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ToolMATH: A Math Tool Benchmark for Realistic Long-Horizon Multi-Tool Reasoning

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

Automatic Metrics Long Horizon Math
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 benchmark that evaluates tool-augmented language models in realistic multi-tool environments where the output depends on calling schema-specified tools and sustaining multi-step execution. It turns math problems into a controlled, correctness-checkable benchmark with tool sets, enabling systematic evaluation of model reliability under (1) large, overlapping tool catalogs and (2) the absence of the intended capability. \ToolMATH provides actionable diagnostic evidence of failure modes in tool-augmented agents, helping identify the control mechanisms required for robustness. \ToolMATH roughly contains 8k questions and 12k tools; we provide an additional hard-set \ToolMATHHard with questions and tools. Our evaluation reveals that the key failure factor is due to the inability to reason, leading to the accumulation of intermediate results' errors and constrain later decisions. Tool-list redundancy do not simply add noise, but amplify small early deviations into irreversible execution drift. The benchmark highlights that when the intended capability is missing, distractor tools can sometimes serve as partial substitutes in solution paths, yet they can also mislead models into ungrounded tool trajectories. Finally, comparisons between tool-use protocols emphasize that improvements come less from local action selection and more from long-range plan coherence and disciplined use of observations.

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 benchmark that evaluates tool-augmented language models in realistic multi-tool environments where the output depends on calling schema-specified tools and sustaining multi-step execution."

Evaluation Modes

partial

Automatic Metrics

Includes extracted eval setup.

"We introduce \ToolMATH, a math-grounded benchmark that evaluates tool-augmented language models in realistic multi-tool environments where the output depends on calling schema-specified tools and sustaining multi-step execution."

Quality Controls

missing

Not reported

No explicit QC controls found.

"We introduce \ToolMATH, a math-grounded benchmark that evaluates tool-augmented language models in realistic multi-tool environments where the output depends on calling schema-specified tools and sustaining multi-step execution."

Benchmarks / Datasets

missing

Not extracted

No benchmark anchors detected.

"We introduce \ToolMATH, a math-grounded benchmark that evaluates tool-augmented language models in realistic multi-tool environments where the output depends on calling schema-specified tools and sustaining multi-step execution."

Reported Metrics

partial

Coherence

Useful for evaluation criteria comparison.

"Finally, comparisons between tool-use protocols emphasize that improvements come less from local action selection and more from long-range plan coherence and disciplined use of observations."

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: 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

coherence

Research Brief

Metadata summary

We introduce \ToolMATH, a math-grounded benchmark that evaluates tool-augmented language models in realistic multi-tool environments where the output depends on calling schema-specified tools and sustaining multi-step execution.

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

Key Takeaways

  • We introduce \ToolMATH, a math-grounded benchmark that evaluates tool-augmented language models in realistic multi-tool environments where the output depends on calling schema-specified tools and sustaining multi-step execution.
  • It turns math problems into a controlled, correctness-checkable benchmark with tool sets, enabling systematic evaluation of model reliability under (1) large, overlapping tool catalogs and (2) the absence of the intended capability.
  • \ToolMATH provides actionable diagnostic evidence of failure modes in tool-augmented agents, helping identify the control mechanisms required for robustness.

Researcher Actions

  • Compare this paper against others mentioning MATH.
  • Validate inferred eval signals (Long-horizon tasks) 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

Research Summary

Contribution Summary

  • We introduce \ToolMATH, a math-grounded benchmark that evaluates tool-augmented language models in realistic multi-tool environments where the output depends on calling schema-specified tools and sustaining multi-step execution.
  • It turns math problems into a controlled, correctness-checkable benchmark with tool sets, enabling systematic evaluation of model reliability under (1) large, overlapping tool catalogs and (2) the absence of the intended capability.
  • \ToolMATH provides actionable diagnostic evidence of failure modes in tool-augmented agents, helping identify the control mechanisms required for robustness.

Why It Matters For Eval

  • We introduce \ToolMATH, a math-grounded benchmark that evaluates tool-augmented language models in realistic multi-tool environments where the output depends on calling schema-specified tools and sustaining multi-step execution.
  • It turns math problems into a controlled, correctness-checkable benchmark with tool sets, enabling systematic evaluation of model reliability under (1) large, overlapping tool catalogs and (2) the absence of the intended capability.

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: coherence

Related Papers

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

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