Week 1 01/09, 01/11 
Lecture 1

 Logistics and course overview
 Topic modeling, matrix completion, and basic neural networks



Lecture 2 
 Review of linear algebera
 Matrix methods

 SVD, and power methods
 Matrix perturbation


Week 2 01/18 
Lecture 3

 Tensor decompositions and their applications

 Tensor rank and Jennrich's algorithm
 Phylogenetic reconstruction and topic models


Week 3 01/23, 01/25 
Lecture 4 

 Smoothness; convergence rates for smooth objectives


Lecture 5

 Basics of convex optimization

 Convexity and Strong convexity
 Stochastic Gradidents


Week 4 01/30, 02/01 
Lecture 6 

 Basics of Kernel methods
 NTK for Shallow Networks


Lecture 7


 Global convergence of GD for NTK
 Multilayer neural nets


Week 5 02/06, 02/08 
Lecture 8 

 Nonsmoothness
 Gradient descent maximizes margin on separable data


Lecture 9 

 Fixed design linear regression
 Finite and realizable hypothesis class


Week 6 02/13, 02/15 
Lecture 10

 Concentration inequalities

 MGF, Finite hypothesis class
 Introducing Rademacher complexity


Lecture 11 

 Generalization bound based on Rademacher complexity
 Logistic regression and Margin bounds


Week 7 02/22 
Lecture 12

 Rademacher complexity (cont'd)

 Norm bounded hypothesis classes
 Binary classification using linear predictors


Week 8 02/27, 03/01 
Lecture 13 
 Applications of Rademacher complexity based generalization bounds

 Matrix completion
 Generalization bounds for twolayer neural nets using path norm


Lecture 14

 Shattering coefficient and VC dimension

 VC dimension based generalization bounds


Week 10 03/13, 03/15 
Lecture 15 
 Covering numbers, Algorithmic Stability

 Deriving Generalization bounds using covering numbers
 Chaining


Lecture 16

 Algorithmic Stability
 PACBayesian analysis

 Occam's bound
 McAllester's bound


Week 11 03/20, 03/22 
Lecture 17 
 Nonvacuous PACBayesian bounds for deepnets

 Hessianbased generalization analysis for deep neural networks


Lecture 18 
 Graph neural networks
 Applications of PACBayesian analysis to graph neural networks

 Hessianbased measures for graph neural networks


Week 12 03/27, 03/29 
Lecture 19 



Lecture 20 



Week 13 04/03, 04/05 
Lecture 21 



Lecture 22




Week 14 04/10, 04/12 
Lecture 23 



Lecture 24




Week 15 04/19 
Lecture 25

 In class discussion of final project reports


