Beyond Entropy: Learning from Token-Level Distributional Deviations for LLM Reasoning

Computer Science > Artificial Intelligence [Submitted on 18 Jun 2026] Beyond Entropy: Learning from Token-Level Distributional Deviations for LLM Reasoning Xuanzhi Feng, Zhengyang Li, Zeyu Liu, Haoxi Li, Yuming Jiang, Bing Guo, Jingcai Guo, Jie Zhang, Song Guo Reinforcement Learning with Verifiable Rewards (RLVR) has significantly advanced Large Language Model (LLM) reasoning; however, it faces a fundamental optimization instability: uniform token updates precipitate entropy collapse, leading to premature convergence to suboptimal strategies, whereas excessive Shannon Entropy maximization can cause entropy explosion, driving blind exploration toward incoherent reasoning chains. To resolve this dichotomy, we introduce the Independent Combinatorial Tokens (ICT) framework, which shifts the optimization focus from scalar uncertainty to the distributional properties of token logits. By leveraging the Jensen-Shannon (JS) divergence between token logits distributions, ICT identifies tokens with distinctive distributional patterns as critical branching points for guiding effective exploration in LLM reasoning. Our theoretical analysis, grounded in both Shannon and second-order Rényi entropy, proves that selectively updating on these tokens regulates policy concentration: it reduces the overall distribution uncertainty measured by Shannon entropy, while controlling probability concentration captured by second-order Rényi entropy. This dual effect prevents over-concentrated token generation from weakening exploration and effectively stabilizes the training landscape. Empirical results demonstrate that updating only the top 10% of unique tokens on Qwen2.5 (0.5B/1.5B/7B) models yields an average pass@4 improvement of 4.58%, with a maximum gain of 14.9%, over GRPO, 20-Entropy, and STAPO baselines across seven benchmarks spanning math, commonsense, and Olympiad-level problems. Subjects: Artificial Intelligence (cs.AI) Cite as: arXiv:2606.19771 [cs.AI]   (or arXiv:2606.19771v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2606.19771 Focus to learn more Submission history From: Zhengyang Li [view email] [v1] Thu, 18 Jun 2026 04:11:56 UTC (9,470 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-06 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)