Seminar Geometry, Algebra and Physics in Deep Neural Networks

Abstract: We start from geometric first principles to construct a machine learning framework for 3D point set analysis. We argue that spherical decision surfaces are a natural choice for this type of problems, and we represent them using a non-linear embedding of 3D Euclidean space into a Minkowski space, represented by a 5D Euclidean space. Via classification experiments on a 3D Tetris dataset, we show that we can get a geometric handle on the network weights, allowing us to directly apply transformations to the network. The model is further extended into a steerable filter bank, facilitating classification in arbitrary poses.

Additionally, we study equivariance and invariance properties with respect to O(3) transformations.