Open Daily: 10am - 10pm | Alley door pickup 10am - 7pm 3038 Hennepin Ave Minneapolis, MN
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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Application of Differential Geometry in Artificial Intelligence

Application of Differential Geometry in Artificial Intelligence

Vats, Pooja

Paperback

General Mathematics

ISBN10: 6630304225
ISBN13: 9786630304220
Publisher: LAP Lambert Academic Publishing
Published: Aug 12 2026
Pages: 60
Weight: 0.21
Height: 0.14 Width: 6.00 Depth: 9.00
Language: English
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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