A Four-Stage Decomposition of Word-Problem Solving and Mechanistic Fragility in LLM Math Reasoning
Published 17 Sept 2026arXiv:2609.17804
Updated 24 h ago · first seen 17 Sept 2026
paper_01M2Q5C6R2C7ZRF8Y8CDJ0SWTY
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.
Organizations
Organizations 0
No organization stated. arXiv metadata does not carry affiliations; an organization is linked only when a model card or lab page cites the paper.
Models
Models introduced or described 0
Inbound described_by relations from model cards and documentation.
No model links this paper yet
Datasets
Datasets used 0
No dataset relation recorded.
Benchmarks
Benchmarks used 0
No benchmark relation recorded.
Code
Repositories & frameworks 0
No repository linked.
Timeline
Timeline 2
- Property changedPaperA Four-Stage Decomposition of Word-Problem Solving and Mechanistic Fragility in LLM Math Reasoning
A Four-Stage Decomposition of Word-Problem Solving and Mechanistic Fragility in LLM Math Reasoning: arxiv announce type changed from cross to new
Arxiv announce typecross→newarxiv - New paperPaperA Four-Stage Decomposition of Word-Problem Solving and Mechanistic Fragility in LLM Math Reasoning
New paper: A Four-Stage Decomposition of Word-Problem Solving and Mechanistic Fragility in LLM Math Reasoning
arxiv
Sources
Sources 2
Tier 1 = official/primary, 2 = quality secondary, 3 = community, 4 = unverified. Every snapshot is archived; see all sources and the methodology.