Convolutional Neural Networks combined with Runge-Kutta Methods

A convolutional neural network can be constructed using numerical methods for solving dynamical systems, since the forward pass of the network can be regarded as a trajectory of a dynamical system. However, existing models based on numerical solvers cannot avoid the iterations of implicit methods, which makes the models inefficient at inference time. In this paper, we reinterpret the pre-activation Residual Networks (ResNets) and their variants from the dynamical systems view. We consider that the iterations of implicit Runge-Kutta methods are fused into the training of these models. Moreover, we propose a novel approach to constructing network models based on high-order Runge-Kutta methods in order to achieve higher efficiency. Our proposed models are referred to as the Runge-Kutta Convolutional Neural Networks (RKCNNs). The RKCNNs are evaluated on multiple benchmark datasets. The experimental results show that RKCNNs are vastly superior to other dynamical system network models: they achieve higher accuracy with much fewer resources. They also expand the family of network models based on numerical methods for dynamical systems.