Scaling Laws for Associative Memories
This provides theoretical insights into memory mechanisms in learning systems, with potential implications for transformer models.
The paper studied associative memory mechanisms using high-dimensional matrix models related to transformer language models, deriving precise scaling laws for sample and parameter sizes and analyzing statistical efficiency of estimators.
Learning arguably involves the discovery and memorization of abstract rules. The aim of this paper is to study associative memory mechanisms. Our model is based on high-dimensional matrices consisting of outer products of embeddings, which relates to the inner layers of transformer language models. We derive precise scaling laws with respect to sample size and 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.