Applied Mathematics : From Theory to Computation in Research and Industry

What The Videos

• Introductory lecture - optimization on manifolds
• The eigenvalue problem
• Generalized eigenvalue problem as an optimization problem
• Newton's method applied to the Rayleigh quotient
• Benefits of the optimization approach
• Manifolds, charts, and atlases
• Differentiable functions on manifolds
• Immersions and submersions
• Embedded submanifolds
• Stiefel manifold
• Quotient manifolds
• Functions on quotient manifolds
• Real projective space
• Grassman manifold
• Tangent vectors and differential maps
• Tangent bundles and vector fields
• Differential of a mapping
• Tangent vectors to embedded submanifolds
• Tangent vectors to quotient manifolds
• Riemannian metric, distance, and gradients
• Riemannian submanifolds
• Riemannian quotient manifolds
• Retractions and Line-search algorithms on manifolds
• Retractions on embedded manifolds
• Retractions on quotient manifolds
• Gradient-related sequences, Armijo points, and accelerated line search
• Convergence on manifolds
• Convergence of line-search methods on manifolds
• Stability of fixed points
• Order of convergence
• Second-order methods for optimization on manifolds
• Newton's method on vector spaces
• Affine connections on linear manifolds
• Affine connections on nonlinear manifolds
• Riemannian (Levi-Civita) connections and symmetry
• Definition of the Riemannian (Levi-Civita) connection
• Riemannian connection on Riemannian submanifolds
• Riemannian connection on quotient manifolds
• Geodesics in terms of affine connections
• Exponential mapping and parallel translation
• Properties of the Hessian Operator
• Definition of the Riemannian Hessian Operator
• Properties of the Riemannian Hessian Operator
• Relating the Riemannian Hessian to the Classical Hessian via the Riemannian Exponential
• Relating the Riemannin Hessian Operator to the Classical Hessian via Retractions
• Geometric Newton Method for Vector Fields on Manifolds
• Riemannian Newton Method for Real-Valued Functions on Manifolds
• Local Quadratic Convergence of the Geometric Newton Method on Manifolds
• Introduction to trust-region methods
• Local (quadratic) models of cost functions
• Local (quadratic) models on Riemannian manifolds
• Trust-region methods in R^n
• Trust-region methods on Riemannian manifolds
• Computing the trust-region step using the nearly exact solution of the subproblem

• Truncated conjugate-gradient method for the trust-region subproblem on Riemannian manifolds

• Applied Accelerated Artificial Intelligence

• Introduction to AI Systems Hardware part 1
• Introduction to AI Systems Hardware - part 2
• Introduction to Operating Systems, Virtualization, Cloud - part 1
• Introduction to Operating Systems, Virtualization, Cloud part 2
• Introduction to AI Accelerators,GPUs
• Introduction to Containers and IDE Dockers part1
• Introduction to Containers and IDE Dockers part 2
• Scheduling and Resource Management part 1
• Scheduling and Resource Management part 2
• "DeepOps: Deep Dive into Kubernetes with deployment of various AI based Services." Part 1
• "DeepOps: Deep Dive into Kubernetes with deployment of various AI based Services." Part 2
• "DeepOps: Deep Dive into Kubernetes with deployment of various AI based Services Session II part1"
• "DeepOps: Deep Dive into Kubernetes with deployment of various AI based Services Session II part 2"
• Design principles for Building High Performance Clusters part 1
• Design principles for Building High Performance Clusters part 2
• Design principles for Building High Performance Clusters part 3
• Design principles for Building High Performance Clusters part 4
• Introduction to Pytorch part 1
• Introduction to Pytorch part 2
• Introduction to Pytorch part 3
• Introduction to Pytorch part 4
• Profiling with DLProf Pytorch Catalyst part 1
• Profiling with DLProf Pytorch Catalyst part 2
• Introduction to TensorFlow part 1
• Introduction to TensorFlow part 2
• Accelerated TensorFlow Part 1
• Accelerated TensorFlow Part 2
• Accelerated TensorFlow - XLA Approach Part 1
• Accelerated TensorFlow - XLA Approach part 2
• Optimizing Deep learning Training: Automatic Mixed Precision part 1
• Optimizing Deep learning Training: Automatic Mixed Precision part 2
• Optimizing Deep learning Training: Transfer Learning part 1
• Optimizing Deep learning Training: Transfer Learning part 2
• Fundamentals of Distributed AI Computing Session 1 Part 1
• Fundamentals of Distributed AI Computing Session 1 Part 2
• Fundamentals of Distributed AI Computing Session 2 Part 1
• Distributed Deep Learning using Tensorflow and Horovod
• Fundamentals of Distributed AI Computing Session 2 Part 2
• Challenges with Distributed Deep Learning Training Convergence
• Fundamentals of Accelerating Deployment part 1
• Fundamentals of Accelerating Deployment part 2
• Accelerating neural network inference in PyTorch and TensorFlow part 1
• Accelerating neural network inference in PyTorch and TensorFlow part 2
• Accelerated Data Analytics part 1
• Accelerated Data Analytics part 2
• Accelerated Data Analytics part 3
• Accelerated Data Analytics part 4
• Accelerated Machine Learning
• Applied AI: Smart City ( Intelligent Video Analytics) Session 1 part 1
• Applied AI: Smart City ( Intelligent Video Analytics) Session 1 part 2
• Applied AI: Smart City ( Intelligent Video Analytics) Session 2 Deepstream part 1
• Applied AI: Smart City ( Intelligent Video Analytics) Session 2 Deepstream part 2
• Introduction to NLP part 1
• Introduction to NLP part 2
• Introduction to word embedding
• Text classification using word embedding

References To Read

1. GNN though the lence of differential geometry
2. Deep learning for 3D human body synthesis
3. NeuralIPS-Talk on Differential Geometry meets Deep Learning
4. Discrete Differential Geometric Algorithic Implementation
5. Mesh Editing of 20 Years
6. Geometric Deep Learning
7. Geometric Deep Learning
8. Optimization on Manifolds
9. Optimization Algorithms on Matrix Manifolds 10.