Related papers: Graph Automorphism Group Equivariant Neural Networ…
We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge equivariant neural networks. We develop gauge equivariant convolutional neural networks on arbitrary manifolds $\mathcal{M}$ using…
Social and information networks are gaining huge popularity recently due to their various applications. Knowledge representation through graphs in the form of nodes and edges should preserve as many characteristics of the original data as…
Graph Neural Networks (GNNs) have emerged as a flexible and powerful approach for learning over graphs. Despite this success, existing GNNs are constrained by their local message-passing architecture and are provably limited in their…
These notes concern aspects of various graphs whose vertex set is a group $G$ and whose edges reflect group structure in some way (so that they are invariant under the action of the automorphism group of $G$). The graphs I will discuss are…
Graph neural networks (GNNs) are a powerful tool to learn representations on graphs by iteratively aggregating features from node neighbourhoods. Many variant models have been proposed, but there is limited understanding on both how to…
The orchestration of agents to optimize a collective objective without centralized control is challenging yet crucial for applications such as controlling autonomous fleets, and surveillance and reconnaissance using sensor networks.…
Graph Neural Networks (GNNs) have attracted increasing attention in recent years and have achieved excellent performance in semi-supervised node classification tasks. The success of most GNNs relies on one fundamental assumption, i.e., the…
This paper studies asynchronous message passing (AMP), a new paradigm for applying neural network based learning to graphs. Existing graph neural networks use the synchronous distributed computing model and aggregate their neighbors in each…
Graphs can model networked data by representing them as nodes and their pairwise relationships as edges. Recently, signal processing and neural networks have been extended to process and learn from data on graphs, with achievements in tasks…
Graph representation learning (GRL) methods, such as graph neural networks and graph transformer models, have been successfully used to analyze graph-structured data, mainly focusing on node classification and link prediction tasks.…
Two vertices $u$ and $v$ of a graph $\Gamma$ are strucuturally equivalent if and only if the transposition $(u\,v)$ is in Aut($\Gamma$), the automorphism group of $\Gamma$. Some properties of structural equivalence and the group of vertex…
We describe a technique to determine the automorphism group of a geometrically represented graph, by understanding the structure of the induced action on all geometric representations. Using this, we characterize automorphism groups of…
In this draft paper, we introduce a novel architecture for graph networks which is equivariant to the Euclidean group in $n$-dimensions. The model is designed to work with graph networks in their general form and can be shown to include…
Permutation equivariant neural networks are often constructed using tensor powers of $\mathbb{R}^{n}$ as their layer spaces. We show that all of the weight matrices that appear in these neural networks can be obtained from Schur-Weyl…
In this work we propose a new neural network architecture that efficiently implements and learns general purpose set-equivariant functions. Such a function f maps a set of entities x = {x1, . . . , xn} from one domain to a set of same…
Graph neural network (GNN) is a popular tool to learn the lower-dimensional representation of a graph. It facilitates the applicability of machine learning tasks on graphs by incorporating domain-specific features. There are various options…
Equivariant Graph Neural Networks (GNNs) have demonstrated significant success across various applications. To achieve completeness -- that is, the universal approximation property over the space of equivariant functions -- the network must…
Traditional supervised learning aims to learn an unknown mapping by fitting a function to a set of input-output pairs with a fixed dimension. The fitted function is then defined on inputs of the same dimension. However, in many settings,…
Despite the success of equivariant neural networks in scientific applications, they require knowing the symmetry group a priori. However, it may be difficult to know which symmetry to use as an inductive bias in practice. Enforcing the…
Local gauge symmetry underlies fundamental interactions and strongly correlated quantum matter, yet existing machine-learning approaches lack a general, principled framework for learning under site-dependent symmetries, particularly for…