Deep learning explained

A collection of papers that try to explain the mysteries of deep learning with theories and empirical evidences. And here is a curated resource of deep learning theory papers by Prof. Boris Hanin at Princeton.

• Theory-oriented explanations

  • Differential equation view
  • Interpolation-Extrapolation tradeoffs
  • Deep PAC and PAC-Bayes
  • Information-theoretic
  • Theory of training
    • Neural Tangent Kernel
    • Understanding training tricks
  • Implicit regularization
  • Theory of representation learning

• Empirical observations and explanations

  • Self-supervised learning
  • Contrastive learning
  • Generalization metrics
  • Decision boundary
  • Data-centric understanding
  • Spurious correlation
  • Lottery ticket hypothesis
  • Memorization

Theory-oriented explanations

Differential equation view

• The Principles of Deep Learning Theory, Jun. 18 2021.

Interpolation-Extrapolation tradeoffs

• Overfitting or perfect fitting? Risk bounds for classification and regression rules that interpolate, NeurIPS 2018.
• The Power of Interpolation: Understanding the Effectiveness of SGD in Modern Over-parametrized Learning, ICML 2018.
• Training Neural Networks for and by Interpolation, ICML 2019.
• Learning in High Dimension Always Amounts to Extrapolation, Oct. 18 2021, Yann LeCun et al.
• Benign, Tempered, or Catastrophic: A Taxonomy of Overftting, Jul. 14 2022.
• Benign Overfitting for Two-layer ReLU Networks, Mar. 7 2023.

Inductive Bias

• On Margin Maximization in Linear and ReLU Networks, Nathan Srebro's group, 2021.
• The Role of Permutation Invariance in Linear Mode Connectivity of Neural Networks, 2021, Google Research.
• On the Implicit Biases of Architecture & Gradient Descent, 2021, Yisong Yue's group.
  • "This paper finds that while typical networks that fit the training data already generalise fairly well, gradient descent can further improve generalisation by selecting networks with a large margin."
• The Deep Bootstrap Framework: Good Online Learners Are Good Offline Generalizers, Feb. 2021. iclr2021
• No One Representation to Rule Them All: Overlapping Features of Training Methods, Oct. 26 2021.
• Gradient Descent on Two-layer Nets: Margin Maximization and Simplicity Bias, Oct. 26. 2021.
• Diversity and Generalization in Neural Network Ensembles, Oct. 6 2021.
• The Limitations of Large Width in Neural Networks: A Deep Gaussian Process Perspective, Jun. 11 2021.

Deep PAC and PAC-Bayes

• How Tight Can PAC-Bayes be in the Small Data Regime?, Oct. 27 2021.

Information-theoretic

• Towards a Unified Information-Theoretic Framework for Generalization, Nov. 9 2021. nips2021 Daniel Roy's group. non-vacuous generalization bound

Theory of training

SGD, loss landscape, learning dynamics, stochacity, sgd for feature learning, learning curriculum etc.

• Don't Decay the Learning Rate, Increase the Batch Size, Nov. 2017. iclr2018.
• Implicit Bias of Gradient Descent for Wide Two-layer Neural Networks Trained with the Logistic Loss, COLT 2020.
• Stochastic Training is Not Necessary for Generalization, Tom Goldstein's group, nips2021.
• Large Learning Rate Tames Homogeneity: Convergence and Balancing Effect, Tuo Zhao's group.
• Momentum Doesn't Change The Implicit Bias.
• On the Implicit Biases of Architecture & Gradient Descent, 2021, Yisong Yue's group, implicit bias of gd
• Parameter Prediction for Unseen Deep Architectures, Oct. 25 2021.
• Gradient Starvation: A Learning Proclivity in Neural Networks, Oct. 26 2021. nips2021
• What training reveals about neural network complexity, Oct. 29 2021.
• A Loss Curvature Perspective on Training Instabilities of Deep Learning Models, iclr2022 submit
• Permutation-Based SGD: Is Random Optimal?, iclr2022 submit
• A General Analysis of Example-Selection for Stochastic Gradient Descent, iclr2022 submit
• How many degrees of freedom do we need to train deep networks: a loss landscape perspective, Jul. 13 2021.
• The Benefits of Implicit Regularization from SGD in Least Squares Problems, Aug. 10 2021 nips2021
• The Limiting Dynamics of SGD: Modified Loss, Phase Space Oscillations, and Anomalous Diffusion, Dec. 2 2022.
• Understanding Gradient Descent on Edge of Stability in Deep Learning, May 22 2022.
• Understanding Edge-of-Stability Training Dynamics with a Minimalist Example, Oct. 7 2022.
• Neural Networks can Learn Representations with Gradient Descent, Jun. 30 2022. colt2022
• Git Re-Basin: Merging Models modulo Permutation Symmetries, Sep. 11 2022. tweet1, tweet2, tweet3.
• The Dynamics of Sharpness-Aware Minimization: Bouncing Across Ravines and Drifting Towards Wide Minima, Oct. 4 2022.
• From Gradient Flow on Population Loss to Learning with Stochastic Gradient Descent, Oct. 13 2022.
• Grokking phase transitions in learning local rules with gradient descent, Oct. 26 2022.
• High-dimensional Asympototics of Feature Learning: How One Gradient Step Improves the Representation, Jimmy Ba et al. arXiv May 3 2022.
• Exact learning dynamics of deep linear networks with prior knowledge, nips2022. learning dynamics.
• Handbook of Convergence Theorems for (Stochastic) Gradient Methods, Jan. 26 2023.

Neural Tangent Kernel

• Learning sparse features can lead to overfitting in neural networks, Jun. 24 2022.
• Limitations of the NTK for Understanding Generalization in Deep Learning, Jun. 20 2022.
• The Influence of Learning Rule on Representation Dynamics in Wide Neural Networks, Oct. 5 2022.

Understanding training tricks

• Does Knowledge Distillation Really Work?, Jun. 10 2021. nips2021
• Understanding Why Generalized Reweighting Does Not Improve Over ERM, Jan. 28 2022.

Implicit regularization

• Limitation of characterizing implicit regularization by data-independent functions, Jan. 28 2022.
• Implicit Bias in Leaky ReLU Networks Trained on High-Dimensional Data, Oct. 2022.

Theory of representation learning

• Neural Networks Efficiently Learn Low-Dimensional Representations with SGD, Sep. 29 2022. sgd
• Deep Learning meets Nonparametric Regression: Are Weight-Decayed DNNs Locally Adaptive?, Jun. 13 2022.
• Feature learning in neural networks and kernel machines that recursively learn features, Dec. 28 2022.
  • From Mikhail Belkin's group.

Self-supervised learning

• Exploring the Limits of Large Scale Pre-training, Google Research.

Contrastive learning

• The Power of Contrast for Feature Learning: A Theoretical Analysis, Oct. 2021. James Zou's group.
• Sharp Learning Bounds for Contrastive Unsupervised Representation Learning, Oct. 2021. RIKEN AIP.
• Can contrastive learning avoid shortcut solutions?, Jun. 21 2021. MIT and Pittsburg univ.
• Intriguing Properties of Contrastive Losses, Oct. 23 2021. Google Research.
• Stochastic Contrastive Learning, Oct. 2021. interpretability
• How Does Contrastive Pre-training Connect Disparate Domains?, nipst2021
• Contrastive Learning Can Find An Optimal Basis for Approximately View-Invariant Functions, arXiv Oct. 4 2022.
• Do More Negative Samples Necessarily Hurt In Contrastive Learning?, Jun. 22 2022. icml2022.
• Understanding Deep Contrastive Learning via Coordinate-wise Optimization, nips2022.
• Understanding Contrastive Learning Requires Incorporating Inductive Biases, Feb. 28 2022.
• Feature Dropout: Revisiting the Role of Augmentations in Contrastive Learning, Dec. 15 2022.

Explaining representational power

• Emergence of Invariance and Disentanglement in Deep Representations, jmlr2018
• Grounding Representation Similarity with Statistical Testing, Nov. 3 2021. representation comparison
• Revisiting Model Stitching to Compare Neural Representations, Jun. 14 2021. representation comparison
• Comparing Text Representations: A Theory-Driven Approach, Sep. 2021. sentence embedding
• Discovering and Explaining The Representation Bottleneck of DNNs, iclr2022 submit
• A theory of representation learning in deep neural networks gives a deep generalisation of kernel methods, Apr. 23 2023. icml2023.

Neural collapse

• Prevalence of Neural Collapse during the terminal phase of deep learning training, Aug. 21 2020.

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Empirical observations and explanations

Double descent

• Double Descent Demystified: Identifying, Interpreting & Ablating the Sources of a Deep Learning Puzzle, Mar. 24 2023.

Mechanistic interpretability of DL

• An Extremely Opinionated Annotated List of My Favourite Mechanistic Interpretability Papers, Oct. 18 2022.

Generalization metrics

• Neural Tangent Kernel Eigenvalues Accurately Predict Generalization, UCB，nips2021 spotlight.
• Predicting Unreliable Predictions by Shattering a Neural Network, 2021, Yoshua Bengio's group.
• On Predicting Generalization using GANs, Nov. 28 2021.
• Intrinsic Dimension, Persistent Homology and Generalization in Neural Networks, Nov. 25 2021.

Flatness

• On the Maximum Hessian Eigenvalue and Generalization, Jun. 22 2022.

Decision boundary

• Can You Learn the Same Model Twice? Investigating Reproducibility and Double Descent from the Decision Boundary Perspective, Dec. 16 2021.

Data-centric understanding

• Deep Learning Through the Lens of Example Difficulty, Google Research 2021.
• Deep Learning on a Data Diet: Finding Important Examples Early in Training, Jul. 15 2021. nips2021

Spurious correlation

See here for the detailed discussion on spurious correlation.

Lottery ticket hypothesis

• Can You Win Everything with A Lottery Ticket?, TMLR 2022.

Memorization

• Network size and weights size for memorization with two-layers neural networks, Nov. 3 2020.
• What Do Neural Networks Learn When Trained With Random Labels?, nips2020.
• Neural Networks Learning and Memorization with (almost) no Over-Parameterization, nips2020.
• On the geometry of generalization and memorization in deep neural networks, iclr2021.
• The Curious Case of Benign Memorization, Oct. 25 2022.
  • "only the very last layers are used for memorization, while preceding layers encode performant features which remain largely unaffected by the label noise"
• Distinguishing rule and exemplar-based generalization in learning systems, icml2022.
  • The experiment setting has been applied to study in-context ability of Transformers tweet.
• Unintended memorisation of unique features in neural networks, May 20 2022.