Related papers: On the Completeness of Invariant Geometric Deep Le…

Heterogeneous graphs, comprising diverse node and edge types connected through varied relations, are ubiquitous in real-world applications. Message-passing heterogeneous graph neural networks (HGNNs) have emerged as a powerful model class…

This paper studies faithful explanations for Graph Neural Networks (GNNs). First, we provide a new and general method for formally characterizing the faithfulness of explanations for GNNs. It applies to existing explanation methods,…

Graph neural networks (GNNs) are a well-regarded tool for learned control of networked dynamical systems due to their ability to be deployed in a distributed manner. However, current distributed GNN architectures assume that all nodes in…

Graph convolutional networks (GCNs) are a widely used method for graph representation learning. To elucidate the capabilities and limitations of GCNs, we investigate their power, as a function of their number of layers, to distinguish…

Scene graphs have been proven to be useful for various scene understanding tasks due to their compact and explicit nature. However, existing approaches often neglect the importance of maintaining the symmetry-preserving property when…

Molecular interactions often involve high-order relationships that cannot be fully captured by traditional graph-based models limited to pairwise connections. Hypergraphs naturally extend graphs by enabling multi-way interactions, making…

Graph neural networks (GNNs) are powerful machine learning models for various graph learning tasks. Recently, the limitations of the expressive power of various GNN models have been revealed. For example, GNNs cannot distinguish some…

Deep Neural Networks (DNNs) are widely used for their ability to effectively approximate large classes of functions. This flexibility, however, makes the strict enforcement of constraints on DNNs an open problem. Here we present a framework…

Message-passing neural networks (MPNNs) have been successfully applied to representation learning on graphs in a variety of real-world applications. However, two fundamental weaknesses of MPNNs' aggregators limit their ability to represent…

This paper presents $\mathrm{E}(n)$ Equivariant Message Passing Simplicial Networks (EMPSNs), a novel approach to learning on geometric graphs and point clouds that is equivariant to rotations, translations, and reflections. EMPSNs can…

Deep learning has consistently defied state-of-the-art techniques in many fields over the last decade. However, we are just beginning to understand the capabilities of neural learning in symbolic domains. Deep learning architectures that…

A fundamental challenge in understanding graph neural networks (GNNs) lies in characterizing their optimization dynamics and loss landscape geometry, critical for improving interpretability and robustness. While mode connectivity, a lens…

Physics-based deep learning frameworks have shown to be effective in accurately modeling the dynamics of complex physical systems with generalization capability across problem inputs. However, time-independent problems pose the challenge of…

The analysis of 3D point clouds has diverse applications in robotics, vision and graphics. Processing them presents specific challenges since they are naturally sparse, can vary in spatial resolution and are typically unordered. Graph-based…

This paper studies the expressive power of graph neural networks falling within the message-passing framework (GNNmp). Two results are presented. First, GNNmp are shown to be Turing universal under sufficient conditions on their depth,…

Ground-state 3D geometries of molecules are essential for many molecular analysis tasks. Modern quantum mechanical methods can compute accurate 3D geometries but are computationally prohibitive. Currently, an efficient alternative to…

Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…

Learning powerful data embeddings has become a center piece in machine learning, especially in natural language processing and computer vision domains. The crux of these embeddings is that they are pretrained on huge corpus of data in a…

We present a novel physics-informed deep learning framework for solving steady-state incompressible flow on multiple sets of irregular geometries by incorporating two main elements: using a point-cloud based neural network to capture…

We propose an end-to-end deep learning learning model for graph classification and representation learning that is invariant to permutation of the nodes of the input graphs. We address the challenge of learning a fixed size graph…