Related papers: Gaussian Mixture Convolution Networks

Gaussian Mixture Convolution Networks

URL: http://arxiv.org/abs/2202.09153v1
Date: Fri, 18 Feb 2022 12:07:52 GMT
Title: Gaussian Mixture Convolution Networks
Authors: Adam Celarek, Pedro Hermosilla, Bernhard Kerbl, Timo Ropinski, Michael Wimmer
Abstract summary: This paper proposes a novel method for deep learning based on the analytical convolution of multidimensional Gaussian mixtures. We demonstrate that networks based on this architecture reach competitive accuracy on Gaussian mixtures fitted to the MNIST and ModelNet data sets.
Score: 13.493166990188278
License: http://creativecommons.org/licenses/by/4.0/
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.

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