The paper introduces Proof‑R1, a reinforcement‑learning framework that trains large language models to generate verifiable proofs for natural‑language logical reasoning tasks. Proof‑R1 only accepts a generated conclusion into the proof state when it satisfies formal verification constraints, ensuring each reasoning step is machine‑checkable. The method also reconstructs the dependency closure that supports the final answer, aligning credit with valid proof steps, and shows improved answer accuracy and verifiability across multiple benchmarks and models.
arXiv:2605. 12519v2 Announce Type: replace-cross Abstract: Training language models to produce both correct answers and sound reasoning remains an open challenge.
arXiv:2603. 09803v2 Announce Type: replace Abstract: Reinforcement Learning with Verifiable Rewards (RLVR) improves reasoning in large language models but treats all correct solutions equally, potentially reinforcing flawed traces that arrive at correct answers by chance.
arXiv:2606. 20068v1 Announce Type: new Abstract: While reinforcement learning from verifiable rewards (RLVR) typically has relied on a single binary verification signal, symbolic proof assistants in formal reasoning offer rich, fine-grained structured feedback.
arXiv:2609.38409v1 Announce Type: new Abstract: Recent progress in large language model reasoning has been driven by benchmarks and reinforcement learning environments with automatically verifiable r...
arXiv:2602.02377v3 Announce Type: replace Abstract: While large language models (LLMs) have achieved strong performance on mathematical problems with verifiable answers, many advanced problems are pr...
arXiv:2604. 02621v2 Announce Type: replace-cross Abstract: Reinforcement Learning (RL) substantially improves the reasoning capabilities of language models, but most existing RL fine-tuning approaches rely entirely on ground-truth verifiable rewards and thus labeled datasets with verifiable answers.
arXiv:2606. 29984v1 Announce Type: new Abstract: Reinforcement Learning (RL) is an important paradigm for improving the reasoning capabilities of Vision-Language Models (VLMs).
arXiv:2608. 03119v1 Announce Type: new Abstract: Reinforcement Learning with Verifiable Rewards (RLVR) improves LLM reasoning but typically relies on ground-truth (GT) answers, limiting scalability.
arXiv:2601. 22642v2 Announce Type: replace Abstract: Large Language Models (LLMs) show remarkable capabilities, yet their stochastic next-token prediction creates logical inconsistencies and reward hacking that formal symbolic systems avoid.
arXiv:2511. 07317v2 Announce Type: replace-cross Abstract: We introduce Reinforcement Learning (RL) with Adaptive Verifiable Environments (RLVE), an approach using verifiable environments that procedurally generate problems and provide algorithmically verifiable rewards, to scale up RL for language models (LMs).
The paper introduces Ask-Condition-Abstain Reinforcement Learning (ACA‑RL), a framework that trains reasoning models to handle queries missing a premise by either asking for it, conditioning on the unknown, or abstaining. ACA‑RL uses a reasoning‑graph‑guided pipeline to generate training instances with localized gap annotations and a structured reward over five observable response behaviors. The authors also present the Missing‑Premise Benchmark (MPB), a 274‑instance, human‑verified dataset covering mathematical, logical, and real‑world word problems, and show that ACA‑RL improves performance on MPB while maintaining competitive results on well‑posed tasks for Qwen3 and Llama models.
arXiv:2604. 23333v2 Announce Type: replace Abstract: Scaling test-time computation with reinforcement learning (RL) has emerged as a reliable path to improve large language models (LLM) reasoning ability.