[2310.02984] Scaling Laws for Associative Memories
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Statistics > Machine Learning

arXiv:2310.02984 (stat)
[Submitted on 4 Oct 2023 (v1), last revised 20 Feb 2024 (this version, v2)]

Title:Scaling Laws for Associative Memories

Authors:Vivien Cabannes, Elvis Dohmatob, Alberto Bietti
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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 and interpret theoretical results, including fine-grained visualizations of the stored memory associations.
Subjects: Machine Learning (stat.ML); Artificial Intelligence (cs.AI); Computation and Language (cs.CL); Machine Learning (cs.LG); Neural and Evolutionary Computing (cs.NE)
ACM classes: I.2.6; G.1.6
Cite as: arXiv:2310.02984 [stat.ML]
  (or arXiv:2310.02984v2 [stat.ML] for this version)
  https://doi.org/10.48550/arXiv.2310.02984

Submission history

From: Vivien Cabannes [view email]
[v1] Wed, 4 Oct 2023 17:20:34 UTC (4,877 KB)
[v2] Tue, 20 Feb 2024 19:17:52 UTC (5,340 KB)
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