Memorization Capacity of Multi-Head Attention in Transformers

Published: 16 Jan 2024, Last Modified: 05 Mar 2024ICLR 2024 spotlightEveryoneRevisionsBibTeX
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Keywords: Learning Theory, Expressivity, Multi-Head Attention, Transformers
Submission Guidelines: I certify that this submission complies with the submission instructions as described on
TL;DR: We propose a lower bound for the memorization capacity of multi-head attention in Transformers
Abstract: Transformers have become the go-to architecture for language and vision tasks, yet their theoretical properties, especially memorization capacity, remain elusive. This paper investigates the memorization abilities of multi-head attention mechanisms, examining how many example sequences they can memorize, as a function of the number of heads and sequence length. Motivated by experimental findings on vision transformers, we introduce novel assumptions about the linear independence of input data, distinct from the commonly used general-position assumption. Under these assumptions, we demonstrate that an attention layer with $H$ heads, dimension $d$, and context size $n < d,$ featuring $\Theta(Hd^2)$ parameters, can memorize $\Omega(Hn)$ examples. Our analysis sheds light on how different attention heads handle various example sequences, aided by the softmax operator’s saturation property. We validate our findings through experiments on synthetic data.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors' identity.
Supplementary Material: zip
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Primary Area: learning theory
Submission Number: 8187