On the approximation properties of recurrent encoder-decoder architectures

Encoder-decoder architectures have recently gained popularity in sequence to sequence modelling, featuring in state-of-the-art models such as transformers. However, a mathematical understanding of their working principles remains limited. In this paper, we study the approximation properties of recurrent encoder-decoder architectures. Prior work established theoretical results for classical RNNs in the linear setting, where approximation capabilities can be related to smoothness and memory. Here, we find that the encoder and decoder together form a particular “temporal product structure” which determines the approximation efficiency. Moreover, the encoder-decoder architecture generalises RNNs with the capability to learn time-inhomogeneous relationships. Our results provide the theoretical understanding of approximation properties of the recurrent encoder-decoder architecture, which characterises, in the considered setting, the types of temporal relationships that can be efficiently learned.