mathematical steps. Manual analysis reveals that models struggle with problems requiring multi-step deduction or real-world knowledge, despite possessing broad mathematical knowledge. Our results underscore the importance of evaluating reasoning processes, not just answers, and caution against overestimating LLMs' problem-solving proficiency. The study highlights persistent gaps in LLMs' generalization abilities, emphasizing the need for targeted improvements in structured reasoning and constraint handling.

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

Fact verification aims to automatically probe the veracity of a claim based on several pieces of evidence. Existing works are always engaging in the accuracy improvement, let alone the explainability, a critical capability of fact verification system. Constructing an explainable fact verification system in a complex multi-hop scenario is consistently impeded by the absence of a relevant high-quality dataset. Previous dataset either suffer from excessive simplification or fail to incorporate essential considerations for explainability. To address this, we present EX-FEVER, a pioneering dataset for multi-hop explainable fact verification. With over 60,000 claims involving 2-hop and 3-hop reasoning, each is created by summarizing and modifying information from hyperlinked Wikipedia documents. Each instance is accompanied by a veracity label and an explanation that outlines the reasoning path supporting the veracity classification. Additionally, we demonstrate a novel baseline system on our EX-FEVER dataset, showcasing document retrieval, explanation generation, and claim verification and observe that existing fact verification models trained on previous datasets struggle to perform well on our dataset. Furthermore, we highlight the potential of utilizing Large Language Models in the fact verification task. We hope our dataset could make a significant contribution by providing ample opportunities to explore the integration of natural language explanations in the domain of fact verification.

The integration of retrieved passages and large language models (LLMs), such as ChatGPTs, has significantly contributed to improving open-domain question answering. However, there is still a lack of exploration regarding the optimal approach for incorporating retrieved passages into the answer generation process. This paper aims to fill this gap by investigating different methods of combining retrieved passages with LLMs to enhance answer generation. We begin by examining the limitations of a commonly-used concatenation approach. Surprisingly, this approach often results in generating "unknown" outputs, even when the correct document is among the top-k retrieved passages. To address this issue, we explore four alternative strategies for integrating the retrieved passages with the LLMs. These strategies include two single-round methods that utilize chain-of-thought reasoning and two multi-round strategies that incorporate feedback loops. Through comprehensive analyses and experiments, we provide insightful observations on how to effectively leverage retrieved passages to enhance the answer generation capability of LLMs.

The use of Large Language Models (LLMs) has increased significantly with users frequently asking questions to chatbots. In the time when information is readily accessible, it is crucial to stimulate and preserve human cognitive abilities and maintain strong reasoning skills. This paper addresses such challenges by promoting the use of hints as an alternative or a supplement to direct answers. We first introduce a manually constructed hint dataset, WikiHint, which is based on Wikipedia and includes 5,000 hints created for 1,000 questions. We then finetune open-source LLMs such as LLaMA-3.1 for hint generation in answer-aware and answeragnostic contexts. We assess the effectiveness of the hints with human participants who answer questions with and without the aid of hints. Additionally, we introduce a lightweight evaluation method, HintRank, to evaluate and rank hints in both answeraware and answer-agnostic settings. Our findings show that (a) the dataset helps generate more effective hints, (b) including answer information along with questions generally improves quality of generated hints, and (c) encoder-based models perform better than decoder-based models in hint ranking.

One of the emerging research trends in natural language understanding is machine reading comprehension (MRC) which is the task to find answers to human questions based on textual data. Existing Vietnamese datasets for MRC research concentrate solely on answerable questions. However, in reality, questions can be unanswerable for which the correct answer is not stated in the given textual data. To address the weakness, we provide the research community with a benchmark dataset named UIT-ViQuAD 2.0 for evaluating the MRC task and question answering systems for the Vietnamese language. We use UIT-ViQuAD 2.0 as a benchmark dataset for the challenge on Vietnamese MRC at the Eighth Workshop on Vietnamese Language and Speech Processing (VLSP 2021). This task attracted 77 participant teams from 34 universities and other organizations. In this article, we present details of the organization of the challenge, an overview of the methods employed by shared-task participants, and the results. The highest performances are 77.24% in F1-score and 67.43% in Exact Match on the private test set. The Vietnamese MRC systems proposed by the top 3 teams use XLM-RoBERTa, a powerful pre-trained language model based on the transformer architecture. The UIT-ViQuAD 2.0 dataset motivates researchers to further explore the Vietnamese machine reading comprehension task and related tasks such as question answering, question generation, and natural language inference.

Verification is crucial for effective mathematical reasoning. We present a new temporal consistency method where verifiers iteratively refine their judgments based on the previous assessment. Unlike one-round verification or multi-model debate approaches, our method leverages consistency in a sequence of self-reflection actions to improve verification accuracy. Empirical evaluations across diverse mathematical process error identification benchmarks (Mathcheck, ProcessBench, and PRM800K) show consistent performance improvements over baseline methods. When applied to the recent DeepSeek R1 distilled models, our method demonstrates strong performance, enabling 7B/8B distilled models to outperform all 70B/72B models and GPT-4o on ProcessBench. Notably, the distilled 14B model with our method achieves performance comparable to Deepseek-R1. Our codes are available at https://github.com/jcguo123/Temporal-Consistency

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

Traditional language model-based theorem proving assumes that by training on a sufficient amount of formal proof data, a model will learn to prove theorems. Our key observation is that a wealth of informal information that is not present in formal proofs can be useful for learning to prove theorems. For instance, humans think through steps of a proof, but this thought process is not visible in the resulting code. We present Lean-STaR, a framework for training language models to produce informal thoughts prior to each step of a proof, thereby boosting the model's theorem-proving capabilities. Lean-STaR uses retrospective ground-truth tactics to generate synthetic thoughts for training the language model. At inference time, the trained model directly generates the thoughts prior to the prediction of the tactics in each proof step. Building on the self-taught reasoner framework, we then apply expert iteration to further fine-tune the model on the correct proofs it samples and verifies using the Lean solver. Lean-STaR achieves state-of-the-art results on the miniF2F-test benchmark within the Lean theorem proving environment, significantly outperforming base models (43.4% rightarrow 46.3%, Pass@64). We also analyze the impact of the augmented thoughts on various aspects of the theorem proving process, providing insights into their effectiveness.

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

Scaling the test-time compute of large language models has demonstrated impressive performance on reasoning benchmarks. However, existing evaluations of test-time scaling make the strong assumption that a reasoning system should always give an answer to any question provided. This overlooks concerns about whether a model is confident in its answer, and whether it is appropriate to always provide a response. To address these concerns, we extract confidence scores during reasoning for thresholding model responses. We find that increasing compute budget at inference time not only helps models answer more questions correctly, but also increases confidence in correct responses. We then extend the current paradigm of zero-risk responses during evaluation by considering settings with non-zero levels of response risk, and suggest a recipe for reporting evaluations under these settings.

From a simple text prompt, generative-AI image models can create stunningly realistic and creative images bounded, it seems, by only our imagination. These models have achieved this remarkable feat thanks, in part, to the ingestion of billions of images collected from nearly every corner of the internet. Many creators have understandably expressed concern over how their intellectual property has been ingested without their permission or a mechanism to opt out of training. As a result, questions of fair use and copyright infringement have quickly emerged. We describe a method that allows us to determine if a model was trained on a specific image or set of images. This method is computationally efficient and assumes no explicit knowledge of the model architecture or weights (so-called black-box membership inference). We anticipate that this method will be crucial for auditing existing models and, looking ahead, ensuring the fairer development and deployment of generative AI models.

Large language models (LLMs) have demonstrated solid zero-shot reasoning capabilities, which is reflected in their performance on the current test tasks. This calls for a more challenging benchmark requiring highly advanced reasoning ability to be solved. In this paper, we introduce such a benchmark, consisting of 191 long-form (1200 words on average) mystery narratives constructed as detective puzzles. Puzzles are sourced from the "5 Minute Mystery" platform and include a multiple-choice question for evaluation. Only 47% of humans solve a puzzle successfully on average, while the best human solvers achieve over 80% success rate. We show that GPT-3 models barely outperform random on this benchmark (with 28% accuracy) while state-of-the-art GPT-4 solves only 38% of puzzles. This indicates that there is still a significant gap in the deep reasoning abilities of LLMs and humans and highlights the need for further research in this area. Our work introduces a challenging benchmark for future studies on reasoning in language models and contributes to a better understanding of the limits of LLMs' abilities.

Transformers have been shown to emulate logical deduction over natural language theories (logical rules expressed in natural language), reliably assigning true/false labels to candidate implications. However, their ability to generate implications of a theory has not yet been demonstrated, and methods for reconstructing proofs of answers are imperfect. In this work we show that a generative model, called ProofWriter, can reliably generate both implications of a theory and the natural language proof(s) that support them. In particular, iterating a 1-step implication generator results in proofs that are highly reliable, and represent actual model decisions (rather than post-hoc rationalizations). On the RuleTaker dataset, the accuracy of ProofWriter's proofs exceed previous methods by +9% absolute, and in a way that generalizes to proof depths unseen in training and on out-of-domain problems. We also show that generative techniques can perform a type of abduction with high precision: Given a theory and an unprovable conclusion, identify a missing fact that allows the conclusion to be proved, along with a proof. These results significantly improve the viability of neural methods for systematically reasoning over natural language.

Verifiers or reward models are often used to enhance the reasoning performance of large language models (LLMs). A common approach is the Best-of-N method, where N candidate solutions generated by the LLM are ranked by a verifier, and the best one is selected. While LLM-based verifiers are typically trained as discriminative classifiers to score solutions, they do not utilize the text generation capabilities of pretrained LLMs. To overcome this limitation, we instead propose training verifiers using the ubiquitous next-token prediction objective, jointly on verification and solution generation. Compared to standard verifiers, such generative verifiers (GenRM) can benefit from several advantages of LLMs: they integrate seamlessly with instruction tuning, enable chain-of-thought reasoning, and can utilize additional inference-time compute via majority voting for better verification. We demonstrate that when using Gemma-based verifiers on algorithmic and grade-school math reasoning tasks, GenRM outperforms discriminative verifiers and LLM-as-a-Judge, showing a 16-64% improvement in the percentage of problems solved with Best-of-N. Furthermore, we show that GenRM scales favorably across dataset size, model capacity, and inference-time compute.

Reinforcement Learning (RL) has become a powerful tool for enhancing the reasoning abilities of large language models (LLMs) by optimizing their policies with reward signals. Yet, RL's success relies on the reliability of rewards, which are provided by verifiers. In this paper, we expose and analyze a widespread problem--false negatives--where verifiers wrongly reject correct model outputs. Our in-depth study of the Big-Math-RL-Verified dataset reveals that over 38% of model-generated responses suffer from false negatives, where the verifier fails to recognize correct answers. We show, both empirically and theoretically, that these false negatives severely impair RL training by depriving the model of informative gradient signals and slowing convergence. To mitigate this, we propose tinyV, a lightweight LLM-based verifier that augments existing rule-based methods, which dynamically identifies potential false negatives and recovers valid responses to produce more accurate reward estimates. Across multiple math-reasoning benchmarks, integrating TinyV boosts pass rates by up to 10% and accelerates convergence relative to the baseline. Our findings highlight the critical importance of addressing verifier false negatives and offer a practical approach to improve RL-based fine-tuning of LLMs. Our code is available at https://github.com/uw-nsl/TinyV.

State-of-the-art deep-learning-based approaches to Natural Language Processing (NLP) are credited with various capabilities that involve reasoning with natural language texts. In this paper we carry out a large-scale empirical study investigating the detection of formally valid inferences in controlled fragments of natural language for which the satisfiability problem becomes increasingly complex. We find that, while transformer-based language models perform surprisingly well in these scenarios, a deeper analysis re-veals that they appear to overfit to superficial patterns in the data rather than acquiring the logical principles governing the reasoning in these fragments.

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

In recent years, many neural network (NN) verifiers have been developed to formally verify certain properties of neural networks such as robustness. Although many benchmarks have been constructed to evaluate the performance of NN verifiers, they typically lack a ground-truth for hard instances where no current verifier can verify and no counterexample can be found, which makes it difficult to check the soundness of a new verifier if it claims to verify hard instances which no other verifier can do. We propose to develop a soundness benchmark for NN verification. Our benchmark contains instances with deliberately inserted counterexamples while we also try to hide the counterexamples from regular adversarial attacks which can be used for finding counterexamples. We design a training method to produce neural networks with such hidden counterexamples. Our benchmark aims to be used for testing the soundness of NN verifiers and identifying falsely claimed verifiability when it is known that hidden counterexamples exist. We systematically construct our benchmark and generate instances across diverse model architectures, activation functions, input sizes, and perturbation radii. We demonstrate that our benchmark successfully identifies bugs in state-of-the-art NN verifiers, as well as synthetic bugs, providing a crucial step toward enhancing the reliability of testing NN verifiers. Our code is available at https://github.com/MVP-Harry/SoundnessBench and our benchmark is available at https://huggingface.co/datasets/SoundnessBench/SoundnessBench.