Liquid Time-constant Networks
This work addresses the need for more expressive and stable neural network models for time-series prediction, offering a novel approach that could benefit applications in fields like finance or healthcare, though it appears incremental as an enhancement within neural ODEs.
The authors tackled the problem of designing time-continuous recurrent neural networks with improved expressivity and stability by introducing Liquid Time-Constant Networks, which use linear dynamical systems modulated by nonlinear gates, resulting in superior performance on time-series prediction tasks compared to classical and modern RNNs.
We introduce a new class of time-continuous recurrent neural network models. Instead of declaring a learning system's dynamics by implicit nonlinearities, we construct networks of linear first-order dynamical systems modulated via nonlinear interlinked gates. The resulting models represent dynamical systems with varying (i.e., liquid) time-constants coupled to their hidden state, with outputs being computed by numerical differential equation solvers. These neural networks exhibit stable and bounded behavior, yield superior expressivity within the family of neural ordinary differential equations, and give rise to improved performance on time-series prediction tasks. To demonstrate these properties, we first take a theoretical approach to find bounds over their dynamics and compute their expressive power by the trajectory length measure in latent trajectory space. We then conduct a series of time-series prediction experiments to manifest the approximation capability of Liquid Time-Constant Networks (LTCs) compared to classical and modern RNNs. Code and data are available at https://github.com/raminmh/liquid_time_constant_networks