Associative Memories with Heavy-Tailed Data

Vivien Cabannes, Elvis Dohmatob, Alberto Bietti

Keywords: associative memory, scaling law, Zipf data, optimization-based algorithm, mechanistic interpretability

TL;DR: Scaling law for associative memory model with Zipf data + optimization study

Abstract:

Learning arguably involves the discovery and memorization of abstract rules.
But how associative memories appear in transformer architectures optimized with gradient descent algorithms?
We derive precise scaling laws for a simple input-output associative memory model with respect to parameter size, and discuss the statistical efficiency of different estimators, including optimization-based algorithms.
We provide extensive numerical experiments to validate and interpret theoretical results, including fine-grained visualizations of the stored memory associations.

Submission Number: 9