Forward and Inverse Approximation Theory for Linear Temporal Convolutional Networks
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Abstract (arXiv)
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.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 10 of its 14 references that are in the map. First posted on arXiv 29 May 2023.
Builds on
10 of 14 references.
References · 10
- 2016WaveNet: A Generative Model for Raw Audiocited by 1,710
- 2018An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modelingcited by 1,447
- 2015Multi-Scale Context Aggregation by Dilated Convolutionscited by 1,128
- 2015Compression of Deep Convolutional Neural Networks for Fast and Low Power Mobile Applicationscited by 161
- 2017Comparative Study of CNN and RNN for Natural Language Processingcited by 81
- 2020Stable Low-rank Tensor Decomposition for Compression of Convolutional Neural Networkcited by 74
- 2019Einconv: Exploring Unexplored Tensor Network Decompositions for Convolutional Neural Networkscited by 24
- 2023A Brief Survey on the Approximation Theory for Sequence Modellingcited by 15
- 2021Approximation Theory of Convolutional Architectures for Time Series Modellingcited by 10
- 2021Low-rank Tensor Decomposition for Compression of Convolutional Neural Networks Using Funnel Regularizationcited by 6
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