# Forward and Inverse Approximation Theory for Linear Temporal Convolutional Networks

arXiv: https://arxiv.org/abs/2305.18478 · HTML: https://mlsanity.com/paper/2305.18478/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 14 references that are in the map.
- First posted on arXiv 29 May 2023.

## Builds on (most cited first, 10 of 10)

- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Multi-Scale Context Aggregation by Dilated Convolutions](https://mlsanity.com/paper/1511.07122/) (2015)
- [Compression of Deep Convolutional Neural Networks for Fast and Low Power Mobile Applications](https://mlsanity.com/paper/1511.06530/) (2015)
- [Comparative Study of CNN and RNN for Natural Language Processing](https://mlsanity.com/paper/1702.01923/) (2017)
- [Stable Low-rank Tensor Decomposition for Compression of Convolutional Neural Network](https://mlsanity.com/paper/2008.05441/) (2020)
- [Einconv: Exploring Unexplored Tensor Network Decompositions for Convolutional Neural Networks](https://mlsanity.com/paper/1908.04471/) (2019)
- [A Brief Survey on the Approximation Theory for Sequence Modelling](https://mlsanity.com/paper/2302.13752/) (2023)
- [Approximation Theory of Convolutional Architectures for Time Series Modelling](https://mlsanity.com/paper/2107.09355/) (2021)
- [Low-rank Tensor Decomposition for Compression of Convolutional Neural Networks Using Funnel Regularization](https://mlsanity.com/paper/2112.03690/) (2021)

## Built on by (most cited first, 1 of 1)

- [A unified framework for establishing the universal approximation of transformer-type architectures](https://mlsanity.com/paper/2506.23551/) (2025)

## 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.