MathAgent: Adversarial Evolution of Constraint Graphs for Mathematical 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.

Large Language Models (LLMs) exhibit strong mathematical reasoning when trained on high-quality Chain-of-Thought (CoT) that articulates intermediate steps, yet costly CoT curation hinders further progress. While existing remedies such as distillation from stronger LLMs and self-synthesis based on test-time search alleviate this issue, they often suffer from diminishing returns or high computing overhead.In this work, we propose CoTEvol, a genetic evolutionary framework that casts CoT generation as a population-based search over reasoning trajectories.Candidate trajectories are iteratively evolved through reflective global crossover at the trajectory level and local mutation guided by uncertainty at the step level, enabling holistic recombination and fine-grained refinement. Lightweight, task-aware fitness functions are designed to guide the evolutionary process toward accurate and diverse reasoning. Empirically, CoTEvol improves correct-CoT synthesis success by over 30% and enhances structural diversity, with markedly improved efficiency. LLMs trained on these evolutionary CoT data achieve an average gain of 6.6% across eight math benchmarks, outperforming previous distillation and self-synthesis approaches. These results underscore the promise of evolutionary CoT synthesis as a scalable and effective method for mathematical reasoning tasks.

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.