Memorization Capacity of Multi-Head Attention in Transformers

TL;DR

This paper analyzes the memorization capacity of multi-head attention in transformers, revealing how the number of heads and sequence length influence their ability to memorize data, supported by theoretical analysis and experiments.

Contribution

It introduces new assumptions about input data independence and provides a theoretical framework for understanding how attention heads memorize data, with validation on synthetic datasets.

Findings

Attention layers with H heads can memorize Ω(Hn) examples.

The number of parameters scales as Θ(Hd^2).

Different heads specialize in different sequences.

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.