arXiv Machine Learning

Online Learnability of Chain-of-Thought Verifiers: Soundness and Completeness Trade-offs

arXiv:2603. 03538v4 Announce Type: replace Abstract: Large Language Models (LLMs) using chain-of-thought reasoning have demonstrated great potential for solving complex reasoning and planning tasks.

arXiv AI
Jun 9

Correct Is Not Enough: Training Reasoning Planners with Executor-Grounded Rewards

arXiv:2605. 03862v4 Announce Type: replace Abstract: Reinforcement learning with verifiable rewards has become a common way to improve explicit reasoning in large language models, but final-answer correctness alone does not reveal whether the reasoning trace is faithful, reliable, or useful to the model that consumes it.

By Tianyang Han, Hengyu Shi, Junjie Hu, Xu Yang, Zhiling Wang, Junhao Su
arXiv Computation and Language
Aug 28

Neuro-symbolic PRM: Enhancing Scientific Reasoning via Structured Traces and Symbolic Verification

The paper introduces a neuro‑symbolic framework for scientific reasoning that separates symbolic validity and semantic groundedness. A deterministic symbolic verifier acts as a hard filter to guarantee syntactic and arithmetic correctness, while a Process Reward Model (PRM) is trained on verifier‑accepted steps to assess contextual grounding. The authors propose Counterfactual Symbolic Perturbation (CSP) to generate hard negative examples that pass the verifier but are logically flawed, enabling efficient PRM training and a verifier‑first constrained search at inference.

By Yuxin Zi, Cong Xu, Suparna Bhattacharya, Martin Foltin, Amit Sheth
arXiv Machine Learning
Aug 28

Learning to Reason with Curriculum I: Provable Benefits of Autocurriculum

The paper investigates whether the high costs of training chain-of-thought reasoning models can be reduced through algorithmic design. It introduces an autocurriculum approach that lets the model select which problems to focus on during training, showing that this method provably improves both supervised fine‑tuning and reinforcement learning. For supervised fine‑tuning, autocurriculum requires exponentially fewer reasoning demonstrations by targeting prompts where the model struggles, while for reinforcement learning it decouples computational cost from the quality of the reference model, making the burn‑in cost nearly independent of target accuracy.

By Nived Rajaraman, Audrey Huang, Miro Dudik, Robert Schapire, Dylan J. Foster, Akshay Krishnamurthy
arXiv AI
Sep 7

Extremely Sparse Supervision Incentivizes Reasoning Ability

The paper reports that in on‑policy distillation for large language models, reasoning performance can be improved by supervising only a tiny fraction of generated tokens—sometimes just one or two tokens per reasoning trajectory, about 0.05% of all tokens. This sparse supervision consistently matches or exceeds full‑token training across nine teacher‑student setups on mathematical reasoning, and is also validated on coding reasoning, Llama models, and PPO‑based reinforcement learning with verifiable reward. The findings suggest that effective post‑training does not require token‑intensive supervision and may align more closely with natural learning processes that focus on critical reasoning steps.

By Zhishuai Liu, Xingzi Xu, Mehmet Saygin Seyfioglu, Pan Xu, Karim Bouyarmane
arXiv AI
2d ago

The Weakest Link: Distilling LLM Reasoning with Worst-Case Constrained Reinforcement Learning

The paper introduces a new approach to distill reasoning abilities from large language models (LLMs) into smaller student models by framing the task as a constrained reinforcement learning problem. It enforces a worst‑case constraint on the teacher’s log‑likelihood for every prefix of the reasoning chain, avoiding reward hacking and excessive teacher regularization. Experiments on mathematical reasoning and code generation show that this method improves the balance between accuracy and fidelity, achieving the highest rigorous reasoning success rate among evaluated settings.

By Matthieu Zimmer, Xiaotong Ji, Tu Nguyen, Haitham Bou-Ammar