Application of Differential Geometry in Artificial Intelligence - Softcover

Vats, Pooja

Softcover

ISBN 10: 6630304225 ISBN 13: 9786630304220

Verlag: LAP LAMBERT Academic Publishing, 2026

Inhaltsangabe

This book, Application of Differential Geometry in Artificial Intelligence, argues that modern AI is best understood not through flat Euclidean assumptions but through the lens of curved manifolds, since data, model parameters, and probability distributions naturally possess non-Euclidean structure. It begins by laying the mathematical foundations-manifolds, Riemannian metrics, geodesics, curvature, and connections-before showing how these tools reshape core areas of machine learning: information geometry and natural gradient optimization, Riemannian optimization on constrained spaces like orthogonal and SPD matrices, geometric deep learning on graphs and meshes via equivariant architectures, and the geometric analysis of neural network loss landscapes. It then turns to manifold learning and dimensionality reduction techniques, geometry-aware architectures such as hyperbolic and Lie-group equivariant networks, and differential-geometric generative models including Riemannian diffusion and optimal transport. A dedicated chapter surveys applications across robotics, computer vision, NLP, and scientific AI (quantum machine learning, physics-informed networks).

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Über die Autorin bzw. den Autor

Pooja Vats, with her profound mathematical knowledge and a passion for education, continues to inspire both her students and colleagues. Her dedication to pushing the boundaries of mathematical research, coupled with her commitment to nurturing the next generation, makes her a true luminary in the field of mathematics and education.

Details zur Ausgabe

• Verlag: LAP LAMBERT Academic Publishing
• Erscheinungsdatum: 2026
• Sprache: Englisch
• ISBN 10: 6630304225
• ISBN 13: 9786630304220
• Einband: Taschenbuch
• Anzahl der Seiten: 60
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: KreGa Onlinehandel GmbH; 4950000000000; info@krega-onlinehandel.de; ; Birkenweg 31; Brakel; 33034; Deutschland