Adam Celarek, Pedro Hermosilla, Bernhard Kerbl, Timo Ropinski, Michael Wimmer
Gaussian Mixture Convolution Networks
In The Tenth International Conference on Learning Representations (ICLR 2022), pages 1-23. April 2022.
[paper] [Code on github]

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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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BibTeX

@inproceedings{celarek-2022-gmcn,
  title =      "Gaussian Mixture Convolution Networks",
  author =     "Adam Celarek and Pedro Hermosilla and Bernhard Kerbl and
               Timo Ropinski and Michael Wimmer",
  year =       "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.",
  month =      apr,
  booktitle =  "The Tenth International Conference on Learning
               Representations (ICLR 2022)",
  event =      "ICLR | 2022",
  publisher =  "OpenReview.org",
  pages =      "1--23",
  URL =        "https://www.cg.tuwien.ac.at/research/publications/2022/celarek-2022-gmcn/",
}