Related papers: Geometric Algebra Model of Distributed Representat…

Generative Adversarial Network (GAN) and its variants exhibit state-of-the-art performance in the class of generative models. To capture higher-dimensional distributions, the common learning procedure requires high computational complexity…

Dimensionality reduction techniques map data represented on higher dimensions onto lower dimensions with varying degrees of information loss. Graph dimensionality reduction techniques adopt the same principle of providing latent…

We propose a new hologram representation based on structured complex-valued 2D Gaussian primitives, which replaces per-pixel information storage and reduces the parameter search space by up to 10:1. To enable end-to-end training, we develop…

Genetic Programming (GP) has traditionally entangled the evolution of symbolic representations with their performance-based evaluation, often relying solely on raw fitness scores. This tight coupling makes GP solutions more fragile and…

The current methods for learning representations with auto-encoders almost exclusively employ vectors as the latent representations. In this work, we propose to employ a tensor product structure for this purpose. This way, the obtained…

We propose a new encoder-decoder approach to learn distributed sentence representations that are applicable to multiple purposes. The model is learned by using a convolutional neural network as an encoder to map an input sentence into a…

Representation learning is the foundation for the recent success of neural network models. However, the distributed representations generated by neural networks are far from ideal. Due to their highly entangled nature, they are di cult to…

We continue our study of Hilbert space representations of the Reflection Equation Algebra, again focusing on the algebra constructed from the $R$-matrix associated to the $q$-deformation of $GL(N,\mathbb{C})$ for $0<q<1$. We develop a form…

Understanding the deep representations of complex networks is an important step of building interpretable and trustworthy machine learning applications in the age of internet. Global surrogate models that approximate the predictions of a…

Representation learning is at the heart of what makes deep learning effective. In this work, we introduce a new framework for representation learning that we call "Holographic Neural Architectures" (HNAs). In the same way that an observer…

3D Gaussian Splatting (3D-GS) has emerged as an efficient 3D representation and a promising foundation for semantic tasks like segmentation. However, existing 3D-GS-based segmentation methods typically rely on high-dimensional category…

Formal/symbolic semantics can provide canonical, rigid controllability and interpretability to sentence representations due to their \textit{localisation} or \textit{composition} property. How can we deliver such property to the current…

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…

Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges,…

Undirected graphical models are compact representations of joint probability distributions over random variables. To solve inference tasks of interest, graphical models of arbitrary topology can be trained using empirical risk minimization.…

State-of-the-art neural rendering methods optimize Gaussian scene representations from a few photographs for novel-view synthesis. Building on these representations, we develop an efficient algorithm, dubbed Gaussian Wave Splatting, to turn…

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…

Randomized iterative algorithms, such as the randomized Kaczmarz method and the randomized Gauss-Seidel method, have gained considerable popularity due to their efficacy in solving matrix-vector and matrix-matrix regression problems. Our…

We present a program that allows for the computation of tensor products of irreducible representations of Lie algebras A-G based on the explicit construction of weight states. This straightforward approach (which is slower and more…

We introduce Graph Memory (GM), a structured non-parametric framework that represents an embedding space through a compact graph of reliability-annotated prototype regions. GM encodes local geometry and regional ambiguity through prototype…