Related papers: Sheaf Neural Networks on SPD Manifolds: Second-Ord…

Normalizing flows are a powerful technique for obtaining reparameterizable samples from complex multimodal distributions. Unfortunately current approaches fall short when the underlying space has a non trivial topology, and are only…

In this paper, we propose a new neural architecture search (NAS) problem of Symmetric Positive Definite (SPD) manifold networks, aiming to automate the design of SPD neural architectures. To address this problem, we first introduce a…

Deep neural networks implement a sequence of layer-by-layer operations that are each relatively easy to understand, but the resulting overall computation is generally difficult to understand. We consider a simple hypothesis for interpreting…

Neural implicit representations are widely used for 3D shape modeling due to their smoothness and compactness, but traditional MLP-based methods struggle with sharp features, such as edges and corners in CAD models, and require long…

Learning and reasoning about 3D molecular structures with varying size is an emerging and important challenge in machine learning and especially in drug discovery. Equivariant Graph Neural Networks (GNNs) can simultaneously leverage the…

Despite much research, Graph Neural Networks (GNNs) still do not display the favorable scaling properties of other deep neural networks such as Convolutional Neural Networks and Transformers. Previous work has identified issues such as…

Recent studies have shown that aggregating convolutional features of a pre-trained Convolutional Neural Network (CNN) can obtain impressive performance for a variety of visual tasks. The symmetric Positive Definite (SPD) matrix becomes a…

Graph Neural Networks (GNNs) have significant advantages in handling non-Euclidean data and have been widely applied across various areas, thus receiving increasing attention in recent years. The framework of GNN models mainly includes the…

Geometric graph neural networks (GNNs) that respect E(3) symmetries have achieved strong performance on small molecule modeling, but they face scalability and expressiveness challenges when applied to large biomolecules such as RNA and…

In this work, we introduce a novel approach based on algebraic topology to enhance graph convolution and attention modules by incorporating local topological properties of the data. To do so, we consider the framework of sheaf neural…

This work develops the global equations of neural networks through stacked piecewise manifolds, fixed-point theory, and boundary-conditioned iteration. Once fixed coordinates and operators are removed, a neural network appears as a…

Graph Neural Networks (GNNs) address two key challenges in applying deep learning to graph-structured data: they handle varying size input graphs and ensure invariance under graph isomorphism. While GNNs have demonstrated broad…

We study data-driven representations for three-dimensional triangle meshes, which are one of the prevalent objects used to represent 3D geometry. Recent works have developed models that exploit the intrinsic geometry of manifolds and…

Deep neural networks (DNNs) on Riemannian manifolds have garnered increasing interest in various applied areas. For instance, DNNs on spherical and hyperbolic manifolds have been designed to solve a wide range of computer vision and nature…

Recent methods in geometric deep learning have introduced various neural networks to operate over data that lie on Riemannian manifolds. Such networks are often necessary to learn well over graphs with a hierarchical structure or to learn…

Geometric trees are characterized by their tree-structured layout and spatially constrained nodes and edges, which significantly impacts their topological attributes. This inherent hierarchical structure plays a crucial role in domains such…

We consider the ability of deep neural networks to represent data that lies near a low-dimensional manifold in a high-dimensional space. We show that deep networks can efficiently extract the intrinsic, low-dimensional coordinates of such…

The rapid expansion of Internet of Things (IoT) ecosystems has led to increasingly complex and heterogeneous network topologies. Traditional network monitoring and visualization tools rely on aggregated metrics or static representations,…

We propose a new method for embedding graphs while preserving directed edge information. Learning such continuous-space vector representations (or embeddings) of nodes in a graph is an important first step for using network information…

By folding into particular 3D structures, proteins play a key role in living beings. To learn meaningful representation from a protein structure for downstream tasks, not only the global backbone topology but the local fine-grained…