Related papers: Reducing SO(3) Convolutions to SO(2) for Efficient…

Optical spectroscopies provide a powerful tool for harnessing light-matter interactions for unraveling complex electronic features such as the flat bands and nontrivial topologies of materials. These insights are crucial for the development…

Equivariant neural networks (ENNs) are graph neural networks embedded in $\mathbb{R}^3$ and are well suited for predicting molecular properties. The ENN library e3nn has customizable convolutions, which can be designed to depend only on…

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…

We propose the use of group convolutional neural network architectures (GCNNs) equivariant to the 2D Euclidean group, $E(2)$, for the task of galaxy morphology classification by utilizing symmetries of the data present in galaxy images as…

Accurately predicting the elastic properties of crystalline solids is vital for computational materials science. However, traditional atomistic scale ab initio approaches are computationally intensive, especially for studying complex…

This paper proposes a set of rules to revise various neural networks for 3D point cloud processing to rotation-equivariant quaternion neural networks (REQNNs). We find that when a neural network uses quaternion features under certain…

In representation learning on the graph-structured data, under heterophily (or low homophily), many popular GNNs may fail to capture long-range dependencies, which leads to their performance degradation. To solve the above-mentioned issue,…

This paper presents an adaptive convolutional neural network (CNN) architecture that can automate diverse topology optimization (TO) problems having different underlying physics. The architecture uses the encoder-decoder networks with dense…

The semi-tensor product of vectors generalizes the conventional inner product, enabling algebraic operations between vectors of different dimensions. Building upon this foundation, we introduce a domain-based convolutional product and…

Graph convolutional neural networks have been instrumental in machine learning of material properties. When representing tensorial properties, weights and descriptors of a physics-informed network must obey certain transformation rules to…

Recent studies have indicated that Graph Convolutional Networks (GCNs) act as a \emph{low pass} filter in spectral domain and encode smoothed node representations. In this paper, we consider their opposite, namely Graph Deconvolutional…

We present O-CNN, an Octree-based Convolutional Neural Network (CNN) for 3D shape analysis. Built upon the octree representation of 3D shapes, our method takes the average normal vectors of a 3D model sampled in the finest leaf octants as…

Deep learning for predicting the electronic-structure Hamiltonian of quantum systems necessitates satisfying the covariance laws, among which achieving SO(3)-equivariance without sacrificing the non-linear expressive capability of networks…

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…

3D meshes are fundamental data representations for capturing complex geometric shapes in computer vision and graphics applications. While Convolutional Neural Networks (CNNs) have excelled in structured data like images, extending them to…

Most existing neural networks for learning graphs address permutation invariance by conceiving of the network as a message passing scheme, where each node sums the feature vectors coming from its neighbors. We argue that this imposes a…

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…

The translation equivariance of convolutions can make convolutional neural networks translation equivariant or invariant. Equivariance to other transformations (e.g. rotations, affine transformations, scalings) may also be desirable as soon…

Graph Neural Networks (GNNs), particularly Graph Convolutional Neural Networks (GCNNs), have emerged as pivotal instruments in machine learning and signal processing for processing graph-structured data. This paper proposes an analysis…

In recent years, neural implicit representations have made remarkable progress in modeling of 3D shapes with arbitrary topology. In this work, we address two key limitations of such representations, in failing to capture local 3D geometric…