START: Self-taught Reasoner with Tools

Abstract

Large Reasoning Models (LRMs) have demonstrated remarkable capabilities in complex reasoning through long chain-of-thought, yet they struggle with precise computations and algorithmic operations. Integrating computational tools with LRMs remains challenging, particularly in activating and enhancing models’ tool-use capabilities without compromising their reasoning strengths. We address these challenges through START (Self-taught Reasoner with Tools), introducing two key innovations: (1) Hint-infer, a training-free approach that activates LRMs’ latent tool-use capabilities through artificial hints, enabling test-time performance scaling; (2) Hint-RFT, a self-training framework that enables models to learn effective tool utilization through diverse hint patterns and rejection-based data synthesis. Experiments show that START significantly improves state-of-the-art LRMs across challenging benchmarks, including competition-level mathematics (AMC23: 95.0%, AIME24: 75.6%) and graduate-level science questions (GPQA: 64.6%). Our analysis reveals that START not only enhances accuracy but also improves reasoning efficiency through strategic tool utilization, demonstrating broad applicability in complex reasoning scenarios.