How Large Language Models Perform Arithmetic Using Only Matrices
By
By Alvaro Videla
Front-window bakery material. Catches the eye, delivers the goods.
Summary
This article explores how large language models (LLMs) perform arithmetic operations like finding greatest common divisors using only matrix operations and token embeddings, without any of the physical or symbolic aids humans use (fingers, abacuses, calculators). It delves into the internal mechanics of LLMs—tokens, activations, logits—and examines the surprising capabilities and limitations of these models when tackling mathematical problems with nothing but learned statistical patterns in high-dimensional spaces.
Key quotes
· 3 pulledIf you learned arithmetic the ordinary human way, you probably learned it with a body.
A language model has none of that. It has matrices.
Tokens enter, activations flow, logits come out.
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