A Four-Stage Decomposition of Word-Problem Solving and Mechanistic Fragility in LLM Math Reasoning

Zhongdi Qu; Carla P. Gomes

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arXiv · 2609.17804

A Four-Stage Decomposition of Word-Problem Solving and Mechanistic Fragility in LLM Math Reasoning

Zhongdi Qu·Carla P. Gomes

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Abstract

Large language models solve grade-school math word problems with high accuracy, yet a single irrelevant clause inserted into the problem can collapse it. We reconcile these observations with a mechanistic account. We show that the model's internal computation decomposes into a four-stage sequential pipeline, Schema Abstraction, Operation Planning, Operand Binding, and Computation, each stage producing a distinct intermediate representation in an identifiable band of layers. Using the same scaffold to diagnose distractor-induced failure, we localize the corruption to a single stage, Operation Planning, implemented by a set of attention heads whose causal role we validate bidirectionally. In short, we provide a mechanistic interpretation of math word problem reasoning in LLMs, and their failure when distracted.

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Zhongdi Qu, Carla P. Gomes. 2026-09-15. A Four-Stage Decomposition of Word-Problem Solving and Mechanistic Fragility in LLM Math Reasoning. https://arxiv.org/abs/2609.17804

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