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

Hyeonje Choi, Jeongsoo Lee, Hyojun Lee, Jay-Yoon Lee · Feb 24, 2026 · Citations: 0

Automatic Metrics Long Horizon Math Tool Use
Open arXiv Find Implementation RSS feed Shortlist (0)

How to use this page

Low trust

Use this as background context only. Do not make protocol decisions from this page alone.

Best use

Background context only

What to verify

Validate the evaluation procedure and quality controls in the full paper before operational use.

Evidence quality

Low

Derived from extracted protocol signals and abstract evidence.

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.

Low-signal caution for protocol decisions

Use this page for context, then validate protocol choices against stronger HFEPX references before implementation decisions.

  • The available metadata is too thin to trust this as a primary source.
Human Eval Hub LLM-as-Judge Hub Pairwise Preference Hub

Should You Rely On This Paper?

This paper is adjacent to HFEPX scope and is best used for background context, not as a primary protocol reference.

Best use

Background context only

Use if you need

A secondary eval reference to pair with stronger protocol papers.

Main weakness

The available metadata is too thin to trust this as a primary source.

Trust level

Low

Usefulness score

25/100 • Low

Treat as adjacent context, not a core eval-method reference.

Human Feedback Signal

Not explicit in abstract metadata

Evaluation Signal

Detected

Usefulness for eval research

Adjacent candidate

Extraction confidence 45%

If you are doing eval pipeline work, start here:

Human Eval Hub LLM-as-Judge Hub Pairwise Preference Hub Tool-Use Eval Hub

What We Could Verify

These are the protocol signals we could actually recover from the available paper metadata. Use them to decide whether this paper is worth deeper reading.

Human Feedback Types

missing

None explicit

No explicit feedback protocol extracted.

"We introduce \ToolMATH, a math-grounded diagnostic benchmark for evaluating long-horizon tool use under controllable tool-catalog conditions."

Evaluation Modes

partial

Automatic Metrics

Includes extracted eval setup.

"We introduce \ToolMATH, a math-grounded diagnostic benchmark for evaluating long-horizon tool use under controllable tool-catalog conditions."

Quality Controls

missing

Not reported

No explicit QC controls found.

"We introduce \ToolMATH, a math-grounded diagnostic benchmark for evaluating long-horizon tool use under controllable tool-catalog conditions."

Benchmarks / Datasets

missing

Not extracted

No benchmark anchors detected.

"We introduce \ToolMATH, a math-grounded diagnostic benchmark for evaluating long-horizon tool use under controllable tool-catalog conditions."

Reported Metrics

partial

Accuracy

Useful for evaluation criteria comparison.

"\ToolMATH also incorporates behavior-conditioned metrics, enabling diagnostic evaluation beyond final accuracy."

Human Feedback Details

  • Uses human feedback: No
  • Feedback types: None
  • Rater population: Not reported
  • Expertise required: Math

Evaluation Details

  • Evaluation modes: Automatic Metrics
  • Agentic eval: Tool Use, Long Horizon
  • Quality controls: Not reported
  • Evidence quality: Low
  • Use this page as: Background context only

Protocol And Measurement Signals

Benchmarks / Datasets

No benchmark or dataset names were extracted from the available abstract.

Reported Metrics

accuracy

Research Brief

Metadata summary

We introduce \ToolMATH, a math-grounded diagnostic benchmark for evaluating long-horizon tool use under controllable tool-catalog conditions.

Based on abstract + metadata only. Check the source paper before making high-confidence protocol decisions.

Key Takeaways

  • 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.

Researcher Actions

  • Compare this paper against others mentioning MATH.
  • Validate inferred eval signals (Automatic metrics, Simulation environment) against the full paper.
  • Use related-paper links to find stronger protocol-specific references.

Caveats

  • Generated from abstract + metadata only; no PDF parsing.
  • Signals below are heuristic and may miss details reported outside the abstract.

Recommended Queries

MATH Accuracy

Research Summary

Contribution Summary

  • We introduce \ToolMATH, a math-grounded diagnostic benchmark for evaluating long-horizon tool use under controllable tool-catalog conditions.
  • \ToolMATH also incorporates behavior-conditioned metrics, enabling diagnostic evaluation beyond final accuracy.
  • Building on these measurements, \ToolMATH emphasizes three evaluation axes: (1) Adaptability measures how much Gold-only success is retained when gold tools are replaced entirely by distractors; (2) Robustness measures stability under…

Why It Matters For Eval

  • We introduce \ToolMATH, a math-grounded diagnostic benchmark for evaluating long-horizon tool use under controllable tool-catalog conditions.
  • \ToolMATH also incorporates behavior-conditioned metrics, enabling diagnostic evaluation beyond final accuracy.

Researcher Checklist

  • Gap: Human feedback protocol is explicit

    No explicit human feedback protocol detected.

  • Pass: Evaluation mode is explicit

    Detected: Automatic Metrics

  • Gap: Quality control reporting appears

    No calibration/adjudication/IAA control explicitly detected.

  • Gap: Benchmark or dataset anchors are present

    No benchmark/dataset anchor extracted from abstract.

  • Pass: Metric reporting is present

    Detected: accuracy

Related Papers

Papers are ranked by protocol overlap, extraction signal alignment, and semantic proximity.

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