SAGE: Multi-Agent Self-Evolution for LLM Reasoning

Recent advances in large language model (LLM) reasoning through reinforcement learning rely on annotated datasets for verifiable rewards, which may limit models' ability to surpass human-level performance. While self-play offers a promising alternative, prior methods yield only marginal or even negative gains on post-trained models because they generate problems that cluster around familiar concepts rather than discovering novel ones. We introduce Open-Ended Self-Improving Reasoner (OpenSIR), a self-play framework in which a single LLM alternates teacher and student roles to generate and solve novel problems without external verifiers or annotated data. Starting from a single seed problem, OpenSIR sustains open-ended exploration through diversity rewards that push the model toward unfamiliar concepts and difficulty calibration that keeps problems learnable. Across seven math benchmarks, OpenSIR consistently improves all models, averaging +3.6 points on instruction models and +3.1 on reasoning models, while recent self-play baselines yield marginal or even negative gains; starting from a single trivial seed, it also surpasses GRPO baselines trained on over 7K annotated examples. Despite training only on self-generated math, OpenSIR is the only self-play method that transfers to general reasoning, improving by at least +4.4 points on reasoning models.

Large Language Model (LLM) Agents, often trained with Reinforcement Learning (RL), are constrained by a dependency on human-curated data, limiting scalability and tethering AI to human knowledge. Existing self-evolution frameworks offer an alternative but are typically restricted by the model's inherent capabilities and single-round interactions, hindering the development of complex curricula involving tool use or dynamic reasoning. We introduce Agent0, a fully autonomous framework that evolves high-performing agents without external data through multi-step co-evolution and seamless tool integration. Agent0 establishes a symbiotic competition between two agents initialized from the same base LLM: a curriculum agent that proposes increasingly challenging frontier tasks, and an executor agent that learns to solve them. We integrate external tools to enhance the executor's problem-solving capacity; this improvement, in turn, pressures the curriculum agent to construct more complex, tool-aware tasks. Through this iterative process, Agent0 establishes a self-reinforcing cycle that continuously produces high-quality curricula. Empirically, Agent0 substantially boosts reasoning capabilities, improving the Qwen3-8B-Base model by 18% on mathematical reasoning and 24% on general reasoning benchmarks. Code is available at https://github.com/aiming-lab/Agent0.

Can a language model improve reasoning by learning from its own imperfect responses, without rewards or teacher-provided solutions? We present Self-evolving Post-Training (SePT), a simple method that alternates temperature-controlled self-generation with next-token likelihood training. Each round uses the updated model to generate new training responses, with one response per prompt by default and no correctness filtering. Across six mathematical benchmarks, SePT improves a temperature-selected no-training baseline by 11.4 and 6.7 AVG points on Qwen2.5-Math-7B and Qwen2.5-7B, respectively, where AVG averages Pass@1, Pass@8 and Pass@32 across benchmarks. We analyze how sampling temperature shapes the learning signal and investigate the value of the resulting responses. Responses from a SePT-trained model improve a student initialized from the original weights, while their reasoning prefixes help an unchanged model complete solutions, even when matched in length to prefixes from a colder initial model. Comparing next-token predictions at identical contexts also reveals changes in token rankings that decoding-temperature adjustment cannot reproduce. Further evaluations across nine starting models, general reasoning and code generation examine broader applicability. Together, these results show that reward-free self-training can improve both a model's predictions and the supervision it provides. Our code is available at https://github.com/ElementQi/SePT.