Related papers: Propose, Solve, Verify: Self-Play Through Formal V…

Verification is one of the central tasks in circuit and system design. While simulation and emulation are widely used, complete correctness can only be ensured based on formal proof techniques. But these approaches often have very high run…

AI coding agents are increasingly used to write real-world software, but ensuring that their outputs are correct remains a fundamental challenge. Formal verification offers a promising path: an agent generates code together with a…

We present StepFun-Prover Preview, a large language model designed for formal theorem proving through tool-integrated reasoning. Using a reinforcement learning pipeline that incorporates tool-based interactions, StepFun-Prover can achieve…

Reliably knowing when a language model is correct is almost as important as being correct. We introduce prover-verifier deliberation (PVD), an inference-time protocol grounded in interactive proof theory, as a mechanism for selective…

Large language models (LLMs) have recently demonstrated impressive performance on complex, multi-step reasoning tasks, especially when post-trained with outcome-rewarded reinforcement learning Guo et al. 2025. However, it has been observed…

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…

Self-Correction aims to enable large language models (LLMs) to self-verify and self-refine their initial responses without external feedback. However, LLMs often fail to effectively self-verify and generate correct feedback, further…

Reinforcement learning with verifiable rewards (RLVR) has advanced the reasoning capabilities of large language models. However, existing methods rely solely on outcome rewards, without explicitly optimizing verification or leveraging…

Test-time scaling for complex reasoning tasks shows that leveraging inference-time compute, by methods such as independently sampling and aggregating multiple solutions, results in significantly better task outcomes. However, a critical…

Large language models (LLMs) can act as both problem solvers and solution verifiers, where the latter select high-quality answers from a pool of solver-generated candidates. This raises the question of under what conditions verification…

While large language models have made significant progress in mathematical reasoning, they remain unreliable at judging the correctness of their own solutions. Existing approaches that equip models with self-verification typically treat…

Interactive theorem provers (ITPs) are powerful tools for the formal verification of mathematical proofs down to the axiom level. However, their lack of a natural language interface remains a significant limitation. Recent advancements in…

Large Language Models (LLMs) have achieved remarkable progress through Reinforcement Learning with Verifiable Rewards (RLVR), yet still rely heavily on external supervision (e.g., curated labels). Adversarial learning, particularly through…

Machine learning models are increasingly deployed for critical decision-making tasks, making it important to verify that they do not contain gender or racial biases picked up from training data. Typical approaches to achieve fairness…

Process Reward Models (PRMs) have emerged as a promising approach for improving LLM reasoning capabilities by providing process supervision over reasoning traces. However, existing approaches for constructing PRM training data remain costly…

There has been considerable divergence of opinion on the reasoning abilities of Large Language Models (LLMs). While the initial optimism that reasoning might emerge automatically with scale has been tempered thanks to a slew of…

Ensuring correctness is crucial for code generation. Formal verification offers a definitive assurance of correctness, but demands substantial human effort in proof construction and hence raises a pressing need for automation. The primary…

Proof-oriented programming languages (POPLs) empower developers to write code alongside formal correctness proofs, providing formal guarantees that the code adheres to specified requirements. Despite their powerful capabilities, POPLs…

Reinforcement Learning from Verifiable Rewards (RLVR) has improved language models in domains such as mathematics and code, where correctness can be checked automatically. However, many important tasks are only partially verifiable: prompts…

We introduce a self-play framework for semantic equivalence in Haskell, utilizing formal verification to guide adversarial training between a generator and an evaluator. The framework leverages Liquid Haskell proofs for validating…