Neural Generalized Ordinary Differential Equations with Layer-varying Parameters
This work provides a more flexible continuous model for deep learning, but it is incremental as it extends existing Neural-ODE frameworks.
The authors tackled the problem of approximating discrete ResNets with continuous models by proposing a neural generalized ordinary differential equation (Neural-GODE) with layer-varying parameters, showing it is more flexible than standard Neural-ODEs and performs comparably to ResNets in accuracy on MNIST and CIFAR-10 datasets.
Deep residual networks (ResNets) have shown state-of-the-art performance in various real-world applications. Recently, the ResNets model was reparameterized and interpreted as solutions to a continuous ordinary differential equation or Neural-ODE model. In this study, we propose a neural generalized ordinary differential equation (Neural-GODE) model with layer-varying parameters to further extend the Neural-ODE to approximate the discrete ResNets. Specifically, we use nonparametric B-spline functions to parameterize the Neural-GODE so that the trade-off between the model complexity and computational efficiency can be easily balanced. It is demonstrated that ResNets and Neural-ODE models are special cases of the proposed Neural-GODE model. Based on two benchmark datasets, MNIST and CIFAR-10, we show that the layer-varying Neural-GODE is more flexible and general than the standard Neural-ODE. Furthermore, the Neural-GODE enjoys the computational and memory benefits while performing comparably to ResNets in prediction accuracy.