IFT6085: Class bibliography

This list has been maintained during the previous iterations on the class. Last update, February 2020. Papers marked with an asterisk where added in 2019. Papers marked with two asterisks where added in 2020. Please feel free to make paper suggestions in the class’s discussion group.

This is a non-exhaustive list of relatively recent papers that include theoretical or theory-driven work that applies on deep learning.

We will draw from this list for the seminar section of the class, including student paper presentations. Students are welcome to suggest other papers that they like as long as they are relevant to the class.

Note: some of these results are not given in a deep learning setting, however the ideas and techniques there are very useful for our exploration in class.

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Assorted papers

**(Review) Monte Carlo Gradient Estimation in Machine Learning , Shakir Mohamed, Mihaela Rosca, Michael Figurnov, Andriy Mnih, 2019.

**(Review) Causality for Machine Learning, Bernhard Schölkopf, 2019.

**(Review) Computational Optimal Transport, Gabriel Peyré, Marco Cuturi, 2019.

Learning and Generalization

**Backward Feature Correction: How Deep Learning Performs Deep Learning, Zeyuan Allen-Zhu, Yuanzhi Li, 2020.

**Do ImageNet Classifiers Generalize to ImageNet?, Benjamin Recht, Rebecca Roelofs, Ludwig Schmidt, Vaishaal Shankar, 2019.

**Rethinking statistical learning theory: learning using statistical invariants, Vladimir Vapnik & Rauf Izmailov, 2019.

**Memory capacity of neural networks with threshold and ReLU activations, Roman Vershynin, 2020.

**The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks, Jonathan Frankle, Michael Carbin

**More Data Can Hurt for Linear Regression: Sample-wise Double Descent,

**Reconciling modern machine learning practice and the bias-variance trade-off, Mikhail Belkin, Daniel Hsu, Siyuan Ma, Soumik Mandal, 2019

*A Modern Take on the Bias-Variance Tradeoff in Neural Networks, Brady Neal, Sarthak Mittal, Aristide Baratin, Vinayak Tantia, Matthew Scicluna, Simon Lacoste-Julien, Ioannis Mitliagkas

*Provable Bounds for Learning Some Deep Representations, Sanjeev Arora, Aditya Bhaskara, Rong Ge, Tengyu Ma

*On Generalization Error Bounds of Noisy Gradient Methods for Non-Convex Learning, Jian Li, Xuanyuan Luo, Mingda Qiao

*Data-Dependent Stability of Stochastic Gradient Descent, Ilja Kuzborskij, Christoph H. Lampert

*Understanding deep learning requires rethinking generalization, Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, Oriol Vinyals

Data-dependent path normalization in neural networks, Behnam Neyshabur, Ryota Tomioka, Ruslan Salakhutdinov, Nathan Srebro

High-dimensional dynamics of generalization error in neural networks, Madhu S. Advani, Andrew M. Saxe

Robustness and Generalization, Huan Xu, Shie Mannor

A PAC-Bayesian Approach to Spectrally-Normalized Margin Bounds for Neural Networks, Behnam Neyshabur, Srinadh Bhojanapalli, David McAllester, Nathan Srebro

Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data, Gintare Karolina Dziugaite, Daniel M. Roy

Entropy-SGD optimizes the prior of a PAC-Bayes bound: Data-dependent PAC-Bayes priors via differential privacy, Gintare Karolina Dziugaite, Daniel M. Roy

Exponential convergence of testing error for stochastic gradient methods, Loucas Pillaud-Vivien, Alessandro Rudi, Francis Bach

Spectrally-normalized margin bounds for neural networks, Peter Bartlett, Dylan J. Foster, Matus Telgarsky

Data-Dependent Stability of Stochastic Gradient Descent, Ilja Kuzborskij, Christoph H. Lampert

Why and When Can Deep – but Not Shallow – Networks Avoid the Curse of Dimensionality: a Review, Tomaso Poggio, Hrushikesh Mhaskar, Lorenzo Rosasco, Brando Miranda, Qianli Liao

Distributional robustness, domain adaptation, etc

**Invariant Risk Minimization, Martin Arjovsky, Léon Bottou, Ishaan Gulrajani, David Lopez-Paz, 2019.

**Adversarial Examples Are Not Bugs, They Are Features, Andrew Ilyas, Shibani Santurkar, Dimitris Tsipras, Logan Engstrom, Brandon Tran, Aleksander Madry, 2019.

Certifiable distributional robustness with principled adversarial training, Aman Sinha, Hongseok Namkoong, John Duchi

Optimization landscape of deep networks

Deep Learning without Poor Local Minima, Kenji Kawaguchi

Entropy-SGD: biasing gradient descent into wide valleys, Pratik Chaudhari, Anna Choromanska, Stefano Soatto, Yann LeCun, Carlo Baldassi, Christian Borgs, Jennifer Chayes, Levent Sagun, Riccardo Zecchina

Identity Matters in Deep Learning, Moritz Hardt, Tengyu Ma

The Loss Surfaces of Multilayer Networks, Anna Choromanska, Mikael Henaff, Michael Mathieu, Gérard Ben Arous, Yann LeCun

Theoretical insights into the optimization landscape of over-parameterized shallow neural networks, Mahdi Soltanolkotabi, Adel Javanmard, Jason D. Lee

*(Deep) Reinforcement Learning

**Reinforcement Learning via Fenchel-Rockafellar Duality, Ofir Nachum, Bo Dai, 2020.

*Are Deep Policy Gradient Algorithms Truly Policy Gradient Algorithms?, Andrew Ilyas, Logan Engstrom, Shibani Santurkar, Dimitris Tsipras, Firdaus Janoos, Larry Rudolph, Aleksander Madry

*A Distributional Perspective on Reinforcement Learning, Marc G. Bellemare, Will Dabney, Rémi Munos

*Equivalence Between Policy Gradients and Soft Q-Learning, John Schulman, Xi Chen, Pieter Abbeel

*Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review, Sergey Levine

Optimization and Games

**Poly-time universality and limitations of deep learning, Emmanuel Abbe, Colin Sandon, 2020.

**A Stochastic Gradient Method with an Exponential Convergence _Rate for Finite Training Sets, Nicolas L. Roux Mark Schmidt, Francis R. Bach, 2012

**Near Optimal Methods for Minimizing Convex Functions with Lipschitz p-th Derivatives, Alexander Gasnikov, et al, 2019.

*Negative Momentum for Improved Game Dynamics, Gauthier Gidel, Reyhane Askari Hemmat, Mohammad Pezeshki, Remi Lepriol, Gabriel Huang, Simon Lacoste-Julien, Ioannis Mitliagkas

*The Mechanics of n-Player Differentiable Games, David Balduzzi, Sebastien Racaniere, James Martens, Jakob Foerster, Karl Tuyls, Thore Graepel

*Qualitatively characterizing neural network optimization problems, Ian J. Goodfellow, Oriol Vinyals, Andrew M. Saxe

*SGD Converges to Global Minimum in Deep Learning via Star-convex Path, Yi Zhou, Junjie Yang, Huishuai Zhang, Yingbin Liang, Vahid Tarokh

A geometric alternative to Nesterov’s accelerated gradient descent, Sébastien Bubeck, Yin Tat Lee, Mohit Singh

Accelerated Gradient Descent Escapes Saddle Points Faster than Gradient Descent, Chi Jin, Praneeth Netrapalli, Michael I. Jordan

Adaptive Restart for Accelerated Gradient Schemes, Brendan O’Donoghue, Emmanuel Candes

Efficient Second Order Online Learning by Sketching, Haipeng Luo, Alekh Agarwal, Nicolo Cesa-Bianchi, John Langford

From Averaging to Acceleration, There is Only a Step-size, Nicolas Flammarion and Francis Bach

Optimal rates for zero-order convex optimization: the power of two function evaluations, John C. Duchi, Michael I. Jordan, Martin J. Wainwright, Andre Wibisono

Optimizing Neural Networks with Kronecker-factored Approximate Curvature, James Martens, Roger Grosse

The Marginal Value of Adaptive Gradient Methods in Machine Learning, Ashia C. Wilson, Rebecca Roelofs, Mitchell Stern, Nathan Srebro, Benjamin Recht

Statistical inference using SGD, Tianyang Li, Liu Liu, Anastasios Kyrillidis, Constantine Caramanis

Stochastic Gradient Descent as Approximate Bayesian Inference, Stephan Mandt, Matthew D. Hoffman, David M. Blei

Non-Convex Learning via Stochastic Gradient Langevin Dynamics: A Nonasymptotic Analysis, Maxim Raginsky, Alexander Rakhlin, Matus Telgarsky

Trust Region Policy Optimization, John Schulman, Sergey Levine, Philipp Moritz, Michael I. Jordan, Pieter Abbeel

Generative models (mostly GANs)

**Theoretical guarantees for approximate sampling from smooth and log-concave densities, Arnak S. Dalalyan, 2014.

*Approximability of Discriminators Implies Diversity in GANs, Yu Bai, Tengyu Ma, Andrej Risteski

*Tighter Variational Bounds are Not Necessarily Better, Tom Rainforth, Adam R. Kosiorek, Tuan Anh Le, Chris J. Maddison, Maximilian Igl, Frank Wood, Yee Whye Teh

Stabilizing GAN Training with Multiple Random Projections, Behnam Neyshabur, Srinadh Bhojanapalli, Ayan Chakrabarti

Stabilizing Training of Generative Adversarial Networks through Regularization, Kevin Roth, Aurelien Lucchi, Sebastian Nowozin, Thomas Hofmann

Compressed Sensing using Generative Models, Ashish Bora, Ajil Jalal, Eric Price, Alexandros G. Dimakis

Demystifying MMD GANs, Mikołaj Bińkowski, Dougal J. Sutherland, Michael Arbel, Arthur Gretton

Generalization and Equilibrium in Generative Adversarial Nets (GANs), Sanjeev Arora, Rong Ge, Yingyu Liang, Tengyu Ma, Yi Zhang

Do GANs actually learn the distribution? An empirical study, Sanjeev Arora, Yi Zhang

The Numerics of GANs, Lars Mescheder, Sebastian Nowozin, Andreas Geiger

PacGAN: The power of two samples in generative adversarial networks, Zinan Lin, Ashish Khetan, Giulia Fanti, Sewoong Oh


*Meta-Learning and Universality: Deep Representations and Gradient Descent can Approximate any Learning Algorithm Chelsea Finn, Sergey Levine

*On First-Order Meta-Learning Algorithms, Alex Nichol, Joshua Achiam, John Schulman

*Understanding Short-Horizon Bias in Stochastic Meta-Optimization, Yuhuai Wu, Mengye Ren, Renjie Liao, Roger Grosse

Information Theory

**An Information-Theoretic Analysis of Thompson Sampling, Daniel Russo, Benjamin Van Roy, 2016.

*On variational lower bounds of mutual information, Ben Poole, Sherjil Ozair, Aaron van den Oord, Alexander A. Alemi, George Tucker

*Estimating Information Flow in Neural Networks, Ziv Goldfeld, Ewout van den Berg, Kristjan Greenewald, Igor Melnyk, Nam Nguyen, Brian Kingsbury, Yury Polyanskiy

Opening the Black Box of Deep Neural Networks via Information, Ravid Shwartz-Ziv, Naftali Tishby

On the information bottleneck theory of deep learning, Andrew Michael Saxe, Yamini Bansal, Joel Dapello, Madhu Advani, Artemy Kolchinsky, Brendan Daniel Tracey, David Daniel Cox

Emergence of Invariance and Disentanglement in Deep Representations, Alessandro Achille, Stefano Soatto

MINE: Mutual information neural estimation, Ishmael Belghazi, Sai Rajeswar, Aristide Baratin, R Devon Hjelm, Aaron Courville