Transformers Provably Learn Sparse Token Selection While Fully-Connected Nets Cannot

TL;DR

This paper proves that transformers can learn sparse token selection efficiently and generalize well, unlike fully-connected networks which fail in worst-case and average-case scenarios, supported by theoretical and empirical evidence.

Contribution

It establishes a theoretical separation showing transformers' ability to learn sparse token selection while fully-connected networks cannot, even in average-case settings.

Findings

Transformers trained with gradient descent learn sparse token selection.

Transformers exhibit strong out-of-distribution length generalization.

Fully-connected networks fail at the sparse token selection task.

Abstract

The transformer architecture has prevailed in various deep learning settings due to its exceptional capabilities to select and compose structural information. Motivated by these capabilities, Sanford et al. proposed the sparse token selection task, in which transformers excel while fully-connected networks (FCNs) fail in the worst case. Building upon that, we strengthen the FCN lower bound to an average-case setting and establish an algorithmic separation of transformers over FCNs. Specifically, a one-layer transformer trained with gradient descent provably learns the sparse token selection task and, surprisingly, exhibits strong out-of-distribution length generalization. We provide empirical simulations to justify our theoretical findings.