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."
arXiv:2609.01354v1 Announce Type: cross Abstract: Reinforcement learning with verifiable rewards (RLVR) and standard benchmark evaluation both rely on an automatic verifier that turns a free text ans...
The paper introduces the concept of proof‑carrying cognition, aiming to close the verification gap in language‑model reasoning by using reality‑settled rewards. It presents a theoretical framework linking verifier‑gold correlation to compute‑capability trade‑offs, demonstrates that unsound verifiers degrade under best‑of‑N selection while sound verifiers improve, and proposes a new benchmark metric, Soundness‑under‑Pressure, for evaluating reality‑settled reasoning systems.
arXiv:2605.14040v2 Announce Type: replace Abstract: Trackable improvement in multimodal physics reasoning rests on a training-and-evaluation system that is itself rarely verified: the corpora a model...
arXiv:2607. 10139v1 Announce Type: cross Abstract: Selecting the correct answer from a pool of candidate reasoning chains is the engine of test-time scaling, yet the standard selectors each carry a cost: self-consistency inherits the errors of the single model it resamples, and trained reward models need labeled data and transfer poorly off-distribution.
Euston is an 8‑B parameter mathematical claim‑verification model that resists producing false derivations when presented with corrupted theorems. It was trained on 3,026 matched true/corrupted statement pairs generated by GraphSynth, a probabilistic factor‑graph generator, and fine‑tuned from DeepSeek‑R1‑8B using GRPO. On a balanced held‑out split, Euston’s balanced accuracy rose from 29.50 % to 63.75 %, and its discrimination gap improved from –0.5 % to +27.5 %, while maintaining comparable general mathematical ability and reducing response length and truncation rates.
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.
arXiv:2605. 02909v2 Announce Type: replace-cross Abstract: Reinforcement Learning with Verifiable Rewards (RLVR) has become a powerful approach for improving the reasoning capabilities of large language models (LLMs).
arXiv:2608. 00220v1 Announce Type: new Abstract: We show that on-policy reinforcement learning with verifiable rewards (RLVR) can improve the current objective while making successful behaviors for later objectives too rare to sample and reinforce.
arXiv:2607. 05904v1 Announce Type: new Abstract: Training a language model against its own reference-free judgments (the premise of self-rewarding, self-play, and LLM-as-a-judge pipelines) assumes a model's verdict on a shown answer tracks correctness.
arXiv:2607.09709v2 Announce Type: replace Abstract: Post-training a code generator against a learned judge can optimize proxy features that raise the score without improving the artifact. We study th...
arXiv:2608.28421v2 Announce Type: replace Abstract: Post training a language model to reason means updating its weights. Supervised finetuning and reinforcement learning both place the acquired capab...
arXiv:2607. 20543v1 Announce Type: cross Abstract: Reinforcement learning with verifiable rewards (RLVR) can improve one-sample accuracy while making a model worse under repeated sampling.