# Socratic-Zero : Bootstrapping Reasoning via Data-Free Agent Co-evolution

arXiv: https://arxiv.org/abs/2509.24726 · HTML: https://mlsanity.com/paper/2509.24726/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 1 of its 37 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)
- LLM agents and tool use / [General LLM agent frameworks and benchmarks](https://mlsanity.com/agents/general-llm-agent-frameworks-and-benchmarks/)
- Synthetic data and self-improvement for LLMs / [Synthetic reasoning data and bootstrapping](https://mlsanity.com/synth/synthetic-reasoning-data-and-bootstrapping/)

## Builds on (most cited first, 1 of 1)

- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)

## Built on by (most cited first, 27 of 27)

- [Agent0: Unleashing Self-Evolving Agents from Zero Data via Tool-Integrated Reasoning](https://mlsanity.com/paper/2511.16043/) (2025)
- [VisPlay: Self-Evolving Vision-Language Models from Images](https://mlsanity.com/paper/2511.15661/) (2025)
- [Dr. Zero: Self-Evolving Search Agents without Training Data](https://mlsanity.com/paper/2601.07055/) (2026)
- [Group-Evolving Agents: Open-Ended Self-Improvement via Experience Sharing](https://mlsanity.com/paper/2602.04837/) (2026)
- [Self-Play Only Evolves When Self-Synthetic Pipeline Ensures Learnable Information Gain](https://mlsanity.com/paper/2603.02218/) (2026)
- [Environment Scaling for Interactive Agentic Experience Collection: A Survey](https://mlsanity.com/paper/2511.09586/) (2025)
- [Agentic Proposing: Enhancing Large Language Model Reasoning via Compositional Skill Synthesis](https://mlsanity.com/paper/2602.03279/) (2026)
- [R-Diverse: Mitigating Diversity Illusion in Self-Play LLM Training](https://mlsanity.com/paper/2602.13103/) (2026)
- [Socratic-SWE: Self-Evolving Coding Agents via Trace-Derived Agent Skills](https://mlsanity.com/paper/2606.07412/) (2026)
- [Learning to Pose Problems: Reasoning-Driven and Solver-Adaptive Data Synthesis](https://mlsanity.com/paper/2511.09907/) (2025)
- [SearchEyes: Towards Frontier Multimodal Deep Search Intelligence via Search World Simulation](https://mlsanity.com/paper/2607.05943/) (2026)
- [Scaling Large Reasoning Models beyond Human Supervision: A Path toward Superintelligence](https://mlsanity.com/paper/2608.31075/) (2026)
- [Audio-Zero: Label-Free Self-Evolution for Fine-Grained Audio Reasoning](https://mlsanity.com/paper/2607.20166/) (2026)
- [Socratic-Geo: Synthetic Data Generation and Geometric Reasoning via Multi-Agent Interaction](https://mlsanity.com/paper/2602.03414/) (2026)
- [AERO: Autonomous Evolutionary Reasoning Optimization via Endogenous Dual-Loop Feedback](https://mlsanity.com/paper/2602.03084/) (2026)
- [Vocabulary Dropout for Curriculum Diversity in LLM Co-Evolution](https://mlsanity.com/paper/2604.03472/) (2026)
- [False Frontiers: Diagnosing and Mitigating Co-Cheating in Self-Evolving Search Agents](https://mlsanity.com/paper/2609.39102/) (2026)
- [MedZERO: Self-Evolving Agents for Open-Ended Medical Reasoning Through Controlled Knowledge Accumulation](https://mlsanity.com/paper/2610.08327/) (2026)
- [SynCo: Data Synthesis Co-Training for Self-Evolving LLMs via Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2610.11345/) (2026)
- [UNSEEN: Enhancing Dataset Pruning from a Generalization Perspective](https://mlsanity.com/paper/2511.12988/) (2025)
- [D2Evo: Dual Difficulty-Aware Self-Evolution for Data-Efficient Reinforcement Learning](https://mlsanity.com/paper/2605.17037/) (2026)
- [Beyond Uncertainty: Multi-Solver Disagreement Rewards for Self-Evolving Reasoning Curricula](https://mlsanity.com/paper/2608.30035/) (2026)
- [UnifiedPlayers: Enhance Tool-Integrated Reasoning in Agentic Reinforcement Learning](https://mlsanity.com/paper/2609.20089/) (2026)
- [BEHAVE: Functional Behavior Modeling Enables Self-Improving Agents for Hardware Design and Verification](https://mlsanity.com/paper/2609.34785/) (2026)
- [Self-Evolve With a Reference:Anchored Training of Tool-Integrated Agents](https://mlsanity.com/paper/2610.09856/) (2026)
- [Know What You Don't Know: Agentic Data Synthesis by Evolving Generation Space for Closed-Loop Learning](https://mlsanity.com/paper/2610.12593/) (2026)
- [BoundaryEvo: Data-Model Co-Evolution at the Capability Boundary for Long-Chain Reasoning Distillation](https://mlsanity.com/paper/2610.13285/) (2026)

## Abstract (arXiv)

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.