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Group-convolutional neural networks (GCNNs) are among the most important methods for introducing symmetry as an inductive bias in deep learning: In each linear layer, GCNNs sample a transformation group $G$ densely and correlate data and…

Deep learning is the mainstream technique for many machine learning tasks, including image recognition, machine translation, speech recognition, and so on. It has outperformed conventional methods in various fields and achieved great…

In this paper, we aim to reconstruct a full 3D human shape from a single image. Previous vertex-level and parameter regression approaches reconstruct 3D human shape based on a pre-defined adjacency matrix to encode positive relations…

Expanding the scope of graph-based, deep-learning models to noncovalent protein-ligand interactions has earned increasing attention in structure-based drug design. Modeling the protein-ligand interactions with graph neural networks (GNNs)…

Automated construction of surface geometries of cardiac structures from volumetric medical images is important for a number of clinical applications. While deep-learning-based approaches have demonstrated promising reconstruction precision,…

To learn accurate representations of molecules, it is essential to consider both chemical and geometric features. To encode geometric information, many descriptors have been proposed in constrained circumstances for specific types of…

Recently, graph-based and Transformer-based deep learning networks have demonstrated excellent performances on various point cloud tasks. Most of the existing graph methods are based on static graph, which take a fixed input to establish…

We present a SE(3)-equivariant graph neural network (GNN) approach that directly predicting the formation factor and effective permeability from micro-CT images. FFT solvers are established to compute both the formation factor and effective…

Graph matching aims to establish correspondences between vertices of graphs such that both the node and edge attributes agree. Various learning-based methods were recently proposed for finding correspondences between image key points based…

Graph neural networks (GNN) are very popular methods in machine learning and have been applied very successfully to the prediction of the properties of molecules and materials. First-order GNNs are well known to be incomplete, i.e., there…

Machine learning (ML) and deep learning (DL) techniques have gained significant attention as reduced order models (ROMs) to computationally expensive structural analysis methods, such as finite element analysis (FEA). Graph neural network…

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,…

Generating novel graph structures that optimize given objectives while obeying some given underlying rules is fundamental for chemistry, biology and social science research. This is especially important in the task of molecular graph…

Learning methods for relative camera pose estimation have been developed largely in isolation from classical geometric approaches. The question of how to integrate predictions from deep neural networks (DNNs) and solutions from geometric…

Many scientific problems require to process data in the form of geometric graphs. Unlike generic graph data, geometric graphs exhibit symmetries of translations, rotations, and/or reflections. Researchers have leveraged such inductive bias…

Structure-based drug design (SBDD) leverages the three-dimensional geometry of proteins to identify potential drug candidates. Traditional approaches, rooted in physicochemical modeling and domain expertise, are often resource-intensive.…

Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such…

In 2D image processing, some attempts decompose images into high and low frequency components for describing edge and smooth parts respectively. Similarly, the contour and flat area of 3D objects, such as the boundary and seat area of a…

Graph convolutional neural networks~(GCNs) have recently demonstrated promising results on graph-based semi-supervised classification, but little work has been done to explore their theoretical properties. Recently, several deep neural…

Deep convolutional neural network (CNN) training via iterative optimization has had incredible success in finding optimal parameters. However, modern CNN architectures often contain millions of parameters. Thus, any given model for a single…