Why LLMs Miss Simple Addition: Geometric Mechanism Behind Arithmetic Errors

A recent ICML 2026 paper from Nanjing University reveals that large language models encode correct arithmetic information in structured geometric manifolds, yet errors arise from noisy quantization at decision boundaries, and proposes probing, Iso‑Raw‑Sum Trajectory, and a dual‑stream consistency check to diagnose and correct these mistakes.

Arithmetic ErrorsDual-Stream ConsistencyIso-Raw-Sum Trajectory

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Why LLMs Miss Simple Addition: Geometric Mechanism Behind Arithmetic Errors

Machine Heart

Jun 17, 2026 · Artificial Intelligence

Why Large Language Models Miss Simple Addition: Iso‑Raw‑Sum Trajectories Reveal the Geometry of Errors

Despite excelling at complex reasoning, LLMs often err on multi‑digit addition; probing shows correct answers reside in hidden states, and the authors reveal a structured geometric manifold—digit basins, carry fibers, and Iso‑Raw‑Sum trajectories—explaining how errors arise via noisy quantization at decision boundaries.

Arithmetic ErrorsGeometric AnalysisLLM

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Why Large Language Models Miss Simple Addition: Iso‑Raw‑Sum Trajectories Reveal the Geometry of Errors