Scaling Laws for Associative Memories

arXiv:2310.02984v2 Announce Type: replace-cross
Abstract: 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 …

abstract aim arxiv cs.ai cs.cl cs.lg cs.ne discovery embeddings language language models laws memories memory paper products rules scaling stat.ml study transformer transformer language models type