Memorization Capacity of Multi-Head Attention in Transformers
It addresses a theoretical gap in Transformer properties for researchers, though it is incremental as it builds on prior assumptions.
This paper tackles the problem of understanding the memorization capacity of multi-head attention in Transformers, showing that under novel linear independence assumptions, an attention layer with H heads can memorize Ω(Hn) examples, validated on synthetic data.
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 $Θ(Hd^2)$ parameters, can memorize $Ω(Hn)$ 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.