# From Proof to Program: Characterizing Tool-Induced Reasoning Hallucinations in Large Language Models

arXiv: https://arxiv.org/abs/2511.10899 · HTML: https://mlsanity.com/paper/2511.10899/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 23 of its 71 references that are in the map.
- First posted on arXiv 14 Nov 2025.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)
- LLM agents and tool use / [Tool learning and function calling](https://mlsanity.com/agents/tool-learning-and-function-calling/)

## Builds on (most cited first, 23 of 23)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [ToolLLM: Facilitating Large Language Models to Master 16000+ Real-world APIs](https://mlsanity.com/paper/2307.16789/) (2023)
- [Self-RAG: Learning to Retrieve, Generate, and Critique through Self-Reflection](https://mlsanity.com/paper/2310.11511/) (2023)
- [A Survey on LLM-as-a-Judge](https://mlsanity.com/paper/2411.15594/) (2024)
- [Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Models](https://mlsanity.com/paper/2410.07985/) (2024)
- [Judging the Judges: A Systematic Study of Position Bias in LLM-as-a-Judge](https://mlsanity.com/paper/2406.07791/) (2024)
- [Hallucination-Free? Assessing the Reliability of Leading AI Legal Research Tools](https://mlsanity.com/paper/2405.20362/) (2024)
- [ReDeEP: Detecting Hallucination in Retrieval-Augmented Generation via Mechanistic Interpretability](https://mlsanity.com/paper/2410.11414/) (2024)
- [Beyond Accuracy: Evaluating the Reasoning Behavior of Large Language Models -- A Survey](https://mlsanity.com/paper/2404.01869/) (2024)
- [Acting Less is Reasoning More! Teaching Model to Act Efficiently](https://mlsanity.com/paper/2504.14870/) (2025)
- [Proof or Bluff? Evaluating LLMs on 2025 USA Math Olympiad](https://mlsanity.com/paper/2503.21934/) (2025)
- [ComplexFuncBench: Exploring Multi-Step and Constrained Function Calling under Long-Context Scenario](https://mlsanity.com/paper/2501.10132/) (2025)
- [What Are Tools Anyway? A Survey from the Language Model Perspective](https://mlsanity.com/paper/2403.15452/) (2024)
- [What's Wrong with Your Code Generated by Large Language Models? An Extensive Study](https://mlsanity.com/paper/2407.06153/) (2024)
- [A Survey on Evaluating Large Language Models in Code Generation Tasks](https://mlsanity.com/paper/2408.16498/) (2024)
- [Reducing Tool Hallucination via Reliability Alignment](https://mlsanity.com/paper/2412.04141/) (2024)
- [Learning to Reason for Factuality](https://mlsanity.com/paper/2508.05618/) (2025)
- [VerifyBench: Benchmarking Reference-based Reward Systems for Large Language Models](https://mlsanity.com/paper/2505.15801/) (2025)
- [Search-Time Data Contamination](https://mlsanity.com/paper/2508.13180/) (2025)
- [Enhancing Mathematical Reasoning in Large Language Models with Self-Consistency-Based Hallucination Detection](https://mlsanity.com/paper/2504.09440/) (2025)
- [Towards Reliable Benchmarking: A Contamination Free, Controllable Evaluation Framework for Multi-step LLM Function Calling](https://mlsanity.com/paper/2509.26553/) (2025)
- [Rethinking Reward Models for Multi-Domain Test-Time Scaling](https://mlsanity.com/paper/2510.00492/) (2025)

## Abstract (arXiv)

Tool-augmented Language Models (TaLMs) can invoke external tools to solve problems beyond their parametric capacity. However, it remains unclear whether these tool-enabled gains reflect trustworthy reasoning. Focusing on the Code Interpreter tool, we show that even when tools are selected and executed correctly, TaLMs treat tool outputs as substitutes for reasoning, producing solutions that appear correct but lack coherent justification. We term this failure mode Tool-Induced Myopia (TIM), and study it using PYMATH, a benchmark of 1,679 competition-level mathematical problems for which Python code is helpful but not sufficient. We further develop a multi-dimensional evaluation suite to quantify reasoning degradation in TaLMs relative to their non-tool counterparts. Our findings reveal that while TaLMs achieve up to a 19.3 percentage point gain in final-answer accuracy, their reasoning behavior consistently deteriorates (e.g., non-tool LLMs win up to 41.5% more often in pairwise comparisons of the reasoning process). This degradation intensifies with tool use; the more frequently a model invokes tools, the less coherent its reasoning becomes. Moreover, tool use shifts errors from arithmetic mistakes toward global reasoning failures (logic, assumption, creativity); with TIM present in ~55% of high-risk cases. Finally, we propose a preference-optimization-based framework that realigns TaLMs to use tools as assistive evidence, improving both final-answer accuracy and reasoning depth under tool use. Codes and data are available at: https://github.com/megagonlabs/TIM.