# Gaussian Mixture Convolution Networks

arXiv: https://arxiv.org/abs/2202.09153 · HTML: https://mlsanity.com/paper/2202.09153/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 32 references that are in the map.
- First posted on arXiv 18 Feb 2022.

## Builds on (most cited first, 15 of 15)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Deep Learning for 3D Point Clouds: A Survey](https://mlsanity.com/paper/1912.12033/) (2019)
- [OctNet: Learning Deep 3D Representations at High Resolutions](https://mlsanity.com/paper/1611.05009/) (2016)
- [SpiderCNN: Deep Learning on Point Sets with Parameterized Convolutional Filters](https://mlsanity.com/paper/1803.11527/) (2018)
- [SO-Net: Self-Organizing Network for Point Cloud Analysis](https://mlsanity.com/paper/1803.04249/) (2018)
- [Point Convolutional Neural Networks by Extension Operators](https://mlsanity.com/paper/1803.10091/) (2018)
- [Escape from Cells: Deep Kd-Networks for the Recognition of 3D Point Cloud Models](https://mlsanity.com/paper/1704.01222/) (2017)
- [Monte Carlo Convolution for Learning on Non-Uniformly Sampled Point Clouds](https://mlsanity.com/paper/1806.01759/) (2018)
- [ConvPoint: Continuous Convolutions for Point Cloud Processing](https://mlsanity.com/paper/1904.02375/) (2019)
- [Efficient-CapsNet: Capsule Network with Self-Attention Routing](https://mlsanity.com/paper/2101.12491/) (2021)
- [A survey on Deep Learning Advances on Different 3D Data Representations](https://mlsanity.com/paper/1808.01462/) (2018)

## Built on by (most cited first, 4 of 4)

- [Cinematic Gaussians: Real-Time HDR Radiance Fields with Depth of Field](https://mlsanity.com/paper/2406.07329/) (2024)
- [Dilated Convolution with Learnable Spacings: beyond bilinear interpolation](https://mlsanity.com/paper/2306.00817/) (2023)
- [Performance of Gaussian Mixture Model Classifiers on Embedded Feature Spaces](https://mlsanity.com/paper/2410.13421/) (2024)
- [Rethinking Nonlinearity: Trainable Gaussian Mixture Modules for Modern Neural Architectures](https://mlsanity.com/paper/2510.06660/) (2025)

## Abstract (arXiv)

This paper proposes a novel method for deep learning based on the analytical convolution of multidimensional Gaussian mixtures. In contrast to tensors, these do not suffer from the curse of dimensionality and allow for a compact representation, as data is only stored where details exist. Convolution kernels and data are Gaussian mixtures with unconstrained weights, positions, and covariance matrices. Similar to discrete convolutional networks, each convolution step produces several feature channels, represented by independent Gaussian mixtures. Since traditional transfer functions like ReLUs do not produce Gaussian mixtures, we propose using a fitting of these functions instead. This fitting step also acts as a pooling layer if the number of Gaussian components is reduced appropriately. We demonstrate that networks based on this architecture reach competitive accuracy on Gaussian mixtures fitted to the MNIST and ModelNet data sets.