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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…

By conceiving physical systems as 3D many-body point clouds, geometric graph neural networks (GNNs), such as SE(3)/E(3) equivalent GNNs, have showcased promising performance. In particular, their effective message-passing mechanics make…

Deploying 3D graph neural networks (GNNs) that are equivariant to 3D rotations (the group SO(3)) on edge devices is challenging due to their high computational cost. This paper addresses the problem by compressing and accelerating an…

In this paper, we utilize hyperspheres and regular $n$-simplexes and propose an approach to learning deep features equivariant under the transformations of $n$D reflections and rotations, encompassed by the powerful group of O$(n)$. Namely,…

Incorporating Euclidean symmetries (e.g. rotation equivariance) as inductive biases into graph neural networks has improved their generalization ability and data efficiency in unbounded physical dynamics modeling. However, in various…

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 neural networks have demonstrated significant efficacy in predicting molecular interactions. Introducing equivariant vectorial representations augments expressivity by capturing geometric data symmetries, thereby improving…

Graph Neural Networks (GNNs) with equivariant properties have achieved significant success in modeling complex dynamic systems and molecular properties. However, their expressiveness ability is limited by: (1) Existing methods often…

Geometric deep learning has demonstrated a great potential in non-Euclidean data analysis. The incorporation of geometric insights into learning architecture is vital to its success. Here we propose a curvature-enhanced graph convolutional…

The automated segmentation of cortical areas has been a long-standing challenge in medical image analysis. The complex geometry of the cortex is commonly represented as a polygon mesh, whose segmentation can be addressed by graph-based…

Analyzing scalar and vector fields on the sphere, such as temperature or wind speed and direction on Earth, is a difficult task. Models should respect both the rotational symmetries of the sphere and the inherent symmetries of the vector…

We propose a general architecture that combines the coefficient learning scheme with a residual operator layer for learning mappings between continuous functions in the 3D Euclidean space. Our proposed model is guaranteed to achieve…

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…

Neural networks that process the parameters of other neural networks find applications in domains as diverse as classifying implicit neural representations, generating neural network weights, and predicting generalization errors. However,…

Deep learning has achieved a remarkable performance breakthrough in several fields, most notably in speech recognition, natural language processing, and computer vision. In particular, convolutional neural network (CNN) architectures…

Training a Convolutional Neural Network (CNN) to be robust against rotation has mostly been done with data augmentation. In this paper, another progressive vision of research direction is highlighted to encourage less dependence on data…

Predicting the binding sites of target proteins plays a fundamental role in drug discovery. Most existing deep-learning methods consider a protein as a 3D image by spatially clustering its atoms into voxels and then feed the voxelized…

Machine learning has recently entered into the mainstream of coarse-grained (CG) molecular modeling and simulation. While a variety of methods for incorporating deep learning into these models exist, many of them involve training neural…

We introduce a novel equivariant graph neural network (GNN) architecture designed to predict the tensorial response properties of molecules. Unlike traditional frameworks that focus on regressing scalar quantities and derive tensorial…

Being able to identify regions within or around proteins, to which ligands can potentially bind, is an essential step to develop new drugs. Binding site identification methods can now profit from the availability of large amounts of 3D…