Time Dependence in Non-Autonomous Neural ODEs

Jared Quincy Davis, Krzysztof Choromanski, Vikas Sindhwani, Jake Varley, Honglak Lee, Jean-Jacques Slotine, Valerii Likhosterov, Adrian Weller, Ameesh Makadia

TL;DR: Introduces non-autonomous neural odes that explicitly specify time-dependence via a flexible mechanism, enhancing expressiveness and enabling improved performance on image classification and video prediction tasks.

Abstract: Neural Ordinary Differential Equations (ODEs) are elegant reinterpretations of deep networks where continuous time can replace the discrete notion of depth, ODE solvers perform forward propagation, and the adjoint method enables efficient, constant memory backpropagation. Neural ODEs are universal approximators only when they are non-autonomous, that is, the dynamics depends explicitly on time. We propose a novel family of Neural ODEs with time-varying weights, where time-dependence is non-parametric, and the smoothness of weight trajectories can be explicitly controlled to allow a tradeoff between expressiveness and efficiency. Using this enhanced expressiveness, we outperform previous Neural ODE variants in both speed and representational capacity, ultimately outperforming standard ResNet and CNN models on select image classification and video prediction tasks.