Gradient Descent

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (32)

Page 1 of 4

Optimization on Manifolds

Covers optimization on manifolds, focusing on smooth manifolds and functions, and the process of gradient descent.

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Riemannian connections

Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.

Connections: motivation and definition

Explores the definition of connections for smooth vector fields on manifolds.

Retractions vector fields and tangent bundles: Tangent bundles

Covers retractions, tangent bundles, and embedded submanifolds on manifolds with proofs and examples.

Differentiating vector fields: Why do it?

Explores the importance of differentiating vector fields and the correct methodology to achieve it, emphasizing the significance of going beyond the first order.

General Manifolds and Topology

Covers manifolds, topology, smooth maps, and tangent vectors in detail.

Riemannian metrics and gradients: Why and definition of Riemannian manifolds

Covers Riemannian metrics, gradients, vector fields, and inner products on manifolds.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces, focusing on orientation and orientability.