Related papers: From Algebraic Geometry to Machine Learning

The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry. In this survey, we briefly describe some open problems related to algebraic curves which can be…

Large cosmological datasets have been probing the properties of our universe and constraining the parameters of dark matter and dark energy with increasing precision. Deep learning techniques have shown potential to be smarter, and to…

The combination of tomographic imaging and deep learning, or machine learning in general, promises to empower not only image analysis but also image reconstruction. The latter aspect is considered in this perspective article with an…

The many ways in which machine and deep learning are transforming the analysis and simulation of data in particle physics are reviewed. The main methods based on boosted decision trees and various types of neural networks are introduced,…

The marriage of machine learning and quantum physics may give birth to a new research frontier that could transform both.

Dr. David Blackwell was a mathematician and statistician of the first rank, whose contributions to statistical theory, game theory, and decision theory predated many of the algorithmic breakthroughs that define modern artificial…

Technology has helped to innovate in the teaching-learning process. Today's students are more demanding actors when it comes to the environment, they have at their disposal to learn, experiment and develop critical thinking. The area of…

We argue that explanations for "algorithmic decision-making" (ADM) systems can profit by adopting practices that are already used in the learning sciences. We shortly introduce the importance of explaining ADM systems, give a brief overview…

The past decade has seen a remarkable series of advances in machine learning, and in particular deep learning approaches based on artificial neural networks, to improve our abilities to build more accurate systems across a broad range of…

Deep learning has made tremendous progress in the last decade. A key success factor is the large amount of architectures, layers, objectives, and optimization techniques. They include a myriad of variants related to attention,…

The mathematical foundations of relativistic quantum mechanics is largely based upon the discovery of the Pauli and Dirac matrices. An algebra which lies at an even more fundamental level is the geometric Clifford algebra with metric…

During recent years, the renaissance of neural networks as the major machine learning paradigm and more specifically, the confirmation that deep learning techniques provide state-of-the-art results for most of computer vision tasks has been…

This paper aims at setting out the basics of $\mathbb{Z}$-graded manifolds theory. We introduce $\mathbb{Z}$-graded manifolds from local models and give some of their properties. The requirement to work with a completed graded symmetric…

Advances in machine learning have impacted myriad areas of materials science, ranging from the discovery of novel materials to the improvement of molecular simulations, with likely many more important developments to come. Given the rapid…

Geometric algebra is the natural outgrowth of the concept of a vector and the addition of vectors. After reviewing the properties of the addition of vectors, a multiplication of vectors is introduced in such a way that it encodes the famous…

This is a retrospective of some of William Arveson's many contributions to operator theory and operator algebras.

The aim of this paper is to start a systematic investigation of the arithmetic degree of projective schemes as introduced by D. Bayer and D. Mumford. One main theme concerns itself with the behaviour of this arithmetic degree under…

Machine learning has enabled significant benefits in diverse fields, but, with a few exceptions, has had limited impact on computer architecture. Recent work, however, has explored broader applicability for design, optimization, and…

So far, the most magnificent breakthrough in mathematics in the 21st century is the Geometrization Theorem, a bold conjecture by William Thurston (generalizing Poincar\'e's Conjecture) and proved by Grigory Perelman, based on the program…

Through the subsequent discussion we consider a certain particular sort of (topological) algebras, which may substitute the `` structure sheaf algebras'' in many--in point of fact, in all--the situations of a geometrical character that…