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In graph signal processing, learning the weighted connections between nodes from a set of sample signals is a fundamental task when the underlying relationships are not known a priori. This task is typically addressed by finding a graph…
We introduce the Hierarchical Unified Graph Representation (HUGR): a novel graph based intermediate representation for mixed quantum-classical programs. HUGR's design features high expressivity and extensibility to capture the capabilities…
Multi-step retrieval-augmented generation (RAG) has become a widely adopted strategy for enhancing large language models (LLMs) on tasks that demand global comprehension and intensive reasoning. Although many RAG systems incorporate a…
Recent 2D-to-3D human pose estimation works tend to utilize the graph structure formed by the topology of the human skeleton. However, we argue that this skeletal topology is too sparse to reflect the body structure and suffer from serious…
An alternative, pedagogically simpler derivation of the allowed physical wave fronts of a propagating electromagnetic signal is presented using geometric algebra. Maxwell's equations can be expressed in a single multivector equation using…
These are lecture notes for a course on the theory of Clifford algebras, with special emphasis on their wide range of applications in mathematics and physics. Clifford algebra is introduced both through a conventional tensor algebra…
A tutorial introduction to projective geometric algebra (PGA), a modern, coordinate-free framework for doing euclidean geometry. PGA features: uniform representation of points, lines, and planes; robust, parallel-safe join and meet…
Historically, there have been many attempts to produce an appropriate mathematical formalism for modeling the nature of physical space, such as Euclid's geometry, Descartes' system of Cartesian coordinates, the Argand plane, Hamilton's…
Hypercomplex signal processing (HSP) provides state-of-the-art tools to handle multidimensional signals by harnessing intrinsic correlation of the signal dimensions through Clifford algebra. Recently, the hypercomplex representation of the…
A common starting point for drug design is to find small chemical groups or "fragments" that form interactions with distinct subregions in a protein binding pocket. The subsequent challenge is to assemble these fragments into a molecule…
In this paper we study hypergraphs definable in an algebraically closed field. Our goal is to show, in the spirit of the so-called transference principles in extremal combinatorics, that if a given algebraic hypergraph is "dense" in a…
In this paper, we propose a simple and effective {geometric} model fitting method to fit and segment multi-structure data even in the presence of severe outliers. We cast the task of geometric model fitting as a representative mode-seeking…
Graph embedding methods produce unsupervised node features from graphs that can then be used for a variety of machine learning tasks. Modern graphs, particularly in industrial applications, contain billions of nodes and trillions of edges,…
We study finite-sum nonlinear programs with localized variable coupling encoded by a (hyper)graph. We introduce a graph-compliant decomposition framework that brings message passing into continuous optimization in a rigorous, implementable,…
In this paper we introduce TWIG (Topologically-Weighted Intelligence Generation), a novel, embedding-free paradigm for simulating the output of KGEs that uses a tiny fraction of the parameters. TWIG learns weights from inputs that consist…
We introduce a new formulation of the real-spectral-triple formalism in non-commutative geometry (NCG): we explain its mathematical advantages and its success in capturing the structure of the standard model of particle physics. The idea,…
Hypergraph partitioning is a recurring NP-hard problem in engineering; its efficient solution at scale hinges on parallelism. This work proposes a GPU-centric algorithm for multi-level hypergraph partitioning aimed at a specific set of…
The Clifford algebra over the three-dimensional real linear space includes its linear structure and its exterior algebra, the subspaces spanned by multivectors of the same degree determine a gradation of the Clifford algebra. Through these…
This work presents the introduction of UniSG^GA, a novel integrated scenegraph structure, that to incorporates behavior and geometry data on a 3D scene. It is specifically designed to seamlessly integrate Graph Neural Networks (GNNs) and…
This paper considers structures of systems beyond dyadic (pairwise) interactions and investigates mathematical modeling of multi-way interactions and connections as hypergraphs, where captured relationships among system entities are…