Related papers: E(3)-Equivariant Mesh Neural Networks

Geometric graph neural networks (GNNs) have emerged as powerful tools for modeling molecular geometry. However, they encounter limitations in effectively capturing long-range interactions in large molecular systems. To address this…

Most attempts to represent 3D shapes for deep learning have focused on volumetric grids, multi-view images and point clouds. In this paper we look at the most popular representation of 3D shapes in computer graphics - a triangular mesh -…

In this paper, we propose a novel edge-labeling graph neural network (EGNN), which adapts a deep neural network on the edge-labeling graph, for few-shot learning. The previous graph neural network (GNN) approaches in few-shot learning have…

In hierarchal order of molecular geometry, we compare the performances of Geometric Quantum Machine Learning models. Two molecular datasets are considered: the simplistic linear shaped LiH-molecule and the trigonal pyramidal molecule NH3.…

Learning policies for multi-entity systems in 3D environments is far more complicated against single-entity scenarios, due to the exponential expansion of the global state space as the number of entities increases. One potential solution of…

Evolving Cascade Neural Networks (ECNNs) and a new training algorithm capable of selecting informative features are described. The ECNN initially learns with one input node and then evolves by adding new inputs as well as new hidden…

Highly expressive models such as deep neural networks (DNNs) have been widely applied to various applications. However, recent studies show that DNNs are vulnerable to adversarial examples, which are carefully crafted inputs aiming to…

Various classes of Graph Neural Networks (GNN) have been proposed and shown to be successful in a wide range of applications with graph structured data. In this paper, we propose a theoretical framework able to compare the expressive power…

The accurate description of electrostatic interactions remains a challenging problem for fitted potential-energy functions. The commonly used fixed partial-charge approximation fails to reproduce the electrostatic potential at short range…

The quest for efficient and robust deep learning models for molecular systems representation is increasingly critical in scientific exploration. The advent of message passing neural networks has marked a transformative era in graph-based…

Convolutional neural networks (CNN) have been frequently used to extract subject-invariant features from electroencephalogram (EEG) for classification tasks. This approach holds the underlying assumption that electrodes are equidistant…

Graph neural networks (GNNs) have emerged as powerful surrogates for mesh-based computational fluid dynamics (CFD), but training them on high-resolution unstructured meshes with hundreds of thousands of nodes remains prohibitively…

Recent advances in computational modelling of atomic systems, spanning molecules, proteins, and materials, represent them as geometric graphs with atoms embedded as nodes in 3D Euclidean space. In these graphs, the geometric attributes…

We introduce tensor field neural networks, which are locally equivariant to 3D rotations, translations, and permutations of points at every layer. 3D rotation equivariance removes the need for data augmentation to identify features in…

Group equivariant neural networks have been explored in the past few years and are interesting from theoretical and practical standpoints. They leverage concepts from group representation theory, non-commutative harmonic analysis and…

Graph representation learning has been widely studied and demonstrated effectiveness in various graph tasks. Most existing works embed graph data in the Euclidean space, while recent works extend the embedding models to hyperbolic or…

Generative Adversarial Networks (GANs) are currently the method of choice for generating visual data. Certain GAN architectures and training methods have demonstrated exceptional performance in generating realistic synthetic images (in…

Recent advances in deep learning and Transformers have driven major breakthroughs in robotics by employing techniques such as imitation learning, reinforcement learning, and LLM-based multimodal perception and decision-making. However,…

Computer representations of three-dimensional (3D) geometries are crucial for simulating systems and processes in engineering and science. In medicine, and more specifically, biomechanics and orthopaedics, obtaining and using 3D geometries…

Geometric deep learning has been revolutionizing the molecular modeling field. Despite the state-of-the-art neural network models are approaching ab initio accuracy for molecular property prediction, their applications, such as drug…