Princeton University

Computer Science 597A

Fall 2017

This is a graduate seminar focused on research in theoretical machine learning. Recent successes of machine learning involve nonconvex optimization problems, many of which are are NPhard in the worst case. This complicates developing a theoretical understanding of these problems. List of topics will include: (i) Analysing nonconvex optimization. (ii) Towards a generalization theory for deep learning. (iii) Semantics of natural language. Some other NLP. (iv) Latent variable models. Learning such models via tensor decomposition. (v) Unsupervised learning, Representation Learning, and Generative Adversarial Nets (GANs). (vi) Adversarial examples in deep learning: are they inherent? (vii) Interpretability in ML.
The course is geared towards graduate students in computer science and allied fields, but may be OK for undergrads who're suitably prepared. (Knowledge of machine learning as well as algorithm design/analysis. Ideally, they would have taken at least one of COS 521 and COS 511.)
Enrolled students as well as auditors are expected to come to class regularly and participate in class discussion. To get a grade in the class, students should also be prepared to present a topic some time in the course, and write a brief paper or lecture notes on somebody else's presentation. There may also be an opportunity to do a course project, depending upon student interest.
This course does not satisfy any undergrad requirements in the COS major (BSE or AB).
Instructor: Sanjeev Arora 407 CS Building  6092583869 arora AT the domain name cs.princeton.edu
Date/topic 
Required reading 
Additional reading 
Sept 14: Recap of basic optimization via
1st order methods, Lyapunov functions (measures of
progress), Stochastic Gradient Descent. 
Rong
Ge's intro to convex optimization. Going with the slope: offline, online, and randomly. (COS 521 lecture notes) 
BoydVanderberghe Sec 9.19.3 Optimization for ML; survey lecture by Elad Hazan (includes video and slides) 
Sept 19: Nonconvex optimization. First
order methods. Descent lemma to arrive at critical
point. Arriving at approximate local optima (escaping
saddle points). 
How
to escape saddle points efficiently by Jin et al. Scribe notes. by Misha Khodak 
Blog
post #1 on offconvex.org by Rong Ge Blog post #2 on offconvex.org by Chi Jin and Mike Jordan. 
Sept 21: Recap of generalization
theory. (Conditions which guarantee no overfitting
occurs.) Simple bound, Compression bound, PACBayes bound. 
Lecture
notes by Mannor and ShalevSchwartz (also many other resources on the web) Scribe notes. by Hrishikesh Khanderparker 
(Not)
bounding the true error by J. Langford and R. Caruana. (derives generalization bounds for NNs using PACBayes) 
Sept 26 : Some weirdnesses of
deep learning (wrt generalization). Discussion re:
paper and its controversial title. An interesting video. 
Understanding
deep learning requires rethinking generalization. (Sanjeev's
highlighted copy.) By Zhang, Bengio, Hardt, Recht, Vinyals. 
Geometry,
Optimization, and Generalization in Multilayer Networks. Video
of talk by Nati Srebro at Simons Institute, Berkeley. 
Sept 28: Guest lecture by Behnam
Neyshabur, plus class discussion. 
PACBayesian
Approach to SpectrallyNormalized Generalization Bounds
for Neural Nets (by Neyshabur et al.) 
PathSGD: Path
Normalized Optimization in Neural Networks by Neyshabur, Salakhutdinov and Srebro. Spectrallynormalized margin bounds for neural networks by Bartlett, Foster, and Telgarsky. 
Oct 3: Intro to Tensors and Tensor
Decomposition. Difficulties compared to SVD. Jennrich's
algorithm. 
Moitra
chapter 3. Rong Ge Notes 1 and Notes 2. Scribe notes by Woo Sang Cho 
Rong's
blog post on tensor methods in ML. Wikipedia page
on eigendecomposition provides most linear algebra
background. See also Rong Ge's notes on SVD. 
Oct 5: Latent Variable Models. Topic
Models. ICA. How to learn them via Tensor Decomposition. 
Tensor
Decomposition for Learning Latent Variable Models by
Anandkumar, Ge, Hsu, Kakade, Telgarsky 

Oct 10: Guest lecturer Tengyu Ma. How to show all local minima are approximate global minima.  Matrix
completion has no spurious local minimum, by Ge, Lee,
and Ma. 

Oct 12: Learning topic models via
nonnegative matrix factorization. Efficient algorithms
assuming separability assumption. Brief intro to solving
nonlinear noisyOR model via tensor decomposition. Cameo by Tengyu Ma on more stable tensor decomposition. 
Learning
topic models Provably and Efficiently. Arora et
al. (this version to appear in CACM) Section 10 of Polynomialtime algorithms for Tensor Decompositions via sumofsquares by Ma, Shi and Steurer. Scribe notes by Suqi Liu 
Longer
ICML version of topic model paper. Introductory account of stability issues in linear algebraic procedures appears in this paper by O'Rourke et al. First two sections of Provable Learning of NoisyOr networks. 
Oct 17: No class. 

Oct 19: Compressed sensing and matrix
completion via convex programming: quick intro and proofs.
(Guest lecturer: Pravesh Kothari) 
Moitra Sections 4.1, 4.5, and Chapter 7. 

Oct 24: (Class begins at 5pm.) Language models: ngrams. Perplexity. (Guest lecturer: Sida Wang)  Language Models. (Chapter by Mike Collins)  
Oct 26: Word embeddings and their
fascinating properties. 
A Latent
Variable Model Approach to PMIbased Word Embeddings
by Arora et al. (TACL'16) 
Blog articles: Semantic
word embeddings and Word embeddings: Explaining their properties. 
Nov 7: Unsupervised learning:
formalizations. Bayesian perspective. Sentence
embeddings. 
Unsupervised
learning: one notion or many? by Arora and Risteski. 
Provable benefits
of representation learning by Arora and Risteski. 
Nov 9: Autoencoders; Denoising
Autoencoders. Variational Autoencoders. 
Autoencoding
variational Bayes by Kingma and Welling. 
Stacked
denoising autoencoders by Vincent et al. Importance weighted autoencoders by Burda, Grosse, and Salakhutdinov. 
Nov 14: Generative Adversarial Nets (GANs).  Ian
Goodfellow's tutorial on GANs. Generalization and Equilibrium in GANs by Arora, Ge, Liang, Ma, and Zhang. 
Offconvex.org blogpost1
and blogpost2 (the second reports experimental findings using the birthday paradox test). Theoretical limitations of encoderdecoder GAN architectures. by Arora, Risteski, Zhang. 
Nov 16: Can we replace complicated LSTM
models with simpler, interpretable models? 
A simple
but tough to beat baseline for sentence embeddings. 
Unreasonable
effectiveness by RNNs (blog post by A. Karpathy) Understanding LSTM networks (post on Colah's blog) 
Nov 21: Adversarial examples for deep
nets. 
Is
attacking ML easier than defending it? blog post by Goodfellow and Papernot. Delving into transferable adversarial examples and black box attacks by Liu et al. 
Toward deep
learning models resistant to adversarial attacks, by
Madry et al. 
Nov 28: More on generalization mystery
for deep learning... 
Wait for scribe notes... 
Introduction
to matrix concentration inequalities by J. Tropp. We
used Thm 1.6.2 in class. Nonvacuous PACbayes bounds for deep nets by Dziugaite and Roy. (Sanjeev's highlighted version.) 
Nov 30: FrankWolfe updates as an
approach to nonconvex optimization. (Guest lecturer Elad
Hazan) 

Dec 5: Models for interactive learning.
Machine teaching, curriculum learning etc. 
Lecture
notes on machine teaching by Jerry Zhu Curriculum Learning by Bengio et al. (ICML09) 
Pieter
Abbeel's lecture notes on policy gradient. (Basic
idea is on slide 8.) Hossein Mobahi's talk on homotopy method. (watched for a few min to see connection to curriculum learning) 
Dec 7: No lecture due to NIPS 

Dec 12: No lecture; attend Yann LeCun's talk
at IAS instead. 

Dec 14: Recent progress in making deep
nets resistant to adversarial attacks. 
Provable
defenses against adversarial examples via the convex outer
adversarial polytope by Kolter and Wong (NIPS'17) Countering adversarial images using input transformations, by Anonymous (ICLR'17 submission) 
Toward
deep learning models resistant to adversarial attacks
by Madry, Makelov, Schmidt, Tsipras, Vladu. Certified defenses for data poisoning attacks by Steinhardt, Koh and Liang 