Neural Generalized Ordinary Differential Equations with Layer-varying Parameters

TL;DR

This paper introduces Neural-GODE, a flexible model with layer-varying parameters that generalizes Neural-ODEs and ResNets, balancing complexity and efficiency while maintaining high accuracy.

Contribution

The paper proposes Neural-GODE with layer-varying parameters using B-spline functions, extending Neural-ODEs to better approximate ResNets and improve flexibility.

Findings

Neural-GODE is more flexible than standard Neural-ODE.

Neural-GODE balances model complexity and computational efficiency.

Neural-GODE achieves comparable accuracy to ResNets on benchmarks.

Abstract

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.