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

Liquid Time-constant Recurrent Neural Networks as Universal Approximators