← Back to all news
arXiv AI By William Bolton, Bezawit Tilaye, Huw Day

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

Read the original on arXiv AI →

The paper investigates why large language models (LLMs) struggle with multi‑digit multiplication. By testing several small base LLMs on 16,991 multiplication problems, the authors find that errors do not follow the previously observed noisy‑quantisation pattern seen in addition. Instead, small Qwen models exhibit a new error regime: lower‑order column mistakes tend to preserve parity, while higher‑order digit errors are mainly off‑by‑one carry failures, indicating distinct internal representations for arithmetic in transformers.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv AI.

Related stories

arXiv Machine Learning
Oct 12

Algebraic Integer Quantization for Machine Learning Applications

The paper introduces algebraic integer number formats (AINF) as a framework for highly configurable and accurate compressed computation, emphasizing its reduction to purely integer arithmetic for error‑free multiply‑accumulate operations. A matrix multiplication engine leveraging AINF achieves performance close to the most efficient numerical counterparts on modern hardware accelerators. The authors further propose algebraic integer quantization (AIQ) as a lossy compression format for large language model inference, demonstrating competitive accuracy against the industry‑standard MX format at equivalent bit‑per‑parameter budgets, and suggest that higher‑order algebraic integers could yield even greater computational benefits.

By Anthony Kostal-Vazquez, Vassil Dimitrov, Branden Butler
llmsefficiencybenchmarks
More like this →
arXiv AI
Sep 7

Shared circuits predict whether LLMs generalize across formats in arithmetic reasoning

The study investigates whether large language models (LLMs) can generalize arithmetic reasoning across different input formats, such as numeric and verbal expressions in English, Spanish, and Italian. By using attribution patching, the researchers identified the specific internal circuits each model employs for numeric versus verbal arithmetic tasks. They found that the degree of overlap between a model’s numeric circuit and its verbal circuit predicts how well the model generalizes to verbal formats, explaining variations in performance across languages and formats without requiring labeled data.

By Andrea Gregor de Varda, Sana Pandey, Pengrui Han, Jacob Andreas, Evelina Fedorenko
llms
More like this →