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

arXiv cs.AISeptember 17, 2026en

arXiv:2609.17804v1 Announce Type: new 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 who

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