Direct Self-Evolving Optimization: Evolving LLMs without Challenger Training

Self-evolution offers a scalable path to stronger reasoning: a pretrained language model improves itself with only minimal external supervision. Yet existing methods either depend on extensively curated or teacher-generated training data, or, when the generator runs unsupervised, reward it by a difficulty heuristic that need not improve the solver. We introduce INFUSER, an iterative co-training framework with two co-evolving roles: a Generator that drafts questions and reference golden answers from a pool of unstructured, automatically collected documents, and a Solver that improves by training on them. The solver is trained with standard correctness rewards against the generator-provided answers, while the generator is rewarded by an optimizer-aware influence score that measures whether each proposed question would actually improve the solver on the target distribution. Because this continuous, noisy influence score is poorly served by standard GRPO, we propose DuGRPO, a dual-normalized variant of GRPO, for generator training. Together, these turn the document pool into an adaptive curriculum that favors questions useful to the current solver, not just hard ones. On Qwen3-8B-Base, INFUSER outperforms strong self-evolution baselines with over 20% relative improvement on Olympiad and SuperGPQA benchmarks, and an 8B INFUSER co-evolving generator outperforms a frozen 32B thinking generator on math and coding. Ablations confirm each design choice is necessary, and two extensions, applying INFUSER to an instruction-finetuned anchor and augmenting it with rule-verifiable RLVR data, further demonstrate the flexibility and generalizability of the framework. Code is available at https://github.com/FFishy-git/INFUSER.

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.

Self-play supports the self-evolution of language models, but solver performance can plateau or decline across rounds without guidance. Existing unguided methods typically use difficulty, learnability, or diversity signals to keep questions challenging and varied, without identifying which unresolved reasoning weaknesses to target. Existing guided methods rely on external task resources such as human examples, document corpora, or specified difficulty targets. We introduce DiagEvo, which guides question generation using the solver's failure history from self-play, without external task resources. Its diagnostician extracts recurring error causes and stores them in an error-cause memory. The memory groups related causes under skill nodes and tracks each as Active or Mastered according to self-consistency on targeted questions. The challenger uses these states and recurrence counts to balance cause-targeted generation with free exploration. Double-confidence filtering retains intermediate-difficulty questions only when the most common solver answer has a clear vote lead. With the default 4B diagnostician, DiagEvo outperforms all baselines in mean accuracy across nine benchmarks for each solver: Qwen3-4B, Qwen3-8B, and OctoThinker-8B. On Qwen3-8B, DiagEvo reaches 72.3% mean accuracy across five mathematical reasoning benchmarks, 4.5 percentage points above R-Zero. Its overall mean accuracy across nine benchmarks is 57.4%, 3.5 percentage points above SPICE. Ablations show that mixed generation, memory-state updates with cross-state stitching, and double-confidence filtering contribute to these gains.