Recursive Harness Self-Improvement for Frontier Reasoning Data Synthesis

Data synthesis for training large reasoning models offers a scalable alternative to limited, human-curated datasets, enabling the creation of high-quality data. However, existing approaches face several challenges: (i) indiscriminate generation that ignores the solver's ability and yields low-value problems, or reliance on complex data pipelines to balance problem difficulty; and (ii) a lack of reasoning in problem generation, leading to shallow problem variants. In this paper, we develop a problem generator that reasons explicitly to plan problem directions before synthesis and adapts difficulty to the solver's ability. We recover problem-design CoT from human-authored multi-part questions, using later subquestions as targets to infer the design rationale. These traces initialize the generator, which is then optimized with a seed-conditioned reward based on solver answer consistency. The reward guides difficulty adjustment relative to each seed while favoring problems near the solver's competence boundary. Across 10 mathematical and general reasoning benchmarks, our method outperforms seed-only training by 2.69 and 3.39 percentage points after one and three rounds, respectively. The framework also extends to vision-language models. Our code is publicly available at https://github.com/WalkerWorldPeace/Reasoning-Synthesis.

Self-evolving LLM agents promise to improve autonomously through continual interaction and learning, reducing their dependence on manually curated supervision. Realizing this promise requires not only updating the agent, but also evolving its training experience as its capabilities change. However, most existing pipelines rely on static datasets or separately updated synthesis models, causing previously useful tasks to become trivial while overly difficult tasks remain uninformative. This growing mismatch between agent capability and training experience limits sustained self-improvement. To address this problem, we propose SynCo, an agentic data synthesis co-training framework for self-evolving LLMs based on multi-agent reinforcement learning. SynCo jointly optimizes two independently parameterized agents: a Synthesizer that constructs training tasks from the Reasoner's evolving capability state, and a Reasoner that learns from the resulting experience. Each synthesized task induces multiple Reasoner rollouts whose outcomes provide complementary rewards to both agents. Correctness feedback improves the Reasoner, while task quality, answer reliability, and outcome-grounded teachability guide the Synthesizer. Their updates are fed back into subsequent synthesis rounds, allowing the task-solving policy and its training distribution to evolve together. Extensive experiments across eight mathematical reasoning benchmarks demonstrate that SynCo substantially outperforms a broad range of existing synthetic-data methods and controlled baselines, achieving the strongest overall performance while deriving most of its gains from previously unsolved problems.

Synthesizing high-quality mathematical reasoning data without human priors remains a significant challenge. Current approaches typically rely on seed data mutation or simple prompt engineering, often suffering from mode collapse and limited logical complexity. This paper proposes a hierarchical synthesis framework that formulates data synthesis as an unsupervised optimization problem over a constraint graph followed by semantic instantiation, rather than treating it as a direct text generation task. We introduce a Legislator-Executor paradigm: The Legislator adversarially evolves structured generation blueprints encoding the constraints of the problem, while the Executor instantiates these specifications into diverse natural language scenarios. This decoupling of skeleton design from linguistic realization enables a prioritized focus on constructing complex and diverse logical structures, thereby guiding high-quality data synthesis. Experiments conducted on a total of 10 models across the Qwen, Llama, Mistral, and Gemma series demonstrate that our method achieves notable results: models fine-tuned on 1K synthesized samples outperform widely-used datasets of comparable scale (LIMO, s1K) across eight mathematical benchmarks, exhibiting superior out-of-distribution generalization.