10,493 research outputs found
Weisfeiler and Leman go Hyperbolic: Learning Distance Preserving Node Representations
In recent years, graph neural networks (GNNs) have emerged as a promising
tool for solving machine learning problems on graphs. Most GNNs are members of
the family of message passing neural networks (MPNNs). There is a close
connection between these models and the Weisfeiler-Leman (WL) test of
isomorphism, an algorithm that can successfully test isomorphism for a broad
class of graphs. Recently, much research has focused on measuring the
expressive power of GNNs. For instance, it has been shown that standard MPNNs
are at most as powerful as WL in terms of distinguishing non-isomorphic graphs.
However, these studies have largely ignored the distances between the
representations of nodes/graphs which are of paramount importance for learning
tasks. In this paper, we define a distance function between nodes which is
based on the hierarchy produced by the WL algorithm, and propose a model that
learns representations which preserve those distances between nodes. Since the
emerging hierarchy corresponds to a tree, to learn these representations, we
capitalize on recent advances in the field of hyperbolic neural networks. We
empirically evaluate the proposed model on standard node and graph
classification datasets where it achieves competitive performance with
state-of-the-art models
Neural Message Passing with Edge Updates for Predicting Properties of Molecules and Materials
Neural message passing on molecular graphs is one of the most promising
methods for predicting formation energy and other properties of molecules and
materials. In this work we extend the neural message passing model with an edge
update network which allows the information exchanged between atoms to depend
on the hidden state of the receiving atom. We benchmark the proposed model on
three publicly available datasets (QM9, The Materials Project and OQMD) and
show that the proposed model yields superior prediction of formation energies
and other properties on all three datasets in comparison with the best
published results. Furthermore we investigate different methods for
constructing the graph used to represent crystalline structures and we find
that using a graph based on K-nearest neighbors achieves better prediction
accuracy than using maximum distance cutoff or the Voronoi tessellation graph
Graph Element Networks: adaptive, structured computation and memory
We explore the use of graph neural networks (GNNs) to model spatial processes
in which there is no a priori graphical structure. Similar to finite element
analysis, we assign nodes of a GNN to spatial locations and use a computational
process defined on the graph to model the relationship between an initial
function defined over a space and a resulting function in the same space. We
use GNNs as a computational substrate, and show that the locations of the nodes
in space as well as their connectivity can be optimized to focus on the most
complex parts of the space. Moreover, this representational strategy allows the
learned input-output relationship to generalize over the size of the underlying
space and run the same model at different levels of precision, trading
computation for accuracy. We demonstrate this method on a traditional PDE
problem, a physical prediction problem from robotics, and learning to predict
scene images from novel viewpoints.Comment: Accepted to ICML 201
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