Scaling Laws for Associative Memories
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.
Cite
Text
Cabannes et al. "Scaling Laws for Associative Memories." International Conference on Learning Representations, 2024.Markdown
[Cabannes et al. "Scaling Laws for Associative Memories." International Conference on Learning Representations, 2024.](https://mlanthology.org/iclr/2024/cabannes2024iclr-scaling/)BibTeX
@inproceedings{cabannes2024iclr-scaling,
title = {{Scaling Laws for Associative Memories}},
author = {Cabannes, Vivien and Dohmatob, Elvis and Bietti, Alberto},
booktitle = {International Conference on Learning Representations},
year = {2024},
url = {https://mlanthology.org/iclr/2024/cabannes2024iclr-scaling/}
}