mathematics of deep learning, nyu

From NA, Section 12: Exercises 12.3,12.4, 12.7, Consider the following method for solving y’ = f(y): Why must there always exist at least one Pareto Optimal Strategy in which all players adopt pure strategies? We use optional third-party analytics cookies to understand how you use GitHub.com so we can build better products. What is the intuition for why not all normal form games can be transformed into perfect-form extensive games? Y LeCun MA Ranzato Introduction to Deep Learning Lecture 01 Yann Le Cun Facebook AI Research, Center for Data Science, NYU Courant Institute of Mathematical Sciences, NYU Can you think of any other neural network architectures which can be seen as discretizations of some ODE? Logistics. (Knuth) For Theorem 1. xڵY�w�:~�_��>+H�g��q��4i6N��{{TPlN0�Nn��;# �8n�}hjH3��48��r��;�[��uskq� 3.15: Now consider adding a constant c to all the rewards in an episodic task … would this have any effect, or would it leave the task unchanged as in the continuing task above? The first week only it is 10:30am-12pm. Motivation: In the previous class we introduced some simple schemes to numerically solve ODEs. However, the mathematical reasons for this success remain elusive. 3.13: What is the Bellman equation for action values, that is, for qπ? This course is inspired by Stanford Stats 385, Theories of Deep Learning, taught by Prof. Dave Donoho, Dr. Hatef Monajemi, and Dr. Vardan Papyan, as well as the IAS@HKUST workshop on Mathematics of Deep Learning held during Jan 8 … Landscape of Deep Learning Optimization (Tensor/Matrix factorization, Deep Nets; open problems). $�.�� $�þ��|�Gz��~��η�l t��P�� }�fRʟU!�ؾ�?r$7��h��D You can always update your selection by clicking Cookie Preferences at the bottom of the page. In Chapter 4 the most important idea is value iteration (and exercise 4.10 will ask you to show why iterating the Q function is basically the same algorithm). What was common to both “Mastering the Game of Go …” and “Thinking Fast and Slow …”? (1), why are the successor positions of type 2? The first week only it is 10:30am-12pm. …, 3.14: In the gridworld example … are the signs of these rewards important, or only the intervals between them? 4.6 (important! What are the differences between the approaches taken in DeepStack and in Libratus? Organiser of Mathematics of Deep Learning (DeepMath), Oct’19. (Knuth) Show that the subparts of Theorem 2, are correct. T��F�N$�l}1u6� ��\J�7��PLp�)�MK��KmȻ�:/��Z�� NDߵ]��"�|��W͖�G��W��; ��h�N��2Q��LYHx��.�;�/�m�39P��3�87�2��]�z�R' >��ba�$�!v��F$p铸�W�h=�4�Hu��J�+��T% `C��PUb)G�6 ��f�7?�vPJ�asRdw�5`7�P�p�3��l .�u�tR��b�%�OYh>nJݱ��!��1X�{"{�Ҧu��a�-e��(��|ȑ{|�� Optional Reading: The two below are CFR extensions used in DeepStack. Learn more, We use analytics cookies to understand how you use our websites so we can make them better, e.g. Motivation: What happens when players don’t act simultaneously? The aim of this course is to provide graduate students who are interested in Succinctly describe the technique demonstrated in the Accelerating Best Response paper. We use essential cookies to perform essential website functions, e.g. y_{n+1} = y_n + h. Final Project is due May 1st by email to the instructors, Free-form Continuous Dynamics for Scalable Reversible Generative Models, Automatic Differentiation in Machine Learning: a Survey, Prof. Steven G. Johnson’s notes on adjoint method, Density Estimation by Dual Ascent of the Log-likelihood, A family of non-parametric density estimation algorithms, Variational Inference with Normalizing Flows, High-Dimensional Probability Estimation with Deep Density Models, Multi-level Residual Networks from Dynamical Systems View, Reversible Architectures for Arbitrarily Deep Residual Neural Networks, Deep Residual Learning for Image Recognition, Understanding and Implementing Architectures of ResNet and ResNeXt for state-of-the-art Image Classification, The Reversible Residual Network: Backpropagation Without Storing Activations, Stable Architectures for Deep Neural Networks, Prof. Trefethen’s class ODEs and Nonlinear Dynamics 4.1, Automatic Selection of Methods for Solving Stiff and Nonstiff Systems of Ordinary Differential Equations, Prof. Trefethen’s class ODEs and Nonlinear Dynamics 4.2. Tutoring Session with Parallel Curricula (optional): Fridays 11am-12:30pm CIWW 101. Motivation: These original core ideas did so much for the study of games. Speaker: Kun: Do you understand the argument for why the regret bound is O(sqrt(KTlog(T)))? We use optional third-party analytics cookies to understand how you use GitHub.com so we can build better products. Learn more, We use analytics cookies to understand how you use our websites so we can make them better, e.g. CSCI-GA 3033. Multivariate Calculus, Linear Algebra, Probability and Statistics at solid undergraduate level. they're used to gather information about the pages you visit and how many clicks you need to accomplish a task. stream Sutton: Sections 2.1 - 2.6 (Find on newclasses.nyu.edu in the class materials). If nothing happens, download the GitHub extension for Visual Studio and try again. Why does policy gradient have such high variance? The Policy function is the set of probabilities you give to each possible move. Topics course Mathematics of Deep Learning, NYU, Spring 18. 7.2, 7.3, 7.5, 7.7: Applications of MCTS. Motivation: Monte Carlo Tree Search (MCTS) forms the backbone of AlphaGoZero. Organiser of IAS Workshop on Theory of Deep Learning, Oct’19 Organizer of MIFODS \Deep Learning and Non-convex Optimization" Workshop, MIT, Jan 2019 Organizer of \Space Exploration, Inverse Problems and Deep Learning" Symposium, Rice, Simons Foundation Math+X, jan 2019. What is the computational complexity of evaluating a determinant of a N x N matrix, and why is that relevant in this context? This course is inspired by Stanford Stats 385, Theories of Deep Learning, taught by Prof. Dave Donoho, Dr. Hatef Monajemi, and Dr. Vardan Papyan, as well as the Tutoring Session with Parallel Curricula (optional): Fridays 11am-12:15pm CIWW 101. You can always update your selection by clicking Cookie Preferences at the bottom of the page. (Knuth) For Theorem 1. (LT), Prove that in a zero-sum game, the expected payoff to each player is the same for every equilibrium. Prove …. Class 5: Counterfactual Regret Minimization #2. Part III (time permitting): Open qustions on Reinforcement Learning. ), 13.3, 13.4. Tuesdays from 7.10pm-9pm. Motivation: We saw last week the practical side of CFR and how effective it What were the differences between “Mastering the Game of Go …” and “Thinking Fast and Slow …”? Focus in Chapter 3 on getting used to the notation we’ll use throughout the module, and an introduction to the Bellman operator and fixed point equations. will be helpful. These models have surpassed state of the art performance in many different tasks, and have become the focus of a vast amount of scientific literature. While this representation of a game always has a comparable Normal-Form, it’s much more natural to reason about in this format. What characteristics make MCTS a good choice? Deep Learning usually refers to a set of computational models, composed of multiple processing layers, that perform tasks on data by generating multiple intermediate representations. Work fast with our official CLI. Learn more. Required Reading (note: Sutton from here out refers to the, Sutton: 13.1, 13.2 (important! ): How would policy iteration be defined for action values? Game theory deals with this problem by identifying subsets of outcomes called solution concepts, of which fundamental ones are the Nash Equilibrium, Pareto Optimality, and Correlated Equilibrium. If nothing happens, download Xcode and try again. (14) in Section 8.7 of CSE? (LT). This is used for density estimation and generative modeling, and it is another model which can be seen a time-discretization of its continuous-time counterpart. 5�"��^+��y�A��Ĳ�5L�P��ۺh��|/b2�i@L s�?��s��k��j��(q�{;��Ao��d��c[� *��9!�L�98n6Yڜ�R�9�� u��+��"�U@#k) ��rf#x�ѫ��k�NC��E.T%SA�2��6ع/��J�z�L�ȷo&p*6��[þ.�}(,O��,��D��Dv�.U�2��( N+��i��s];��U�эU �=sk�L ��zV=��ʼRպ\� what do they represent? Why or why not? Unsupervised Learning under Geometric Priors (Implicit vs explicit models, microcanonical, transportation metrics). GitHub is home to over 50 million developers working together to host and review code, manage projects, and build software together. We will cover both the background and the current open problems. How do the authors of (Multi-level […]) explain the phenomena of still having almost as good performances in residual networks when removing a layer? Deep Learning usually refers to a set of computational models, composed of multiple processing layers, that perform tasks on data by generating multiple intermediate representations. Introduction: the Curse of Dimensionality. Tutoring Session with Parallel Curricula (optional): Fridays 11am-12:15pm CIWW 101. Recently there has been a dramatic increase in the performance of recognition systems due to the introduction of deep architectures for representation learning and classification. Motivation: Normal-Form games are the backbone for many of the techniques that later were used in DeepStack and Libratus. MAS Sections 3.3, 3.4.5, 3.4.7, 4.1, 4.2.4, 4.3, 4.6. What are examples of domain knowledge default policies in Go? Do you understand “Continual Re-solving”? Work fast with our official CLI. Date: Courant Classroom Calendar & Reservations. /Filter /FlateDecode Lecture Instructor: Joan Bruna (bruna@cims.nyu.edu), Tutor (Parallel Curricula): Cinjon Resnick (cinjon@nyu.edu).

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