Related papers: Geometric Algebra Transformer
The intersection of deep learning and symbolic mathematics has seen rapid progress in recent years, exemplified by the work of Lample and Charton. They demonstrated that effective training of machine learning models for solving mathematical…
Reconstructing coherent 3D geometry and appearance from unposed multi-view images is a fundamental yet challenging problem in computer vision. Most existing visual geometry foundation models predict explicit geometry by regressing…
We propose a recipe on how to build a general, powerful, scalable (GPS) graph Transformer with linear complexity and state-of-the-art results on a diverse set of benchmarks. Graph Transformers (GTs) have gained popularity in the field of…
We review some recent applications of machine learning to algebraic geometry and physics. Since problems in algebraic geometry can typically be reformulated as mappings between tensors, this makes them particularly amenable to supervised…
Knowledge graph representation learning approaches provide a mapping between symbolic knowledge in the form of triples in a knowledge graph (KG) and their feature vectors. Knowledge graph embedding (KGE) models often represent relations in…
The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of the success of convolutional neural networks (ConvNets) in image data analysis and other tasks. Inspired by recent interest…
We tackle the task of synthesizing novel views of an object given a few input images and associated camera viewpoints. Our work is inspired by recent 'geometry-free' approaches where multi-view images are encoded as a (global) set-latent…
The representations of the observable algebra of a low dimensional quantum field theory form the objects of a braided tensor category. The search for gauge symmetry in the theory amounts to finding an algebra which has the same…
The design and implementation of parallel algorithms is a fundamental task in computer algebra. Combining the computer algebra system Singular and the workflow management system GPI-Space, we have developed an infrastructure for massively…
Graph transformers typically embed every node in a single Euclidean space, blurring heterogeneous topologies. We prepend a lightweight Riemannian mixture-of-experts layer that routes each node to various kinds of manifold, mixture of…
Understanding 4D point cloud videos is essential for enabling intelligent agents to perceive dynamic environments. However, temporal scale bias across varying frame rates and distributional uncertainty in irregular point clouds make it…
We propose to represent both $n$--qubits and quantum gates acting on them as elements in the complex Clifford algebra defined on a complex vector space of dimension $2n.$ In this framework, the Dirac formalism can be realized in…
The geometric calculus based on Clifford algebra is a very useful tool for geometry and physics. It describes a geometric structure which is much richer than the ordinary geometry of spacetime. A Clifford manifold (C-space) consists not…
Mesh models are a promising approach for encoding the structure of 3D objects. Current mesh reconstruction systems predict uniformly distributed vertex locations of a predetermined graph through a series of graph convolutions, leading to…
Euclidean deep learning is often inadequate for addressing real-world signals where the representation space is irregular and curved with complex topologies. Interpreting the geometric properties of such feature spaces has become paramount…
We show that main results of rational trigonometry (as developed by NJ Wildberger, "Divine Proportions", 2005) can be succinctly expressed using projective geometric algebra (PGA). In fact, the PGA representation exhibits distinct…
The Gale transform, an involution on sets of points in projective space, appears in a multitude of guises, in subjects as diverse as optimization, coding theory, theta-functions, and recently in our proof that certain general sets of points…
We explore the generalization of scattering transforms from traditional (e.g., image or audio) signals to graph data, analogous to the generalization of ConvNets in geometric deep learning, and the utility of extracted graph features in…
Gait recognition is an important biometric for human identification at a distance, particularly under low-resolution or unconstrained environments. Current works typically focus on either 2D representations (e.g., silhouettes and skeletons)…
Recently, a geometrical characterization of vector spaces served to generalize them into a new class of algebras. Instead of the algebraic properties of the underlying fields, we generalized the recently discovered property of such spaces…