Related papers: Equivariant Machine Learning on Graphs with Nonlin…

Spherical data is found in many applications. By modeling the discretized sphere as a graph, we can accommodate non-uniformly distributed, partial, and changing samplings. Moreover, graph convolutions are computationally more efficient than…

Including covariant information, such as position, force, velocity or spin is important in many tasks in computational physics and chemistry. We introduce Steerable E(3) Equivariant Graph Neural Networks (SEGNNs) that generalise equivariant…

Density functional theory (DFT) calculations determine the relaxed atomic positions and lattice parameters that minimize the formation energy of a structure. We present an equivariant graph neural network (EGNN) model to predict the outcome…

Most existing neural networks for learning graphs 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 imposes a…

In this paper, we present a novel convolution theorem which encompasses the well known convolution theorem in (graph) signal processing as well as the one related to time-varying filters. Specifically, we show how a node-wise convolution…

Subgraph GNNs enhance message-passing GNNs expressivity by representing graphs as sets of subgraphs, demonstrating impressive performance across various tasks. However, their scalability is hindered by the need to process large numbers of…

Machine learning algorithms are heavily relied on to understand the vast amounts of data from high-energy particle collisions at the CERN Large Hadron Collider (LHC). The data from such collision events can naturally be represented with…

Message passing on hypergraphs has been a standard framework for learning higher-order correlations between hypernodes. Recently-proposed hypergraph neural networks (HGNNs) can be categorized into spatial and spectral methods based on their…

It is desirable for statistical models to detect signals of interest independently of their position. If the data is generated by some smooth process, this additional structure should be taken into account. We introduce a new class of…

Incorporating permutation equivariance into neural networks has proven to be useful in ensuring that models respect symmetries that exist in data. Symmetric tensors, which naturally appear in statistics, machine learning, and graph theory,…

Spectral features are widely incorporated within Graph Neural Networks (GNNs) to improve their expressive power, or their ability to distinguish among non-isomorphic graphs. One popular example is the usage of graph Laplacian eigenvectors…

Recent work has shown deep learning can accelerate the prediction of physical dynamics relative to numerical solvers. However, limited physical accuracy and an inability to generalize under distributional shift limit its applicability to…

Hypergraph neural networks (HNNs) using neural networks to encode hypergraphs provide a promising way to model higher-order relations in data and further solve relevant prediction tasks built upon such higher-order relations. However,…

Recent advances in Graph Neural Networks (GNNs) have explored the potential of random noise as an input feature to enhance expressivity across diverse tasks. However, naively incorporating noise can degrade performance, while architectures…

The crucial role played by the underlying symmetries of high energy physics and lattice field theories calls for the implementation of such symmetries in the neural network architectures that are applied to the physical system under…

Graphs are mathematical tools that can be used to represent complex real-world interconnected systems, such as financial markets and social networks. Hence, machine learning (ML) over graphs has attracted significant attention recently.…

Graph Convolutional Neural Networks (GCNNs) are generalizations of CNNs to graph-structured data, in which convolution is guided by the graph topology. In many cases where graphs are unavailable, existing methods manually construct graphs…

As a powerful tool for modeling complex relationships, hypergraphs are gaining popularity from the graph learning community. However, commonly used frameworks in deep hypergraph learning focus on hypergraphs with edge-independent vertex…

This paper focuses on spectral graph convolutional neural networks (ConvNets), where filters are defined as elementwise multiplication in the frequency domain of a graph. In machine learning settings where the dataset consists of signals…

The translational equivariant nature of Convolutional Neural Networks (CNNs) is a reason for its great success in computer vision. However, networks do not enjoy more general equivariance properties such as rotation or scaling, ultimately…