Related papers: From Algebraic Geometry to Machine Learning

Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this…

Machine learning (ML) may be oblivious to human bias but it is not immune to its perpetuation. Marginalisation and iniquitous group representation are often traceable in the very data used for training, and may be reflected or even enhanced…

We review some practical and philosophical questions raised by the use of machine learning in creative practice. Beyond the obvious problems regarding plagiarism and authorship, we argue that the novelty in AI Art relies mostly on a narrow…

This text is a survey of derived algebraic geometry. It covers a variety of general notions and results from the subject with a view on the recent developments at the interface with deformation quantization.

Deep learning, a branch of artificial intelligence, is a data-driven method that uses multiple layers of interconnected units or neurons to learn intricate patterns and representations directly from raw input data. Empowered by this…

Artificial Intelligence has an important place in the scientific community as a result of its successful outputs in terms of different fields. In time, the field of Artificial Intelligence has been divided into many sub-fields because of…

The aim of these notes is to demonstrate the potential for ideas in machine learning to impact on the fields of inverse problems and data assimilation. The perspective is one that is primarily aimed at researchers from inverse problems…

Here we discuss advances in the field of quantum machine learning. The following document offers a hybrid discussion; both reviewing the field as it is currently, and suggesting directions for further research. We include both algorithms…

The subject of persistent homology has vitalized applications of algebraic topology to point cloud data and to application fields far outside the realm of pure mathematics. The area has seen several fundamentally important results that are…

Some quantum algebras build from deformed oscillator algebras may be described in terms of a particular case of extended umbral calculus. We give here an example of a specific relation between such certain quantum algebras and generalized…

Physical theories grounded in mathematical symmetries are an essential component of our understanding of a wide range of properties of the universe. Similarly, in the domain of machine learning, an awareness of symmetries such as rotation…

Manifold learning is an emerging research domain of machine learning. In this work, we give an introduction into manifold learning and how it is employed for important application fields in multimedia.

The ``geometry'', in the sense of the classical differential geometry of smooth manifolds (CDG), is put under scrutiny from the point of view of Abstract Differential Geometry (ADG), along with resulting, thereby, potential physical…

Recent progress in deep learning, a special form of machine learning, has led to remarkable capabilities machines can now be endowed with: they can read and understand free flowing text, reason and bargain with human counterparts, translate…

Highly accurate force fields are a mandatory requirement to generate predictive simulations. In this regard, Machine Learning Force Fields (MLFFs) have emerged as a revolutionary approach in computational chemistry and materials science,…

This paper introduces a deep learning system based on a quantum neural network for the binary classification of points of a specific geometric pattern (Two-Moons Classification problem) on a plane. We believe that the use of hybrid deep…

This article is a review of theoretical advances in the research field of algebraic geometry and Bayesian statistics in the last two decades. Many statistical models and learning machines which contain hierarchical structures or latent…

Symmetry, a central concept in understanding the laws of nature, has been used for centuries in physics, mathematics, and chemistry, to help make mathematical models tractable. Yet, despite its power, symmetry has not been used extensively…

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…

This paper is to serve as a key to the projective (homogeneous) model developed by Charles Gunn (arXiv:1101.4542 [math.MG]). The goal is to explain the underlying concepts in a simple language and give plenty of examples. It is targeted to…