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.