# Learning with Volterra Neural Networks: A System Theoretic Perspective

arXiv: https://arxiv.org/abs/2609.01928 · HTML: https://mlsanity.com/paper/2609.01928/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 12 references that are in the map.
- First posted on arXiv 1 Sep 2026.

## Builds on (most cited first, 9 of 9)

- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [FFDNet: Toward a Fast and Flexible Solution for CNN based Image Denoising](https://mlsanity.com/paper/1710.04026/) (2017)
- [Bilinear CNNs for Fine-grained Visual Recognition](https://mlsanity.com/paper/1504.07889/) (2015)
- [Conformer: Local Features Coupling Global Representations for Visual Recognition](https://mlsanity.com/paper/2105.03889/) (2021)
- [Tensor Regression Networks](https://mlsanity.com/paper/1707.08308/) (2017)
- [Pi-nets: Deep Polynomial Neural Networks](https://mlsanity.com/paper/2003.03828/) (2020)
- [Kervolutional Neural Networks](https://mlsanity.com/paper/1904.03955/) (2019)
- [VolterraNet: A higher order convolutional network with group equivariance for homogeneous manifolds](https://mlsanity.com/paper/2106.15301/) (2021)
- [DCANet: Dual Convolutional Neural Network with Attention for Image Blind Denoising](https://mlsanity.com/paper/2304.01498/) (2023)

## Abstract (arXiv)

Higher-order interaction components are important for signal, image, and video modeling, but explicit high-order operators often suffer from rapidly increasing parameter and computational costs. This paper presents kVNN, a learnable kernelized Volterra Neural operator for compact higher-order filtering. The motivation is to use kernelization to improve the efficiency of Volterra-type neural operators while providing a structured interpretation of their higher-order components. The proposed formulation combines the order-wise structure of Volterra filtering with learnable polynomial-kernel atoms, allowing different interaction orders to be represented by separate learnable centers and coefficients. This order-decoupled representation avoids explicit high-order tensor parameterization and can be implemented as a CNN-compatible layer. Experiments on representative vision tasks show that kVNN achieves a favorable accuracy--efficiency trade-off.