SAT-RL: Training Language Models for Logical Reasoning with Symbolic Solvers
Read the original on arXiv AI →The Flow has not summarised this story yet — read it at arXiv AI.
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arXiv:2509. 00930v2 Announce Type: replace Abstract: Large language models (LLMs) exhibit strong general reasoning, yet the community lacks controllable, scalable, and verifiable tools to analyze and improve these abilities.
arXiv:2603.00889v2 Announce Type: replace-cross Abstract: Large Language Models (LLMs) have exhibited remarkable reasoning capabilities, largely enabled by supervised fine-tuning (SFT)- and reinforce...
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...
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.
The paper introduces Verifiable Process Rewards (VPR), a framework that uses symbolic or algorithmic task-solving oracles as action-level verifiers to provide dense rewards for intermediate actions in agentic reasoning tasks. VPR is applied to Sokoban, Sudoku, and Minesweeper, and improves policy performance over outcome-reward baselines. The authors also demonstrate VPR’s effectiveness in a tool‑use benchmark, highlighting its reliance on reliable task oracles and the difficulty of extending it to less structured environments.
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.