Forward and Inverse Approximation Theory for Linear Temporal Convolutional Networks

05/29/2023

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by   Haotian Jiang, et al.

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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.