Mathematical Foundations of High-Dimensional Concept Representation in Language Models
By
lawrenceyan
Crackling crust, pillowy middle. The kind of bagel that earns a second cup of coffee.
Summary
This article explores how large language models like GPT-3 can represent billions of concepts in a relatively small 12,288-dimensional embedding space. It examines the mathematical foundations behind this capability, focusing on high-dimensional geometry and the Johnson-Lindenstrauss lemma. The content describes a collaboration with 3Blue1Brown's Grant Sanderson to understand how transformer models pack vast amounts of conceptual information into limited dimensions through sophisticated vector space geometry.
Key quotes
· 3 pulledHow can a relatively modest embedding space of 12,288 dimensions (GPT-3) accommodate millions of distinct real-world concepts?
The answer lies at the intersection of high-dimensional geometry and a remarkable mathematical result known as the Johnson-Lindenstrauss lemma.
I discovered something unexpected that led to an interesting collaboration with Grant and a deeper understanding of vector space geometry.
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