Graph Representation Learning, Deep Generative Models on Graphs, Group Equivariant Molecular Neural Networks and Multiresolution Machine Learning

作     者：Hy, Truong Son 

作者单位：The University of Chicago 

学位级别：Ph.D., Doctor of Philosophy

导师姓名：Kondor, Risi

授予年度：2022年

页      码：367页

主      题：Graph representation learning Deep generative models Graph Molecular neural networks Machine learning 

摘      要：Graph neural networks (GNNs) utilizing various ways of generalizing the concept of convolution to graphs have been widely applied to many learning tasks, including modeling physical systems, finding molecular representations to estimate quantum chemical computation, etc. Most existing GNNs address permutation invariance by conceiving of the network as a message passing scheme, where each node sums the feature vectors coming from its neighbors. We argue that this scheme imposes a limitation on the representation power of GNNs such that each node loses their identity after being aggregated by summing. Thus, we propose a new general architecture called Covariant Compositional Networks (CCNs) in which the node features are represented by higher order tensors and transform covariantly/equivariantly according to a specific representation of the symmetry group of its receptive field. Experiments show that CCNs can outperform competing methods on standard graph learning benchmarks and on estimating the molecular properties calculated by computationally expensive Density Functional Theory (DFT). This novel machine learning approach allows scientists to efficiently extract chemical knowledge and explore the increasingly growing chemical data. Understanding graphs in a multiscale perspective is essential for capturing the large-scale structure of molecules, proteins, genomes, etc. For this reason, we introduce Multiresolution Equivariant Graph Variational Autoencoder (MGVAE), the first hierarchical generative model to learn and generate graphs in a multiresolution and equivariant manner. MGVAE is built upon Multiresolution Graph Network (MGN), an architecture which explicitly learns a multilevel hard clustering of the vertices, leading to a true multiresolution hierarchy. MGVAE then employs the hierarchical variational autoencoder model to stochastically generate a graph in multiple resolution levels given the hierarchy of latent distributions. Our proposed framework achieves