# Liquid Time-constant Networks

**Authors:** Ramin Hasani, Mathias Lechner, Alexander Amini, Daniela Rus, Radu Grosu  
**arXiv:** [2006.04439](https://arxiv.org/abs/2006.04439)  
**Date:** 2020-06-08  
**Summary page:** https://www.summarizepaper.com/en/paper/2006.04439v4/

## Key points

- Introduction of Liquid Time-constant Networks (LTCs) as a new class of time-continuous recurrent neural network models
- LTCs differ from traditional approaches by using networks of linear first-order dynamical systems modulated through nonlinear interlinked gates
- Ability of LTCs to represent dynamical systems with varying time-constants coupled to their hidden state
- LTCs exhibit stable and bounded behavior while offering superior expressivity within the family of neural ordinary differential equations
- Outperformance of LTCs compared to classical and modern recurrent neural networks (RNNs) in time-series prediction tasks
- Theoretical approach establishing bounds over the dynamics of LTCs and measuring their expressive power using trajectory length measure in latent trajectory space
- Experimental evidence showcasing the approximation capability of LTCs compared to other RNN variants in time-series prediction tasks
- Evaluation of how well continuous-time models, including LTCs, can capture physical dynamics through kinematic modeling on Half-Cheetah rollouts using a pre-trained controller for the HalfCheetah-v2 gym environment
- Exceptional performance of LTCs in capturing physical dynamics compared to other models
- Overall, Liquid Time-constant Networks are presented as an innovative approach for modeling dynamical systems with varying time constants, with improved performance in time-series prediction tasks and accurate capture of physical dynamics.

## Summary

In their paper titled "Liquid Time-constant Networks," Ramin Hasani, Mathias Lechner, Alexander Amini, Daniela Rus, and Radu Grosu introduce a new class of time-continuous recurrent neural network models. These models differ from traditional approaches by constructing networks of linear first-order dynamical systems that are modulated through nonlinear interlinked gates. This design allows the models to represent dynamical systems with varying time-constants coupled to their hidden state. The authors demonstrate that these Liquid Time-constant Networks (LTCs) exhibit stable and bounded behavior while offering superior expressivity within the family of neural ordinary differential equations. The LTCs also outperform classical and modern recurrent neural networks (RNNs) in time-series prediction tasks. To support their claims, the authors take a theoretical approach to establish bounds over the dynamics of LTCs and measure their expressive power using the trajectory length measure in latent trajectory space. They then conduct a series of experiments on time-series prediction tasks to showcase the approximation capability of LTCs compared to other RNN variants. Additionally, they evaluate how well continuous-time models can capture physical dynamics by performing kinematic modeling on Half-Cheetah rollouts using a pre-trained controller for the HalfCheetah-v2 gym environment. The results demonstrate that LTCs perform exceptionally well in capturing physical dynamics compared to other models. Overall, this research presents Liquid Time-constant Networks as an innovative approach for modeling dynamical systems with varying time-constants. The experimental results highlight their improved performance in time-series prediction tasks and ability to capture physical dynamics accurately.