ANODEV2: A Coupled Neural ODE Evolution Framework
This work addresses a limitation in neural network optimization by enabling coupled evolution of parameters and states, though it appears incremental as an extension of Neural ODEs.
The authors tackled the problem of extending Neural ODEs to evolve both network states and parameters in a coupled ODE framework, resulting in ANODEV2, which achieved higher accuracy on CIFAR-10 compared to baseline models and Neural ODEs.
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.