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

TL;DR

The Agentic-Proposer-4B is developed, a framework that models problem synthesis as a goal-driven sequential decision process where a specialized agent dynamically selects and composes modular reasoning skills and proves that a small volume of high-quality synthetic signals can effectively substitute for massive human-curated datasets.

Abstract

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 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 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.

Figures (5)

• Figure 1: Comparison of data synthesis paradigms. (a) Traditional: open-loop, single-pass generation from static concepts—often unstable and unverifiable. (b) Agentic proposing: a closed-loop process that composes modular skills and uses tool-assisted verification to produce stable, verifiable, and well-calibrated problems.
• Figure 2: Comparison of model scale versus AIME 2025 accuracy (mean@64). Our Proposing-30B-A3B achieves a state-of-the-art 91.6% accuracy, outperforming open-source models with up to 20$\times$ more parameters (e.g., DeepSeek-v3.1, Mistral-3) and rivaling top-tier proprietary models. This demonstrates the superior parameter efficiency unlocked by our agentic synthesis framework.
• Figure 3: The Agentic-Proposer Synthesis Pipeline. The framework evolves through three sequential phases: (Stage 1) Skill Acquisition: extracting and filtering atomic skills from diverse corpora to build an autonomous skill library. (Stage 2) Agentic SFT: mimicking expert trajectories that incorporate internal reflection, tool execution, and dynamic skill pruning. (Stage 3) Agentic RL (MGPO): optimizing the policy via multi-granularity rewards. The agent follows a structured reasoning flow (Draft $\to$ Check $\to$ Refine $\to$ Finalize), guided by a curriculum-based skill distribution to synthesize high-difficulty, logically sound problems for downstream solver training.
• Figure 4: Overall performance comparison on contest mathematics benchmarks. Our Agentic Proposing-4B (38.3%) significantly outperforms all baselines under a fixed 10,000-trajectory budget, achieving a +4.1% absolute gain over the zero-shot baseline (34.2%).
• Figure 5: A full synthesis trajectory exhibiting the refinement loop. The agent identifies a conflict between the analytical constraint ($f \equiv 0$) and the sequence growth assumption ($c>0$), proactively shifting the problem objective to ensure logical soundness.

Theorems & Definitions (3)

• Lemma 3.1: Emergent Skill Compositionality
• Proposition 3.2: Optimal Policy Form
• Proposition 3.3: Zero-Sum Weighting Property