Related papers: $C^*$-Algebraic Machine Learning: Moving in a New …
The theory of Leavitt path algebras is intrinsically related, via graphs, to the theory of symbolic dynamics and $C^*$-algebras where the major classification programs have been a domain of intense research in the last 50 years. In this…
Hardly any other area of research has recently attracted as much attention as machine learning (ML) through the rapid advances in artificial intelligence (AI). This publication provides a short introduction to practical concepts and methods…
In recent years, machine learning (ML) methods have remarkably improved how cosmologists can interpret data. The next decade will bring new opportunities for data-driven cosmological discovery, but will also present new challenges for…
Abstraction is key to human and artificial intelligence as it allows one to see common structure in otherwise distinct objects or situations and as such it is a key element for generality in AI. Anti-unification (or generalization) is…
Meta continual learning algorithms seek to train a model when faced with similar tasks observed in a sequential manner. Despite promising methodological advancements, there is a lack of theoretical frameworks that enable analysis of…
The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce…
We introduce a new class of C^*-algebras, which is a generalization of both graph algebras and homeomorphism C^*-algebras. This class is very large and also very tractable. We prove the so-called gauge-invariant uniqueness theorem and the…
We present a collection of questions related to the structure and classification of nuclear C*-algebras.
Various notions of joint majorization are examined in continuous matrix algebras. The relative strengths of these notions are established via proofs and examples. In addition, the closed convex hulls of joint unitary orbits are completely…
Cuntz and Li have defined a C*-algebra associated to any integral domain, using generators and relations, and proved that it is simple and purely infinite and that it is stably isomorphic to a crossed product of a commutative C*-algebra. We…
This article is devoted to the investigation of $B^*$-algebras, dual and annihilator ultranormed algebras. Their structure is studied in the paper. Extensions of algebras and fields are considered and using them core radicals and radicals…
We extend known results about commutative $C^*$-algebras generated Toeplitz operators over the unit ball to the supermanifold setup. This is obtained by constructing commutative $C^*$-algebras of super Toeplitz operators over the super ball…
Let $M_{*}({\bf C})$ denote the C$^{*}$-algebra defined as the direct sum of all matrix algebras $\{M_{n}({\bf C}):n\geq 1\}$. It is known that $M_{*}({\bf C})$ has a non-cocommutative comultiplication $\Delta_{\varphi}$. We show that the…
In recent years, machine learning (ML) has become a key enabling technology for the sciences and industry. Especially through improvements in methodology, the availability of large databases and increased computational power, today's ML…
Despite the wide variety of input types in machine learning, this diversity is often not fully reflected in their representations or model architectures, leading to inefficiencies throughout a model's lifecycle. This paper introduces an…
Rational design of compounds with specific properties requires conceptual understanding and fast evaluation of molecular properties throughout chemical compound space (CCS) -- the huge set of all potentially stable molecules. Recent…
We study the elementary C*-algebra whose elements are the sum of a diagonal plus a compact operator. We describe the structure of the unitary group, the sets of ideals, automorhisms and projections.
Continual Learning (CL) focuses on learning from dynamic and changing data distributions while retaining previously acquired knowledge. Various methods have been developed to address the challenge of catastrophic forgetting, including…
We study the ideal structure of $C^*$-algebras arising from $C^*$-correspondences. We prove that gauge-invariant ideals of our $C^*$-algebras are parameterized by certain pairs of ideals of original $C^*$-algebras. We show that our…
We present a continuous formulation of machine learning, as a problem in the calculus of variations and differential-integral equations, in the spirit of classical numerical analysis. We demonstrate that conventional machine learning models…