# Volterra Neural Networks (VNNs)

arXiv: https://arxiv.org/abs/1910.09616 · HTML: https://mlsanity.com/paper/1910.09616/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Oct 2019.

## Built on by (most cited first, 5 of 5)

- [Latent Code-Based Fusion: A Volterra Neural Network Approach](https://mlsanity.com/paper/2104.04829/) (2021)
- [GalaxyEdit: Large-Scale Image Editing Dataset with Enhanced Diffusion Adapter](https://mlsanity.com/paper/2411.13794/) (2024)
- [Towards Differential Handling of Various Blur Regions for Accurate Image Deblurring](https://mlsanity.com/paper/2502.19677/) (2025)
- [VNODE: A Piecewise Continuous Volterra Neural Network](https://mlsanity.com/paper/2509.24659/) (2025)
- [KVNN: Learnable Multi-Kernel Volterra Neural Networks](https://mlsanity.com/paper/2604.15141/) (2026)

## Abstract (arXiv)

The importance of inference in Machine Learning (ML) has led to an explosive number of different proposals in ML, and particularly in Deep Learning. In an attempt to reduce the complexity of Convolutional Neural Networks, we propose a Volterra filter-inspired Network architecture. This architecture introduces controlled non-linearities in the form of interactions between the delayed input samples of data. We propose a cascaded implementation of Volterra Filtering so as to significantly reduce the number of parameters required to carry out the same classification task as that of a conventional Neural Network. We demonstrate an efficient parallel implementation of this Volterra Neural Network (VNN), along with its remarkable performance while retaining a relatively simpler and potentially more tractable structure. Furthermore, we show a rather sophisticated adaptation of this network to nonlinearly fuse the RGB (spatial) information and the Optical Flow (temporal) information of a video sequence for action recognition. The proposed approach is evaluated on UCF-101 and HMDB-51 datasets for action recognition, and is shown to outperform state of the art CNN approaches.