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VNODE: A Piecewise Continuous Volterra Neural Network

arXiv 2509.24659 ↗First posted 29 Sep 2025cs.CV cs.AIcited by 0

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Abstract (arXiv)

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.

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References · 20

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
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  12. 2018Deep Neural Networks Motivated by Partial Differential Equationscited by 187
8 more
  1. 2018Benchmarking Neural Network Robustness to Common Corruptions and Surface Variationscited by 99
  2. 2018Global Second-order Pooling Convolutional Networkscited by 66
  3. 2021MALI: A memory efficient and reverse accurate integrator for Neural ODEscited by 42
  4. 2020Neural Ordinary Differential Equation based Recurrent Neural Network Modelcited by 12
  5. 2019Volterra Neural Networks (VNNs)cited by 5
  6. 2024GalaxyEdit: Large-Scale Image Editing Dataset with Enhanced Diffusion Adaptercited by 2
  7. 2025WaveNet-Volterra Neural Networks for Active Noise Control: A Fully Causal Approachcited by 1
  8. 2025E-ConvNeXt: A Lightweight and Efficient ConvNeXt Variant with Cross-Stage Partial Connectionscited by 1

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