## Mathematical Foundation of Deep Learning## DescriptionTheory of deep neural networks: Basics of deep nets; Universal approximation theory and proof. Approximation errors in deep learning. Network training and nonconvex optimization: Automatic differentiation; Gradient descent, stochastic gradient descent, Adam and their convergence proofs. Constrained optimization; Learnable optimization algorithms. Deep learning and optimal control: Theory of optimal control; Hamiltonian and Pontryagin Maximum Principle; Deep learning from dynamical systems perspective and neural ordinary differential equations. Stochastic differential equations: Brownian motions; Stochastic integrals and Ito formula; Stochastic differential equations and Fokker-Planck equations; Stochastic control, Hamilton-Jacobi-Bellman equations, and reinforcement learning. Stochastic generative models.
## Lecture note and referencesLecture notes and references will be provided in class and on iCollege.
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