Tool-Induced Myopia (TIM) in TaLMs

• Tool-Induced Myopia (TIM) is defined as overreliance on external tools in TaLMs, often replacing detailed internal reasoning with computational shortcuts.
• Empirical evaluations reveal a trade-off: improved final-answer accuracy but degraded logical reasoning, as shown by metrics like Win Rate and PRM Accuracy.
• Direct Preference Optimization (DPO) effectively mitigates TIM by encouraging models to integrate tool outputs with thorough, step-by-step analytical derivations.

Tool-Induced Myopia (TIM) refers to a distinct failure mode observed in tool-augmented LLMs (TaLMs) wherein external tool access—exemplified by a Python Code Interpreter—induces the model to bypass or substitute its internal reasoning capabilities with tool-driven computations. As formalized in (Bayat et al., 14 Nov 2025), TIM emerges not merely from incorrect tool selection or execution, but specifically from an overreliance on tool outputs: enumeration routines, empirical checks, or brute-force searches are substituted for rigorous derivations, analytical proofs, and logically coherent arguments. Critically, this effect manifests even when final answers are correct, resulting in solutions that appear superficially sound but lack the justificatory chains typically produced by non-tool models.

1. Formal Definition and Characterization

TIM is formally defined as follows:

“Tool-Induced Myopia (\task) is a failure mode in which access to an external tool (e.g., a Code Interpreter) causes the model to narrow its reasoning to what the tool can compute, rather than utilizing its full internal reasoning abilities. In practice, it substitutes enumeration for proof, skips necessary derivations, mistakes empirical checks for universal guarantees (e.g., brute-forcing search), and may prematurely stop once code returns a plausible output.”

Essentially, TIM occurs when a TaLM degenerates from constructing principled, human-readable mathematical arguments to providing empirical or computational outputs alone. The phenomenon does not cover scenarios where the tool is used strictly for subcomputation, provided that these are fully embedded in a coherent explanation. Only when essential reasoning steps are replaced or abbreviated is TIM present.

2. Evaluation Methodology: Four-Dimensional Suite

To robustly diagnose TIM, (Bayat et al., 14 Nov 2025) introduces a multidimensional evaluation framework that isolates reasoning quality among correct responses only. The suite comprises four metrics:

Metric Name	Purpose	Key Formula / Protocol
Final-Answer Accuracy	Measures task completion	$$\text{Final-Answer Acc.} = \frac{|\{ i: \hat{a}_i = a_i^{\mathrm{gold}} \}|}{N}$$
Win Rate	LLM judge preference for reasoning	$$\text{WinRate} = \frac{\# \{\text{TaLM Wins}\}}{\# \{\text{All Base vs.\ TaLM correct pairs}\}}$$
Miss Rate	Proportion of omitted reference steps	$$\text{MissRate} = \frac{|\text{missing steps}|}{|\text{gold steps}|}$$
PRM Accuracy	Stepwise logical/symbolic correctness	$$\text{PRM-Acc} = \frac{\#\{\text{steps labeled correct}\}}{\text{total steps}}$$

Implementation Protocol

• Final-Answer Accuracy is computed as the proportion of problems where the model’s answer matches the gold-standard.
• Win Rate is obtained by pairwise comparison of chains-of-thought from Base-LLM and TaLM (both correct final answers), adjudicated by a strong LLM judge (GPT-5), who favors solutions displaying greater reasoning depth and fewer errors.
• Miss Rate leverages a reference-based comparison: an LLM judge counts atomic solution steps present in the gold solution but omitted by the model, normalized by total gold steps.
• PRM Accuracy does not require a reference solution. Each solution step—scored by Qwen2.5-Math-7B-PRM800K—is marked correct or incorrect, with aggregate accuracy computed across steps.

TIM is empirically identified by the following metric pattern: Final-Answer Accuracy increases or remains steady, while Win Rate decreases, Miss Rate increases, and PRM Accuracy declines for TaLMs versus non-tool LLMs.

3. Empirical Findings: Prevalence and Quantitative Impact

Analysis of seven state-of-the-art models on the PYMATH benchmark (1,679 competition-level mathematics problems) reveals:

• Final-Answer Accuracy: Substantial gains under tool use (e.g., o4-mini: 45.1% to 64.4%, a 19.3 percentage point improvement).
• Reasoning Quality (Win Rate): Significant degradation (e.g., GPT-4.1-mini TaLM achieves Win Rate of 41.5%; i.e., Base-LLM solutions are preferred in the majority of correct-answer comparisons).
• Miss Rate: Increases from 45.9% (Base) to 48.8% (TaLM) on average, indicating that more reference derivation steps are omitted.
• PRM Accuracy: Drops from 76.7% to 71.1%, showing reduced stepwise soundness.
• Effect of Tool Frequency: With more tool invocations (0–3, 4–7, 8–11, 12+), TaLMs experience further reasoning degradation: Win Rate and PRM Accuracy decline, while Miss Rate increases.
• High-Risk Solutions: In solutions with correct final answers but flagged process errors (PRM) and Base-LLM judge preference, 54.3% are manually confirmed as containing TIM (~55%).

A central observation is that tool use shifts error types: whereas non-tool LLMs predominantly make arithmetic mistakes, TaLMs with TIM exhibit failures in logic, assumption, or creativity.

4. Mitigation via Direct Preference Optimization (DPO)

To counteract TIM, the framework employs Direct Preference Optimization (DPO) to realign TaLMs to use tools as assistive evidence rather than as substitutes for reasoning.

Preference Data Construction

• Chosen responses are obtained by prompting the LLM to treat code snippets “only as helpful hints,” followed by derivations.
• Rejected responses omit derivations and exaggerate empiricism, e.g., “a straightforward numerical check shows …”.

DPO Objective (following Rafailov et al., 2023):

For a preference pair $(x, r, w)$:

$$s_\theta(y|x) = \log p_\theta(y|x), \quad \Delta s(x) = s_\theta(r|x) - s_\theta(w|x)$$

$$\mathcal{L}_{\mathrm{DPO}}(\theta) = -\,\mathbb{E}_{x,r,w} \left[\log \sigma(\Delta s(x))\right] + \beta\,\mathrm{KL}(p_\theta(\cdot|x)\,\Vert\,p_{\mathrm{orig}}(\cdot|x))$$

where $\sigma$ denotes the sigmoid function and $\beta$ regulates KL divergence from the base model.

Training Details

• Fine-tune GPT-4.1 on preference pairs for 1 epoch (OpenAI API; learning-rate multiplier 0.2, batch size 4, $\beta=0.5$).
• Both positive and negative examples yield the same final answer to isolate style rather than correctness.

Results (on GPT-4.1 TaLM):

Variant	Final Acc (%)	Miss Rate (%)	Win Rate (%)	PRM Acc (%)
Base	24.6	48.1	54.4	88.6
Vanilla TaLM	27.0	49.9	45.6	85.9
TaLM + Prompting	25.1	49.4	52.7	82.9
TaLM + DPO	27.6	46.6	58.2	83.3

DPO-enhanced TaLMs improve both final-answer accuracy and reasoning process metrics, demonstrating that alignment strategies are effective in suppressing TIM without sacrificing outcome quality.

5. Representative Case Studies

Two illustrative instances highlight typical manifestations of TIM and its mitigation:

• Consecutive Integers Problem (Gemini-2.5-Flash):
  • Base LLM: Derives quadratics symbolically, solves analytically, confirms cases manually.
  • TaLM/TIM: Loops over all pairings with a Python script, reporting empirical solutions but omitting general analytical justification.
• Lame-King Tour (o4-mini):
  • Base LLM: Establishes bounds analytically, provides explicit combinatorial construction.
  • TaLM/TIM: Relies on a backtracking code routine for construction, conceding analytical gaps (“explicit construction (by a backtracking computer search)”) and omitting proof.

In both cases, correct answers are produced, but core reasoning chains are replaced—or sharply abbreviated—by computational tool use. Under DPO, models learn to embed code calls within structured, explanatory arguments, restoring logical justification.

6. Implications and Relevance to Broader Research

TIM underscores a critical distinction between solution outcome and solution process in tool-augmented reasoning. The tendency of TaLMs to substitute tool-driven checks for analytic argumentation has concrete ramifications across domains where explanation, interpretability, or formal verification are essential. The multi-dimensional evaluation framework introduced in (Bayat et al., 14 Nov 2025) is immediately applicable to future tool-augmented models, particularly in mathematical, scientific, and engineering contexts where reasoning fidelity is paramount. Preference-optimization, as exemplified by DPO, suggests a viable pathway for aligning model behavior with rigorous standards without sacrificing practical problem-solving efficacy. A plausible implication is that future tool integration strategies must explicitly guard against TIM to maintain trustworthiness in AI reasoning systems.

7. Summary

Tool-Induced Myopia systematically biases TaLMs towards externally computable solutions at the expense of internal reasoning depth and coherence. This phenomenon is quantifiable via an integrated suite that separates outcome accuracy from reasoning process quality. Direct Preference Optimization provides an effective mitigation route, incentivizing models to treat external tools as ancillary aids, thus preserving both problem-solving capacity and reasoning integrity (Bayat et al., 14 Nov 2025).