本文提出了一种新的图像分类模型Volterra Neural Ordinary Differential Equations（VNODE），通过结合非线性Volterra滤波和连续时间神经网络常微分方程，实现了图像的高效分类。VNODE模型借鉴了视觉皮层的工作原理，采用离散Volterra特征提取与连续ODE驱动的状态演化交替进行，有效捕捉复杂模式，同时参数数量远少于传统深度架构。

arXiv:2509.24659v1 Announce Type: cross Abstract: This paper introduces Volterra Neural Ordinary Differential Equations (VNODE), a piecewise continuous Volterra Neural Network that integrates nonlinear Volterra 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 Volterra feature extraction and ODE driven state evolution. This hybrid formulation captures complex patterns while requiring substantially fewer parameters than conventional deep architectures. VNODE consistently outperforms state of the art models with improved computational complexity as exemplified on benchmark datasets like CIFAR10 and Imagenet1K.