---
title: "\"Close enough?\" An investigation into multiplication errors in LLMs"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2610.38634v1"
permalink: "https://feed.astralor.com/items/itm_a7cbfca44ff51d8535ad51b2"
published: "2026-10-28T10:51:03.000Z"
score: 53
channel: "tech"
tags: ["LLM","Close","LLMs Large","LLMs","While","Large"]
---

# "Close enough?" An investigation into multiplication errors in LLMs

## At a glance

Large language models (LLMs) frequently fail at multi-digit arithmetic, but the underlying mechanisms governing these failures remain poorly understood. While recent work demonstrates that addition errors follow a "nois…

## Key points

- Large language models (LLMs) frequently fail at multi-digit arithmetic, but the underlying mechanisms governing these failures remain poorly understood.
- While recent work demonstrates that addition errors follow a "noisy quantisation" model localised around carry boundaries, whether this framework generalises to multiplication remains an open question.
- In this work, we evaluate multiplication capabilities across several small base LLMs on a dataset of 16,991 problems spanning varied operand lengths.

## Full text

Large language models (LLMs) frequently fail at multi-digit arithmetic, but the underlying mechanisms governing these failures remain poorly understood. While recent work demonstrates that addition errors follow a "noisy quantisation" model localised around carry boundaries, whether this framework generalises to multiplication remains an open question. In this work, we evaluate multiplication capabilities across several small base LLMs on a dataset of 16,991 problems spanning varied operand lengths. We show that multiplication errors do not conform to the addition-style noisy quantisation model. Instead, we uncover a novel error regime in small Qwen models: errors in lower-order columns predominantly preserve parity. Conversely, higher-order digit errors shift toward off-by-one carry failures. Our findings suggest that arithmetic computation in LLMs relies on distinct, multi-periodic internal representations where parity is tracked more robustly than exact digit identity, providing new mechanistic insights into numerical reasoning in transformers.

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