# Hyper-Convolutions via Implicit Kernels for Medical Imaging

arXiv: https://arxiv.org/abs/2202.02701 · HTML: https://mlsanity.com/paper/2202.02701/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 63 references that are in the map.
- First posted on arXiv 6 Feb 2022.

## Builds on (most cited first, 30 of 49)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [Non-local Neural Networks](https://mlsanity.com/paper/1711.07971/) (2017)
- [V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation](https://mlsanity.com/paper/1606.04797/) (2016)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Rethinking Atrous Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1706.05587/) (2017)
- [Pyramid Vision Transformer: A Versatile Backbone for Dense Prediction without Convolutions](https://mlsanity.com/paper/2102.12122/) (2021)
- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Multi-Scale Context Aggregation by Dilated Convolutions](https://mlsanity.com/paper/1511.07122/) (2015)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [MnasNet: Platform-Aware Neural Architecture Search for Mobile](https://mlsanity.com/paper/1807.11626/) (2018)
- [CCNet: Criss-Cross Attention for Semantic Segmentation](https://mlsanity.com/paper/1811.11721/) (2018)
- [ProxylessNAS: Direct Neural Architecture Search on Target Task and Hardware](https://mlsanity.com/paper/1812.00332/) (2018)
- [Deformable ConvNets v2: More Deformable, Better Results](https://mlsanity.com/paper/1811.11168/) (2018)
- [The Liver Tumor Segmentation Benchmark (LiTS)](https://mlsanity.com/paper/1901.04056/) (2019)
- [Improving robustness against common corruptions by covariate shift adaptation](https://mlsanity.com/paper/2006.16971/) (2020)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [High Frequency Component Helps Explain the Generalization of Convolutional Neural Networks](https://mlsanity.com/paper/1905.13545/) (2019)
- [A Fourier Perspective on Model Robustness in Computer Vision](https://mlsanity.com/paper/1906.08988/) (2019)
- [Large Kernel Matters -- Improve Semantic Segmentation by Global Convolutional Network](https://mlsanity.com/paper/1703.02719/) (2017)

## Built on by (most cited first, 2 of 2)

- [LSK3DNet: Towards Effective and Efficient 3D Perception with Large Sparse Kernels](https://mlsanity.com/paper/2403.15173/) (2024)
- [SINO: Scale-Invariant Neural Operator](https://mlsanity.com/paper/2609.36890/) (2026)

## Abstract (arXiv)

The convolutional neural network (CNN) is one of the most commonly used architectures for computer vision tasks. The key building block of a CNN is the convolutional kernel that aggregates information from the pixel neighborhood and shares weights across all pixels. A standard CNN's capacity, and thus its performance, is directly related to the number of learnable kernel weights, which is determined by the number of channels and the kernel size (support). In this paper, we present the textithyper-convolution, a novel building block that implicitly encodes the convolutional kernel using spatial coordinates. Hyper-convolutions decouple kernel size from the total number of learnable parameters, enabling a more flexible architecture design. We demonstrate in our experiments that replacing regular convolutions with hyper-convolutions can improve performance with less parameters, and increase robustness against noise. We provide our code here: https://github.com/tym002/Hyper-Convolution