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arXiv · 2602.21265

ToolMATH: A Diagnostic Benchmark for Long-Horizon Tool Use under Systematic Tool-Catalog Constraints

Hyeonje Choi·Jeongsoo Lee·Hyojun Lee·Jay-Yoon Lee
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Abstract

We introduce \ToolMATH, a math-grounded diagnostic benchmark for evaluating long-horizon tool use under controllable tool-catalog conditions. \ToolMATH converts stepwise MATH solutions into reusable Python tools with natural-language descriptions and typed schemas, and pairs each problem with a tool environment requiring sequential tool use, intermediate-output reuse, and logically connected tool-call chains. \ToolMATH controls tool availability and catalog difficulty by constructing gold tools and graded distractors with varying similarity to gold tools. \ToolMATH also incorporates behavior-conditioned metrics, enabling diagnostic evaluation beyond final accuracy. Building on these measurements, \ToolMATH emphasizes three evaluation axes: (1) \emph{Adaptability} measures how much Gold-only success is retained when gold tools are replaced entirely by distractors; (2) \emph{Robustness} measures stability under adding distractors as a noise; and (3) \emph{Tool Connectivity} measures whether models preserve accuracy over long executed tool-call chains. Furthermore, trace-level failure analyses characterize how models fail under each tool-catalog condition. Together, these diagnostics reveal distinct model profiles: reliable tool use, tool avoidance, adaptive substitution, and impacts of unreliable tool catalogs. Overall, \ToolMATH provides a controlled testbed for evaluating how language models adapt to changing tool availability, remain robust to distractors, and maintain correctness across long-horizon tool-use trajectories.

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Hyeonje Choi, Jeongsoo Lee, Hyojun Lee, Jay-Yoon Lee. 2026-02-24. ToolMATH: A Diagnostic Benchmark for Long-Horizon Tool Use under Systematic Tool-Catalog Constraints. https://arxiv.org/abs/2602.21265

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