The evolution of Large Language Model (LLM) reasoning is bottlenecked by the scarcity of high-quality process data. While self-alignment via endogenous rewards offers a solution, mining valid supervision faces three challenges: (1) Label Noise via Mimetic Bias, where rewards prioritize statistical likelihood over logical truth, creating a "correctness illusion" that masks compounding errors; (2) Coarse-Grained Supervision, where sparse global outcomes (e.g., in GRPO) fail to provide granular guidance, treating reasoning chains as monolithic; and (3) Distributional Collapse, where signals fail to generalize without amplifying pre-training biases. To address these, we introduce LC-ERD (Logic-Consistent Endogenous Reward Decomposition), a framework framing self-alignment as latent structure mining. We derive a Variational Logic Potential by aggregating consensus from the model's Latent Logic Expertise (LLE) to denoise the reasoning manifold, and introduce a Multi-Agent Value Decomposition protocol based on the IGM principle to quantify individual step utility. Experiments show LC-ERD delivers a robust self-evolution path, uncovering trade-offs between logic consistency and accuracy while identifying high-value reasoning patterns missed by standard rewards. Our code is available at https://github.com/LC-ERD-repo/LC-ERD.
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.
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.
We present Seirênes, a self-play RL framework that transforms contextual interference from a failure mode of LLM reasoning into an internal training signal for co-evolving more resilient reasoners. While RL with verifiable rewards has significantly advanced reasoning capabilities, models can still exhibit fragility when encountering non-idealized contexts: scenarios characterized by superfluous information, tangential instructions, or incidental correlations that differ from the clean distributions typical of standard benchmarks. Seirênes harnesses this vulnerability through a parameter-shared and adversarial self-play loop. Within this framework, a single model is trained to both construct plausible yet distracting contexts that expose its own reasoning blind spots, and solve problems by discerning the essential task from these perturbations to recover the core underlying logic. By pitting these competing objectives against each other, Seirênes compels the model to move beyond superficial pattern matching and anchors its capabilities in robust underlying reasoning. This continuous interaction sustains an informative co-evolutionary curriculum as the model improves. Across seven mathematical reasoning benchmarks and model scales from 4B to 30B, Seirênes achieves average gains of +10.2, +9.1, and +7.2 points. Besides, distracting contexts produced by the 4B Seirênes model reduce the accuracy of top-tier closed-source models (GPT and Gemini) by roughly 4--5 points, revealing Seirênes' general ability to uncover reasoning models' blind spots.