ANODEV2: A Coupled Neural ODE Evolution Framework

TL;DR

ANODEV2 introduces a coupled neural ODE framework that jointly evolves network parameters and states, leading to improved training and accuracy over existing Neural ODE methods.

Contribution

It extends Neural ODEs by enabling coupled evolution of parameters and states, providing a more general and trainable framework.

Findings

Achieves higher accuracy than baseline models

Demonstrates trainability of coupled ODE framework

Effective on CIFAR-10 dataset

Abstract

It has been observed that residual networks can be viewed as the explicit Euler discretization of an Ordinary Differential Equation (ODE). This observation motivated the introduction of so-called Neural ODEs, which allow more general discretization schemes with adaptive time stepping. Here, we propose ANODEV2, which is an extension of this approach that also allows evolution of the neural network parameters, in a coupled ODE-based formulation. The Neural ODE method introduced earlier is in fact a special case of this new more general framework. We present the formulation of ANODEV2, derive optimality conditions, and implement a coupled reaction-diffusion-advection version of this framework in PyTorch. We present empirical results using several different configurations of ANODEV2, testing them on multiple models on CIFAR-10. We report results showing that this coupled ODE-based framework is indeed trainable, and that it achieves higher accuracy, as compared to the baseline models as well as the recently-proposed Neural ODE approach.