Agentic Proposing: Enhancing Large language Model Reasoning via Compositional Skill Synthesis

Advancing complex reasoning in large language models relies on high-quality, verifiable datasets, yet human annotation remains cost-prohibitive and difficult to scale. Current synthesis paradigms often face a recurring trade-off: maintaining structural validity typically restricts problem complexity, while relaxing constraints to increase difficulty frequently leads to inconsistent or unsolvable instances. To address this, we propose \textbf{Agentic Proposing}, a framework that models problem synthesis as a goal-driven sequential decision process where a specialized agent dynamically selects and composes modular reasoning skills. Through an iterative workflow of internal reflection and tool-use, we develop the \textbf{Agentic-Proposer-4B} using Multi-Granularity Policy Optimization (MGPO) to generate high-precision, verifiable training trajectories across mathematics, coding, and science. Empirical results demonstrate that downstream solvers trained on agent-synthesized data significantly outperform leading baselines and exhibit robust cross-domain generalization. Notably, a 30B solver trained on only 11,000 synthesized trajectories achieves a state-of-the-art 91.6\% accuracy on AIME25, rivaling frontier-scale proprietary models such as GPT-5 and proving that a small volume of high-quality synthetic signals can effectively substitute for massive human-curated datasets.

Training AI systems to solve complex math, coding, and science problems requires large amounts of high-quality practice problems — but creating these by hand is extremely expensive and slow. Existing automated methods struggle with a fundamental tension: simple problems are easy to generate but teach little, while harder problems often contain logical errors that mislead the AI during training. We introduce Agentic Proposing, a system where a small, specialized AI agent learns to create its own challenging practice problems. Like a skilled tutor who designs exercises tailored to a student's weaknesses, our agent drafts a problem, checks it for errors using built-in tools, and refines it until it is both difficult and logically correct. We train this agent using a new reinforcement learning method that rewards not just the final problem quality, but also good intermediate behaviors like self-checking and error correction. The key result is striking: an AI trained on just 11,000 problems created by our small agent (with only 4 billion parameters) achieves 91.6% accuracy on a prestigious math competition benchmark (AIME 2025), matching the performance of much larger commercial AI systems like GPT-5. Our approach also generalizes across domains — the same pipeline produces effective training data for coding and scientific reasoning tasks. Most importantly, once trained, our agent generates problems at roughly 2% of the cost of previous methods, making high-quality AI training data accessible at scale.