Transformers Provably Learn Sparse Token Selection While Fully-Connected Nets Cannot
This provides an algorithmic separation between transformers and fully-connected networks, addressing a foundational problem in understanding neural network capabilities for researchers in machine learning theory.
The paper tackles the sparse token selection task, showing that a one-layer transformer trained with gradient descent provably learns it and exhibits strong out-of-distribution length generalization, while fully-connected networks fail in average-case settings.
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.