Learning How to Use Tools, Not Just When: Pattern-Aware Tool-Integrated Reasoning

[Submitted on 27 Sep 2025 (v1), last revised 29 Jun 2026 (this version, v4)]

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Abstract:Tool-integrated reasoning (TIR) has become a key approach for improving large reasoning models (LRMs) on complex problems. Prior work has mainly studied when to invoke tools, while overlooking how tools are applied. We identify two common patterns: a calculator pattern that uses code for direct computation, and an algorithmic pattern that encodes problems as programs. Misaligned choices often cause failures even when reasoning is sound. We propose a two-stage framework that first builds code competence from both patterns and then aligns pattern selection with teacher preferences. Across challenging math datasets, our pattern-aware method substantially improves both code usage and accuracy, for instance raising Code@1 on MATH500 from 64.0% to 70.5% and on AIME24 from 26.7% to 50.0%. These gains highlight the effectiveness of a pattern-aware approach for tool-integrated reasoning.

Submission history

From: Yuxuan Jiang [view email]
[v1] Sat, 27 Sep 2025 13:10:37 UTC (145 KB)
[v2] Fri, 14 Nov 2025 22:45:01 UTC (144 KB)
[v3] Fri, 9 Jan 2026 03:22:46 UTC (144 KB)
[v4] Mon, 29 Jun 2026 12:46:01 UTC (150 KB)