Approximation theory of transformer networks for sequence modeling

The transformer is a widely applied architecture in sequence modeling applications, but the theoretical understanding of its working principles is limited. In this work, we investigate the ability of transformers to approximate sequential relationships. We first prove a universal approximation theorem for the transformer hypothesis space. From its derivation, we identify a novel notion of regularity under which we can prove an explicit approximation rate estimate. This estimate reveals key structural properties of the transformer and suggests the types of sequence relationships that the transformer is adapted to approximating. In particular, it allows us to concretely discuss the structural bias between the transformer and classical sequence modeling methods, such as recurrent neural networks. Our findings are supported by numerical experiments.