# Universal Approximation of Input-Output Maps by Temporal Convolutional Nets

arXiv: https://arxiv.org/abs/1906.09211 · HTML: https://mlsanity.com/paper/1906.09211/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2019.

## Built on by (most cited first, 3 of 3)

- [Theoretical Foundations of Deep Selective State-Space Models](https://mlsanity.com/paper/2402.19047/) (2024)
- [Provable Benefits of Complex Parameterizations for Structured State Space Models](https://mlsanity.com/paper/2410.14067/) (2024)
- [Universality and approximation bounds for echo state networks with random weights](https://mlsanity.com/paper/2206.05669/) (2022)

## Abstract (arXiv)

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).