Related papers: Clifford Group Equivariant Simplicial Message Pass…

There has been recent interest in novel Clifford geometric invariants of linear transformations. This motivates the investigation of such invariants for a certain type of geometric transformation of interest in the context of root systems,…

This study utilizes community structures to address node degree biases in message-passing (MP) via learnable graph augmentations and novel graph transformers. Recent augmentation-based methods showed that MP neural networks often perform…

Graph neural network have achieved impressive results in predicting molecular properties, but they do not directly account for local and hidden structures in the graph such as functional groups and molecular geometry. At each propagation…

Hypergraph representations are both more efficient and better suited to describe data characterized by relations between two or more objects. In this work, we present a new graph neural network based on message passing capable of processing…

The inclusion of symmetries as an inductive bias, known as equivariance, often improves generalization on geometric data (e.g. grids, sets, and graphs). However, equivariant architectures are usually highly constrained, designed for…

Invariant and equivariant networks have been successfully used for learning images, sets, point clouds, and graphs. A basic challenge in developing such networks is finding the maximal collection of invariant and equivariant linear layers.…

Subsampling is used in convolutional neural networks (CNNs) in the form of pooling or strided convolutions, to reduce the spatial dimensions of feature maps and to allow the receptive fields to grow exponentially with depth. However, it is…

Group equivariance has emerged as a valuable inductive bias in deep learning, enhancing generalization, data efficiency, and robustness. Classically, group equivariant methods require the groups of interest to be known beforehand, which may…

Problems involving geometric data arise in physics, chemistry, robotics, computer vision, and many other fields. Such data can take numerous forms, for instance points, direction vectors, translations, or rotations, but to date there is no…

For approximate inference in the generalized quadratic equations model, many state-of-the-art algorithms lack any prior knowledge of the target signal structure, exhibits slow convergence, and can not handle any analytic prior knowledge of…

The Symmetric group $S_{n}$ manifests itself in large classes of quantum systems as the invariance of certain characteristics of a quantum state with respect to permuting the qubits. The subgroups of $S_{n}$ arise, among many other…

Representing and reasoning about 3D structures of macromolecules is emerging as a distinct challenge in machine learning. Here, we extend recent work on geometric vector perceptrons and apply equivariant graph neural networks to a wide…

Message Passing Neural Networks (MPNNs) have emerged as the {\em de facto} standard in graph representation learning. However, when it comes to link prediction, they often struggle, surpassed by simple heuristics such as Common Neighbor…

Graphical models use the intuitive and well-studied methods of graph theory to implicitly represent dependencies between variables in large systems. They can model the global behaviour of a complex system by specifying only local factors.…

Predicting the pose of objects from a single image is an important but difficult computer vision problem. Methods that predict a single point estimate do not predict the pose of objects with symmetries well and cannot represent uncertainty.…

Graph Neural Networks (GNNs) have demonstrated remarkable success in learning from graph-structured data. However, they face significant limitations in expressive power, struggling with long-range interactions and lacking a principled…

In recent years, deep learning techniques have shown great success in various tasks related to inverse problems, where a target quantity of interest can only be observed through indirect measurements by a forward operator. Common approaches…

We propose Geometric Clifford Algebra Networks (GCANs) for modeling dynamical systems. GCANs are based on symmetry group transformations using geometric (Clifford) algebras. We first review the quintessence of modern (plane-based) geometric…

I apply the algebraic framework developed in arXiv:1101.4542 to study geometry of elliptic spaces in 1, 2, and 3 dimensions. The background material on projectivised Clifford algebras and their application to Cayley-Klein geometries is…

Graph neural networks (GNNs) have achieved champion in wide applications. Neural message passing is a typical key module for feature propagation by aggregating neighboring features. In this work, we propose a new message passing based on…