On the Optimal Memorization Capacity of Transformers

TL;DR

This paper investigates the memorization capacity of Transformers, showing they can efficiently memorize data with near-optimal parameter counts, highlighting the role of self-attention and feed-forward networks in this process.

Contribution

It provides theoretical bounds on the number of parameters Transformers need to memorize data, revealing optimality and the influence of network components.

Findings

Transformers memorize labels with  ilde{O}(\u221a{N}) parameters, which is optimal.

In sequence-to-sequence tasks,  ilde{O}(\u221a{nN}) parameters are both sufficient and necessary.

Self-attention efficiently identifies input sequences; feed-forward networks can be a bottleneck.

Abstract

Recent research in the field of machine learning has increasingly focused on the memorization capacity of Transformers, but how efficient they are is not yet well understood. We demonstrate that Transformers can memorize labels with $\tilde{O}(\sqrt{N})$ parameters in a next-token prediction setting for $N$ input sequences of length $n$, which is proved to be optimal up to logarithmic factors. This indicates that Transformers can efficiently perform memorization with little influence from the input length $n$ owing to the benefit of parameter sharing. We also analyze the memorization capacity in the sequence-to-sequence setting, and find that $\tilde{O}(\sqrt{nN})$ parameters are not only sufficient, but also necessary at least for Transformers with hardmax. These results suggest that while self-attention mechanisms can efficiently identify input sequences, the feed-forward network becomes a bottleneck when associating a label to each token.