Geometric Scattering on Graphs, Manifolds, and other Measure Spaces


Geometric Deep Learning is an emerging field of research that aims to extend the success of convolutional neural networks (CNNs) to data with non-Euclidean geometric structure such as graphs and manifolds. Despite being in its relative infancy, this field has already found great success and is utilized by e.g., Google Maps and Amazon’s recommender systems.

In order to improve our understanding of the networks used in this new field, several works have proposed novel versions of the scattering transform, a wavelet-based model of neural networks for graphs, manifolds, and more general measure spaces. In a similar spirit to the original Euclidean scattering transform, these geometric scattering transforms provide a mathematically rigorous framework for understanding the stability and invariance of the networks used in geometric deep learning. Additionally, they also have many interesting applications such as discovering new drug-like molecules, solving combinatorial optimization problems, and using single-cell data to predict whether or not a cancer patient will respond to treatment.