Universal Approximation of Input-Output Maps by Temporal Convolutional Nets
This provides a theoretical foundation for using TCNs over recurrent networks in sequence-to-sequence modeling, particularly for systems with limited long-term dependencies, but it is incremental as it extends known approximation capabilities.
The paper proves that temporal convolutional nets (TCNs) can approximate a large class of input-output maps with approximately finite memory to arbitrary error tolerance, deriving quantitative approximation rates based on network width, depth, and map continuity.
There has been a recent shift in sequence-to-sequence modeling from recurrent network architectures to convolutional network architectures due to computational advantages in training and operation while still achieving competitive performance. For systems having limited long-term temporal dependencies, the approximation capability of recurrent networks is essentially equivalent to that of temporal convolutional nets (TCNs). We prove that TCNs can approximate a large class of input-output maps having approximately finite memory to arbitrary error tolerance. Furthermore, we derive quantitative approximation rates for deep ReLU TCNs in terms of the width and depth of the network and modulus of continuity of the original input-output map, and apply these results to input-output maps of systems that admit finite-dimensional state-space realizations (i.e., recurrent models).