Reproduce “Gaussian Mixture Convolution Networks” on OpenResearch

About this paper

Adam Celarek, Pedro Hermosilla, Bernhard Kerbl, Timo Ropinski, Michael Wimmer

Researchers from TU Wien and Ulm University introduce Gaussian Mixture Convolution Networks (GMCNs), a deep learning approach that employs Gaussian mixtures as the core data representation to enable efficient processing of high-dimensional data. This method achieved 99.4% accuracy on the MNIST dataset and 93.3% accuracy on ModelNet10, outperforming PointNet with significantly fewer parameters for 3D classification.

Key insights

• Gaussian mixtures offer an unstructured, sparse, and adaptive data representation that enables analytical convolution operations and efficient processing in any number of dimensions, addressing limitations of voxel-based CNNs.
• The analytical convolution of two Gaussian functions results in another Gaussian, providing a mathematically elegant foundation for convolution within the GMCN framework.
• The heuristic fitting process applied after the ReLU activation not only introduces non-linearity but also effectively serves as a pooling mechanism by reducing the number of Gaussian components.

Summary by alphaXiv.