Related papers: Toward a Functional Geometric Algebra for Natural …

Rapid growth of high-dimensional datasets in fields such as single-cell RNA sequencing and spatial genomics has led to unprecedented opportunities for scientific discovery, but it also presents unique computational and statistical…

The set theory relations \in, \backslash, \Delta, \cap, and \cup have corollaries in subspace relations. Geometric Algebra is introduced as the ideal framework to explore these subspace operations. The relations \in, \backslash, and \Delta…

Volume parameterizations abound in recent literature, from the classic voxel grid to the implicit neural representation and everything in between. While implicit representations have shown impressive capacity and better memory efficiency…

We provide a compositional coalgebraic semantics for strategic games. In our framework, like in the semantics of functional programming languages, coalgebras represent the observable behaviour of systems derived from the behaviour of the…

Natural logic offers a powerful relational conception of meaning that is a natural counterpart to distributed semantic representations, which have proven valuable in a wide range of sophisticated language tasks. However, it remains an open…

While the Clifford (geometric) algebra Fourier Transform (CFT) is global, we introduce here the local Clifford (geometric) algebra (GA) wavelet concept. We show how for $n=2,3 (\mod 4)$ continuous $Cl_n$-valued admissible wavelets can be…

Graph neural networks (GNNs) on text--attributed graphs (TAGs) typically encode node texts using pretrained language models (PLMs) and propagate these embeddings through linear neighborhood aggregation. However, the representation spaces of…

This paper develops a geometric model for coupled two-state quantum systems (qubits), which is formulated using geometric (aka Clifford) algebra. It begins by showing how Euclidean spinors can be interpreted as entities in the geometric…

Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…

Text-attributed graphs require models to effectively integrate both structural topology and semantic content. Recent approaches apply large language models to graphs by linearizing structures into token sequences through random walks. These…

The exploitation of syntactic graphs (SyGs) as a word's context has been shown to be beneficial for distributional semantic models (DSMs), both at the level of individual word representations and in deriving phrasal representations via…

We introduce Natural Qubit Algebra (NQA), a compact real operator calculus for qubit systems based on a $2\times2$ block alphabet $\{I,X,Z,W\}\subset\mathrm{Mat}(2,\mathbb{R})$ and tensor-word representations. The resulting multiplication…

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…

While much of the current study on quantum computation employs low-level formalisms such as quantum circuits, several high-level languages/calculi have been recently proposed aiming at structured quantum programming. The current work…

Recently, several studies have explored methods for using KG embedding to answer logical queries. These approaches either treat embedding learning and query answering as two separated learning tasks, or fail to deal with the variability of…

Plane-based Geometric Algebra (PGA) has revealed points in a $d$-dimensional pseudo-Euclidean space $\mathbb{R}_{p,q,1}$ to be represented by $d$-blades rather than vectors. This discovery allows points to be factored into $d$ orthogonal…

Federated learning over graph-structured data exposes a fundamental mismatch between standard aggregation mechanisms and the operator nature of graph neural networks (GNNs). While federated optimization treats model parameters as elements…

With the recent advancements in deep learning, neural solvers have gained promising results in solving math word problems. However, these SOTA solvers only generate binary expression trees that contain basic arithmetic operators and do not…

Recent advancements in multimodal large language models have driven breakthroughs in visual question answering. Yet, a critical gap persists, `conceptualization'-the ability to recognize and reason about the same concept despite variations…

Large language models (LLMs) struggle with the factual error during inference due to the lack of sufficient training data and the most updated knowledge, leading to the hallucination problem. Retrieval-Augmented Generation (RAG) has gained…