# Kervolutional Neural Networks

arXiv: https://arxiv.org/abs/1904.03955 · HTML: https://mlsanity.com/paper/1904.03955/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2019.

## Built on by (most cited first, 20 of 20)

- [B-cos Networks: Alignment is All We Need for Interpretability](https://mlsanity.com/paper/2205.10268/) (2022)
- [Towards Certifying L-infinity Robustness using Neural Networks with L-inf-dist Neurons](https://mlsanity.com/paper/2102.05363/) (2021)
- [SenseFi: A Library and Benchmark on Deep-Learning-Empowered WiFi Human Sensing](https://mlsanity.com/paper/2207.07859/) (2022)
- [B-cos Alignment for Inherently Interpretable CNNs and Vision Transformers](https://mlsanity.com/paper/2306.10898/) (2023)
- [On-Off Center-Surround Receptive Fields for Accurate and Robust Image Classification](https://mlsanity.com/paper/2106.07091/) (2021)
- [Unsupervised Online Learning for Robotic Interestingness with Visual Memory](https://mlsanity.com/paper/2111.09793/) (2021)
- [Convolutional versus Self-Organized Operational Neural Networks for Real-World Blind Image Denoising](https://mlsanity.com/paper/2103.03070/) (2021)
- [Towards Understanding the Effectiveness of Attention Mechanism](https://mlsanity.com/paper/2106.15067/) (2021)
- [SSIVD-Net: A Novel Salient Super Image Classification & Detection Technique for Weaponized Violence](https://mlsanity.com/paper/2207.12850/) (2022)
- [Kernel function impact on convolutional neural networks](https://mlsanity.com/paper/2302.10266/) (2023)
- [Single Domain Generalization via Normalised Cross-correlation Based Convolutions](https://mlsanity.com/paper/2307.05901/) (2023)
- [Infinite-Dimensional Feature Interaction](https://mlsanity.com/paper/2405.13972/) (2024)
- [Universal Adder Neural Networks](https://mlsanity.com/paper/2105.14202/) (2021)
- [Computational and Storage Efficient Quadratic Neurons for Deep Neural Networks](https://mlsanity.com/paper/2306.07294/) (2023)
- [IC Networks: Remodeling the Basic Unit for Convolutional Neural Networks](https://mlsanity.com/paper/2102.03495/) (2021)
- [PowerLinear Activation Functions with application to the first layer of CNNs](https://mlsanity.com/paper/2108.09256/) (2021)
- [Exploring Kervolutional Neural Networks](https://mlsanity.com/paper/2201.07264/) (2022)
- [Regularized PolyKervNets: Optimizing Expressiveness and Efficiency for Private Inference in Deep Neural Networks](https://mlsanity.com/paper/2312.15229/) (2023)
- [Deformable Dynamic Convolution for Accurate yet Efficient Spatio-Temporal Traffic Prediction](https://mlsanity.com/paper/2507.11550/) (2025)
- [Learning with Volterra Neural Networks: A System Theoretic Perspective](https://mlsanity.com/paper/2609.01928/) (2026)

## Abstract (arXiv)

Convolutional neural networks (CNNs) have enabled the state-of-the-art performance in many computer vision tasks. However, little effort has been devoted to establishing convolution in non-linear space. Existing works mainly leverage on the activation layers, which can only provide point-wise non-linearity. To solve this problem, a new operation, kervolution (kernel convolution), is introduced to approximate complex behaviors of human perception systems leveraging on the kernel trick. It generalizes convolution, enhances the model capacity, and captures higher order interactions of features, via patch-wise kernel functions, but without introducing additional parameters. Extensive experiments show that kervolutional neural networks (KNN) achieve higher accuracy and faster convergence than baseline CNN.