Jonathan Siegel - Constructing Symmetry-Preserving Neural Network Models скачать в хорошем качестве

Jonathan Siegel - Constructing Symmetry-Preserving Neural Network Models

Abstract: In many practical applications of machine learning, especially to scientific disciplines like physics, chemistry, or biology, the ground truth satisfies some known symmetries. For example, the chemical properties of a molecule are invariant to rotations, translations, and permutation of identical atoms. In such applications, it is often highly desirable to build these symmetries into the neural network model. We will discuss two methods for doing this: constructing special architectures which preserve the desired symmetries, and building invariance into a standard (non-invariant) architecure via pre- and postprocessing the inputs and outputs. For the former, we will discuss universality and approximation rates for the popular permutation invariant Deep Sets architecture. For the latter, we will discuss the construction of canonicalizations and weighted frames for the actions of permutations and rotations.