Learning to Pose Problems: Reasoning-Driven and Solver-Adaptive Data Synthesis

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.

Although LLMs have made substantial progress in reasoning, systematically producing frontier-level reasoning data remains difficult. Existing synthesis methods often have limited visibility into the structural factors that govern problem difficulty, which can result in narrow diversity and unstable difficulty control. In this work, we view the difficulty of a reasoning problem as arising from the accumulation of atomic knowledge-reasoning transformations, which we term thought modes. Building on this perspective, we propose MindLoom, a framework for synthesizing frontier-level reasoning data through compositional thought mode engineering. Given a collection of hard problems with verified solutions, MindLoom first decomposes those solutions into thought mode chains that reveal each problem's construction logic. It then trains a retrieval model that matches problem states to compatible thought modes, providing guidance on which reasoning challenges to introduce during synthesis. New problems are composed by iteratively applying retrieved thought modes to seed questions, with distribution-aligned sampling to encourage diverse reasoning coverage. Finally, a rollout-based judging stage labels generated questions by difficulty and supplies judged-correct responses for supervised fine-tuning. We evaluate MindLoom on nine benchmarks covering five STEM disciplines and four mathematical reasoning tasks across multiple model families and sizes. Models fine-tuned on MindLoom-generated data achieves favorable performances over base models, distillation, and external-data baselines across the reported benchmarks. Ablation studies indicate the contribution of each component, and further analysis suggests that MindLoom covers a broad range of reasoning patterns while maintaining useful difficulty control. We have open-sourced our implementation at https://github.com/EachSheep/MindLoom.

Generating progressively harder reasoning problems requires synthesis procedures that adapt as the task distribution evolves. Existing task-level recursion reuses generated problems as seeds but leaves the construction harness unchanged. We present task-harness co-evolution, a framework for recursive harness self-improvement (RSI) in reasoning-data synthesis. Online self-improvement converts intermediate solver failures into reusable skills during generation. Post-task self-improvement revises skills, prompts, and workflows after each batch, adopting candidates only when they generate harder valid tasks within a bounded cost increase. Model weights and verification criteria remain fixed. Across mathematics, coding, and science, mean solver accuracy decreases from 100.0% to 54.8% over fourteen evolution rounds. Ablations show that combining both update schedules produces harder tasks than fixed-harness recursion or either schedule alone. The resulting data improves downstream SFT and GRPO performance. In particular, a 27B student fine-tuned on 10K synthesized mathematics examples achieves 62.5% mean-16 accuracy on APEX, competitive with selected frontier-model references. These results support adapting the synthesis harness alongside the tasks to generate increasingly challenging data with downstream training value.