Related papers: $C^*$-Algebraic Machine Learning: Moving in a New …

Quantum Machine Learning (QML) is the intersection of two revolutionary fields: quantum computing and machine learning. It promises to unlock unparalleled capabilities in data analysis, model building, and problem-solving by harnessing the…

We give a definition of hypergraph C*-algebras. These generalize the well-known graph C*-algebras as well as ultragraph C*-algebras. In contrast to those objects, hypergraph C*-algebras are not always nuclear. We provide a number of…

We propose to study some properties of the $C^*$-algebra naturally built out of the fundamental action that an automaton group $G$ admits on a regular rooted trees $\tree$.

In this big data era, the use of large dataset in conjunction with machine learning (ML) has been increasingly popular in both industry and academia. In recent times, the field of materials science is also undergoing a big data revolution,…

1. The popularity of Machine learning (ML), Deep learning (DL), and Artificial intelligence (AI) has risen sharply in recent years. Despite this spike in popularity, the inner workings of ML and DL algorithms are often perceived as opaque,…

Machine learning (ML) is increasingly being used in high-stakes applications impacting society. Therefore, it is of critical importance that ML models do not propagate discrimination. Collecting accurate labeled data in societal…

Clifford Group Equivariant Neural Networks (CGENNs) leverage Clifford algebras and multivectors as an alternative approach to incorporating group equivariance to ensure symmetry constraints in neural representations. In principle, this…

From a planar algebra, we give a functorial construction to produce numerous associated $C^*$-algebras. Our main construction is a Hilbert $C^*$-bimodule with a canonical real subspace which produces Pimsner-Toeplitz, Cuntz-Pimsner, and…

There is a growing consensus that solutions to complex science and engineering problems require novel methodologies that are able to integrate traditional physics-based modeling approaches with state-of-the-art machine learning (ML)…

Given two algebras A and B, sometimes assumed to be C*-algebras, we consider the question of putting algebra or C*-algebra structures on the tensor product A\otimes B. In the C*-case, assuming B to be two-dimensonal, we characterize all…

With the digitization of modern cities, large data volumes and powerful computational resources facilitate the rapid update of intelligent models deployed in smart cities. Continual learning (CL) is a novel machine learning paradigm that…

We associate with the ring $R$ of algebraic integers in a number field a C*-algebra $\cT[R]$. It is an extension of the ring C*-algebra $\cA[R]$ studied previously by the first named author in collaboration with X.Li. In contrast to…

In this note for the joint meeting of DMV and GDM we illustrate with examples the role of computer algebra in university mathematics education. We discuss its potential in teaching algebra, but also computer algebra as a subject in its own…

Machine learning often aims to produce latent embeddings of inputs which lie in a larger, abstract mathematical space. For example, in the field of 3D modeling, subsets of Euclidean space can be embedded as vectors using implicit neural…

We discuss the application of computer algebra to problems commonly arising in numerical relativity, such as the derivation of 3+1-splits, manipulation of evolution equations and automatic code generation. Particular emphasis is put on…

Both conceptual modeling and machine learning have long been recognized as important areas of research. With the increasing emphasis on digitizing and processing large amounts of data for business and other applications, it would be helpful…

Machine Learning (ML) serves as a general-purpose, highly adaptable, and versatile framework for investigating complex systems across domains. However, the resulting computational resource demands, in terms of the number of parameters and…

Machine learning (ML) and artificial intelligence (AI) have become hot topics in many information processing areas, from chatbots to scientific data analysis. At the same time, there is uncertainty about the possibility of extending…

For a long time, practitioners of the art of operator algebras always worked over the complex numbers, and nobody paid much attention to real C*-algebras. Over the last thirty years, that situation has changed, and it's become apparent that…

We write arbitrary separable nuclear C*-algebras as limits of inductive systems of finite-dimensional C*-algebras with completely positive connecting maps. The characteristic feature of such CPC*-systems is that the maps become more and…