# Liquid Time-constant Recurrent Neural Networks as Universal Approximators

arXiv: https://arxiv.org/abs/1811.00321 · HTML: https://mlsanity.com/paper/1811.00321/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Nov 2018.

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

- [The Dual Imperative: Innovation and Regulation in the AI Era](https://mlsanity.com/paper/2407.12690/) (2024)
- [StayLTC: A Cost-Effective Multimodal Framework for Hospital Length of Stay Forecasting](https://mlsanity.com/paper/2504.05691/) (2025)
- [Continuous-Time Machine Learning: A Unified Mathematical Perspective](https://mlsanity.com/paper/2609.16710/) (2026)

## Abstract (arXiv)

In this paper, we introduce the notion of liquid time-constant (LTC) recurrent neural networks (RNN)s, a subclass of continuous-time RNNs, with varying neuronal time-constant realized by their nonlinear synaptic transmission model. This feature is inspired by the communication principles in the nervous system of small species. It enables the model to approximate continuous mapping with a small number of computational units. We show that any finite trajectory of an n-dimensional continuous dynamical system can be approximated by the internal state of the hidden units and n output units of an LTC network. Here, we also theoretically find bounds on their neuronal states and varying time-constant.