VNODE: A Piecewise Continuous Volterra Neural Network

ABSTRACT This paper introduces V olterra Neural Ordinary Differential Equations (VNODE), a piecewise continuous V olterra Neural Network that integrates nonlinear V olterra filtering with continuous-time neural ordinary differential equations for image classification. Drawing inspiration from the visual cortex, where discrete event processing is interleaved with continuous integration, VNODE alternates between discrete V olterra feature extraction and ODE-driven state evolution. VNODE consistently outperforms state-of-the-art models with improved computational complexity as exemplified on benchmark datasets like CIFAR-10 and Imagenet-1K. Index T erms-- Neural ODEs, V olterra Neural Networks, Image Classification, Continuous-time Models 1. INTRODUCTION Over the past decade, deep learning has transformed signal and image processing. Driven by Convolutional Neural Networks, Transformers, and their variants, it has set benchmarks in image classification, action recognition, object detection, and many other computer vision tasks [1].