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:2605. 19723v2 Announce Type: replace-cross Abstract: Mathematical reasoning is essential for problem-solving in education, science, and industry, serving as a crucial benchmark for evaluating artificial intelligence systems.
By Husnain Amjad, Raja Khurram Shahzad, Aamir Shahzad, Mehwish Fatima
arXiv:2609.22553v1 Announce Type: new
Abstract: Effective LLM tutoring depends on correctly identifying the specific error in a student's reasoning before generating feedback. We study this problem i...
By Tahreem Yasir, Arnav Mody, Xioayi Tian, Tiffany Barnes
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
SOD: Step-wise On-policy Distillation for Small Language Model Agents proposes a new framework that adaptively reweights distillation strength at each reasoning step based on step-level divergence. This approach mitigates cascading errors in tool-integrated reasoning by attenuating misleading teacher signals in high-divergence regions while preserving dense guidance where student and teacher align. Experiments on math, science, and code benchmarks show up to 20.86% improvement over the second-best baseline, with a 0.6B student scoring 26.13% on AIME 2025.
By Qiyong Zhong, Mao Zheng, Mingyang Song, Xin Lin, Jie Sun, Houcheng Jiang, Xiang Wang, Junfeng Fang
arXiv:2608. 03972v1 Announce Type: new Abstract: On-policy training has emerged as a powerful post-training paradigm for improving the reasoning capabilities of large language models, and is often enhanced by golden trajectories from stronger expert models.
By Jinhe Bi, Chennan Zhou, Zengjie Jin, Aniri, Shuo Lu, Wenke Huang, Hu Cao, Xun Xiao, Zhihong Zhu, Volker Tresp, Fei Shen, Yunpu Ma, Tat-Seng Chua