Liquid Time-constant Recurrent Neural Networks as Universal Approximators
This provides a theoretical foundation for more efficient continuous-time RNNs in modeling dynamical systems, though it appears incremental as it builds on existing RNN frameworks.
The paper tackles the problem of approximating continuous dynamical systems with recurrent neural networks by introducing liquid time-constant RNNs, which vary neuronal time-constants based on synaptic transmission, and shows they can approximate any finite trajectory of an n-dimensional system with bounds on states and time-constants.
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.