The paper introduces SymCE, a dataset of 4,707 false undergraduate‑algebra and real‑analysis conjectures each paired with a deterministic Python verifier that can be executed to check truth. It studies counterexample generation by training a 4B‑parameter language model (Qwen3‑4B) first with supervised fine‑tuning and then with reinforcement learning (GRPO) using the verifier as a reward. The results show that counterexample‑only fine‑tuning can destroy true‑theorem recognition, while reinforcement learning with a sparse outcome‑only reward restores and surpasses baseline performance, achieving higher success rates than larger open‑weight models and competitive performance on other math benchmarks.
"whyItMatters":"The study demonstrates that reinforcement learning guided by a per‑theorem verifier can effectively repair the shortcomings of supervised fine‑tuning in theorem proving, offering a practical approach to improve language models’ mathematical reasoning capabilities."
By Omar Farouk Zouak, Houssam Eddine Boukhalfa, Soumaya Lakehal, Shiv Katiyar, Samia Nefti-Meziani
arXiv:2601. 00791v2 Announce Type: replace-cross Abstract: Verifying whether a language model is genuinely reasoning or pattern-matching remains an open problem: learned verifiers are expensive, and output-based heuristics are brittle.
By Valentin No\"el
arXiv:2608. 15445v1 Announce Type: new Abstract: When a reward is correct on every training example yet consistent with more than one goal, a model can acquire an unintended one, a failure known as goal misgeneralization.
By Suyash Maniyar, Armaan Sandhu, Abhishek Mishra
arXiv:2606. 21678v2 Announce Type: replace-cross Abstract: Language models can generate plausible rationales for their predictions, but these explanations may not faithfully represent the model's internal reasoning.
By Vatsal Ananthula, Adarsh Kumarappan
arXiv:2610.18862v1 Announce Type: cross
Abstract: Reasoning models achieve strong performance through long chains of thought (CoT), but often spend more tokens than needed to solve a problem. Existin...
By Minghao Luo, Liang Chen
FaithSieve is a Lean‑assisted framework that fine‑grains natural‑language mathematical proofs into local reasoning units, extracts typed proof obligations, and verifies them with formal evidence gated by semantic alignment. It introduces two expert‑verified datasets—ProofLoc‑Olympiad and ProofLoc‑University—to benchmark first‑error localization. On these benchmarks, FaithSieve outperforms direct‑judging baselines, achieving 81.43% and 84.5% exact first‑error accuracy respectively.
By Ziyu Wang, Qiming Dai, Yishan Wu, Zaiwen Wen