Related papers: Geometric Clifford Algebra Networks
We discuss a Clifford algebra framework for discrete symmetry groups (such as reflection, Coxeter, conformal and modular groups), leading to a surprising number of new results. Clifford algebras allow for a particularly simple description…
The conventional CNN, widely used for two-dimensional images, however, is not directly applicable to non-regular geometric surface, such as a cortical thickness. We propose Geometric CNN (gCNN) that deals with data representation over a…
Quadratic surfaces gain more and more attention among the Geometric Algebra community and some frameworks were proposed in order to represent, transform, and intersect these quadratic surfaces. As far as the authors know, none of these…
Group convolutional neural networks (G-CNNs) have been shown to increase parameter efficiency and model accuracy by incorporating geometric inductive biases. In this work, we investigate the properties of representations learned by regular…
Mathematical modelling is a cornerstone of computational biology. While mechanistic models might describe the interactions of interest of a system, they are often difficult to study. On the other hand, abstract models might capture key…
A generalized Clifford manifold is proposed in which there are coordinates not only for the basis vector generators, but for each element of the Clifford group, including the identity scalar. These new quantities are physically interpreted…
We introduce KAN-GCN, a fast and accurate emulator for ice sheet modeling that places a Kolmogorov-Arnold Network (KAN) as a feature-wise calibrator before graph convolution networks (GCNs). The KAN front end applies learnable…
Geometrical interpretations of deep learning models offer insightful perspectives into their underlying mathematical structures. In this work, we introduce a novel approach that leverages differential geometry, particularly concepts from…
3D Euclidean symmetry equivariant neural networks have demonstrated notable success in modeling complex physical systems. We introduce a framework for relaxed $E(3)$ graph equivariant neural networks that can learn and represent symmetry…
Knowledge graph (KG) embedding aims at embedding entities and relations in a KG into a lowdimensional latent representation space. Existing KG embedding approaches model entities andrelations in a KG by utilizing real-valued ,…
The field of geometric deep learning has had a profound impact on the development of innovative and powerful graph neural network architectures. Disciplines such as computer vision and computational biology have benefited significantly from…
Clifford Neural Layers improve PDE modeling by introducing Clifford Algebra into neural networks. In this project we focus on optimizing the inference of 2/3D Clifford convolutional layers and multivector activation layers for one core CPU…
This paper presents a novel paradigm in simulation-based engineering sciences by introducing a new framework called Generative Parametric Design (GPD). The GPD framework enables the generation of new designs along with their corresponding…
Stress prediction in porous materials and structures is challenging due to the high computational cost associated with direct numerical simulations. Convolutional Neural Network (CNN) based architectures have recently been proposed as…
We attach the degenerate signature (n,0,1) to the projectivized dual Grassmann algebra over R(n+1). We explore the use of the resulting Clifford algebra as a model for euclidean geometry. We avoid problems with the degenerate metric by…
We review Bacry and Levy-Leblond's work on possible kinematics as applied to 2-dimensional spacetimes, as well as the nine types of 2-dimensional Cayley-Klein geometries, illustrating how the Cayley-Klein geometries give homogeneous…
Graph neural networks (GNNs) are a class of neural networks that allow to efficiently perform inference on data that is associated to a graph structure, such as, e.g., citation networks or knowledge graphs. While several variants of GNNs…
Graph Convolutional Networks (GCNs) and their variants have achieved significant performances on various recommendation tasks. However, many existing GCN models tend to perform recursive aggregations among all related nodes, which can arise…
This paper introduces a novel approach to sea ice modeling using Graph Neural Networks (GNNs), utilizing the natural graph structure of sea ice, where nodes represent individual ice pieces, and edges model the physical interactions,…
Graph Neural Networks (GNNs) have emerged as a powerful and flexible framework for representation learning on irregular data. As they generalize the operations of classical CNNs on grids to arbitrary topologies, GNNs also bring much of the…