LC-ERD: Mining Latent Logic for Self-Evolving Reasoning via Consistency-Regulated Reward Decomposition

Can language models improve their reasoning performance without external rewards, using only their own sampled responses for training? We show that they can. We propose Self-evolving Post-Training (SePT), a simple post-training method that alternates between self-generation and training on self-generated responses. It repeatedly samples questions, uses the model itself to generate responses under a specified sampling temperature, and then trains the model on the self-generated data. In this self-training loop, we use an online data refresh mechanism, where each new batch is generated by the most recently updated model. Across six math reasoning benchmarks, SePT improves a strong no-training baseline, defined as the untuned base model evaluated at its best swept decoding temperature, on several tested models. Additional ablations demonstrate the importance of online data refresh and temperature dynamics. Overall, our results identify a practical regime where reasoning can be improved using self-generated supervision alone. Our code is available at https://github.com/ElementQiii/SePT.

Large reasoning models achieve strong performance on complex tasks by generating extended chain-of-thought (CoT) traces via reinforcement learning with verifiable rewards (RLVR). While current RLVR methods have achieved strong results with correctness-based reward signals, they provide limited guidance on the quality of the reasoning process itself, leaving the internal reasoning structure largely unoptimized. Through empirical analysis across multiple model families, we identify a consistent pattern: correct reasoning trac es exhibit more frequent and larger token-level entropy drops within the thinking phase than incorrect ones. We propose ERR+, a two-phase RLVR framework grounded in this observation. The first phase trains with the Entropy Relief Reward (ERR), a bonus proportional to cumulative token-level entropy drops in the thinking phase, log-normalized by response length. Unlike prior methods that suppress entropy, ERR rewards the resolution of uncertainty while leaving exploratory high-entropy states unconstrained. The second phase introduces the Robust Relative Efficiency Reward, which scores each response's length against co-generated peers via a $\tanh$-transformed within-group $z$-score. We provide a formal analysis showing that joint optimization of the two objectives induces gradient conflict in early training, motivating the sequential design . Experiments on five datasets demonstrate consistent improvements in both accuracy and response conciseness across model backbones. Our code is available at https://github.com/XrkArul/err_response

Effectively training Large Language Models (LLMs) for complex, long-CoT reasoning is often bottlenecked by the need for massive high-quality reasoning data. Existing methods are either computationally expensive or fail to reliably distinguish high- from low-quality reasoning samples. To address this, we propose High-Entropy Sum (HES), a training-free metric that quantifies reasoning quality by summing only the entropy of the top (e.g., 0.5%) highest-entropy tokens in each reasoning sample. We validate HES across three mainstream training paradigms: Supervised Fine-tuning (SFT), Rejection Fine-tuning (RFT), and Reinforcement Learning (RL), with extensive results demonstrating its consistent effectiveness and significantly reduced computational overhead. In SFT, training on the top 20% HES-ranked data matches full-dataset performance, while using the lowest-HES data degrades it. In RFT, our HES-based training approach significantly outperforms baseline methods. In RL, HES-selected successful trajectories enable the model to learn strong reasoning patterns, significantly surpassing other compared methods. Our findings establish HES as a robust, training-free metric that enables a unified, effective, and efficient method for developing advanced reasoning in LLMs.