Forward and Inverse Approximation Theory for Linear Temporal Convolutional Networks
Machine Learning
2023-05-31 v1
Abstract
We present a theoretical analysis of the approximation properties of convolutional architectures when applied to the modeling of temporal sequences. Specifically, we prove an approximation rate estimate (Jackson-type result) and an inverse approximation theorem (Bernstein-type result), which together provide a comprehensive characterization of the types of sequential relationships that can be efficiently captured by a temporal convolutional architecture. The rate estimate improves upon a previous result via the introduction of a refined complexity measure, whereas the inverse approximation theorem is new.
Cite
@article{arxiv.2305.18478,
title = {Forward and Inverse Approximation Theory for Linear Temporal Convolutional Networks},
author = {Haotian Jiang and Qianxiao Li},
journal= {arXiv preprint arXiv:2305.18478},
year = {2023}
}