Меню
КартаВръзкиТемиБългарияНощта (K-TRIO)Мария Склодовска-КюриЗа ученициЗа учителиМетодологияИзненадай ме
HEОбмен на изследователи2023–2026

CaLIGOLA · Cartan geometry, Lie and representation theory, Integrable Systems, quantum Groups and quantum computing towards the understanding of the geometry of deep Learning and its Applications

„Хоризонт Европа“ — Действия „Мария Склодовска-Кюри“

Период
2023-01-01 → 2026-12-31
Финансиране от ЕС
874 000 €
Участници
28
Схема
HORIZON-TMA-MSCA-SE

Линиите свързват координатора с партньорите.

Накратко на български

Математическите модели от теорията на Ли и квантовите групи се прилагат за анализ на алгоритми за машинно обучение и квантови изчисления. Тези изследвания помагат за по-доброто разбиране на геометрията на дълбокото обучение и оптимизирането на квантовите вериги.

Този кратък обзор е генериран от изкуствен интелект

Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.

Резултати накратко

Cartan geometry, Lie and representation theory, Integrable Systems, quantum Groups and quantum computing towards the understanding of the geometry of deep Learning and its Applications

CaLIGOLA aims to cross-fertilize with ideas coming from Lie Theory, Integrable Systems and Quantum Groups, multidisciplinary fields, like quantum computing, vision algorithms and machine learning, which need a rigorous mathematical approach to boost their advancement. This is essential to provide mathematical models for far reaching applications, strategic to put Europe among the leading actors in the fields which constitute a priority in Horizon Europe. Objectives and overview of the research and innovation programme 1) Develop new methods in Lie theory, more specifically in Cartan Geometry and infinite dimensional representations Harish-Chandra theory of real Lie (super)groups, (super)algebras, to boost the application in physics (e.g., Quantum Geometry, Supersymmetry) and provide the appropriate language for applications in (4) and (5). 2) Investigate the classification of integrable dynamical systems, in particular in its combinatorial aspects, linked to the theory of Harish-Chandra representations in (1). Exploit this study to reach a better understanding of supersymmetric Gauge theories, SUSY (supersymmetric) curves and Dubrovin manifolds (see (1)). 3) Bridge the gap between Connes approach to noncommutative geometry and the Hopf algebraic one, via Spectral triples of quantum symmetric spaces. Develop new tools in quantum representation theory (quantum BGG). Build quantum invariant differential calculus (quantum Dolbeault-Dirac operators); (1) and (2) will be paramount in reaching this objective. Once achieved, it will have a direct impact first on (4) and then on (5).. 4) Define the Quantum Fisher information (Quantum Geometric Tensor) for modeling of optimization tasks in devising quantum algorithms and circuits; . Develop models from quantum representation theory and quantum differential calculus for a topological approach to quantum fault tolerant computation, making essential use of the machinery developed in (3), guided by the insight obtained in (1) and (2).. 5) Develop new vision models and algorithms with the use of persistent homology, Lie Group statistics to boost the machine learning techniques. Understand (Geometric) Deep Learning with the new invariance mathematical tools developed. Provide a new perspective on quantum computing and artificial intelligence algorithms

Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз

Цел на проекта

CaLIGOLA aims at advancing the research in Cartan Geometry, Lie Theory, Integrable Systems and Quantum Groups to provide insight into a variety of multidisciplinary fields oriented towards the applications with a special interest in machine learning and quantum computing. Sound mathematical models for quantum computing, vision and more generally machine learning are a priority for Horizon Europe and strategic to include Europe among the leading actors in such fields. Through the theory of symmetric spaces from the Cartan Geometric and Lie theoretic point of view, we shall implement the Erlangen philosophy for mathematical and physical questions (integrable systems and SUSY gauge field theory), but also for more applied themes including Quantum Computing and (geometric) Deep Learning. Quantum symmetric spaces and quantum representations will be the key to approach the questions of fault tolerant quantum algorithms in topological quantum computing and quantum information geometry on homogeneous spaces. With the language of Cartan geometry and Quantum Groups, we shall reformulate group invariant neural network models. Persistent homology and topological data analysis will take a step forward towards a metric theory on the space of observers. With the help of Lie group thermodynamic, we shall push the understanding of symmetries at a deeper level. Overall, the new algorithms of Deep Learning and Geometric Deep Learning will find a better modeling and understanding towards a comprehensive theory of dimensionality reduction of parameter space via group equivariance.

Оригинален текст от CORDIS (на английски).

Участници

Връзки

Данни: CORDIS, © Европейски съюз