Socratic-Zero : Bootstrapping Reasoning via Data-Free Agent Co-Evolution

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 without requiring large pre-existing task collections or human annotations. 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). Beyond mathematical reasoning, Socratic-Zero further generalizes to a diverse set of domains and modalities, including science reasoning, deep research, software engineering, multimodal chart understanding, and multimodal coding. Furthermore, when using synthetic data from our Socratic-Generator-32B to train student models, they outperform those trained on data from state-of-the-art 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.