Socratic-Zero : Bootstrapping Reasoning via Data-Free Agent Co-evolution
Authors: name: Shaobo Wang, name: Zhengbo Jiao, name: Zifan Zhang, name: Yilang Peng, name: Xu Ze, name: Boyu Yang, name: Wei Wang, name: Hu Wei, name: Linfeng Zhang
Organization: AGI Lab

Recent breakthroughs in large language models (LLMs) on reasoning tasks rely
heavily on massive, high-quality datasets-typically human-annotated and thus
difficult to scale. While data synthesis or distillation offers a promising
alternative, existing methods struggle with inconsistent data quality and an
inability to dynamically adapt to the evolving capabilities of the model,
leading to suboptimal training signals. To address these limitations, we
introduce Socratic-Zero, a fully autonomous framework that generates
high-quality training data from minimal seed examples through the co-evolution
of three agents: the Teacher, the Solver, and the Generator. The Solver
continuously refines its reasoning by learning from preference feedback on both
successful and failed trajectories; the Teacher adaptively crafts increasingly
challenging questions based on the Solver's weaknesses; and the Generator
distills the Teacher's question-design strategy to enable scalable,
high-fidelity curriculum generation. This closed-loop system produces a
self-improving curriculum-requiring no pre-existing tasks or labels.
Remarkably, starting from only 100 seed questions, our Socratic-Solver-8B
achieves an average gain of +20.2 percentage points over prior data synthesis
methods across seven mathematical reasoning benchmarks (AMC23, AIME24-25,
Olympiad, MATH-500, Minerva, and GSM8K), with consistent gains on both Qwen3
and GLM4 series models. Even more surprisingly, synthetic data from
Socratic-Generator-32B enables student LLMs to achieve superior performance
compared to other state-of-the-art (SOTA) commercial LLMs on these benchmarks,
including Qwen3-235B-A22B, DeepSeek-V3.1-671B, GPT-5, Gemini-2.5-Pro, Grok-4,
and Claude-4.1-Opus.