Gaussian Mixture Convolution Networks

Adam Celarek

TU Wien

Pedro Hermosilla

Ulm University

Bernhard Kerbl

TU Wien

Timo Ropinski

Ulm University

Michael Wimmer

TU Wien

International Conference on Learning Representations 2022

Abstract

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.

Bibtex

@inproceedings{celarek2020gaussian,
	title={Gaussian Mixture Convolution Networks},
	author={Celarek, Adam and Hermosilla, Pedro and Kerbl, Bernhard and Ropinski, Timo and Wimmer, Michael},
	bookTitle={Proceedings of International Conference on Learning Representations}
	year={2022}
}