Model Regularization and Optimization in Deep Learning
Chapter 1: The Challenge of Generalization
Introduction to Model Generalization
Understanding Underfitting and Overfitting
The Bias-Variance Tradeoff in Deep Learning
Diagnosing Model Performance: Learning Curves
Validation and Cross-Validation Strategies
The Role of Regularization and Optimization
Setting up the Development Environment
Practice: Visualizing Overfitting
Quiz for Chapter 1
Chapter 2: Weight Regularization Techniques
Intuition Behind Weight Regularization
L2 Regularization (Weight Decay): Mechanism
L2 Regularization: Mathematical Formulation
L1 Regularization: Mechanism and Sparsity
L1 Regularization: Mathematical Formulation
Comparing L1 and L2 Regularization
Elastic Net: Combining L1 and L2
Implementing Weight Regularization
Hands-on Practical: Applying L1/L2 to a Network
Quiz for Chapter 2
Chapter 3: Dropout Regularization
Introducing Dropout: Preventing Co-adaptation
How Dropout Works During Training
Scaling Activations at Test Time
Inverted Dropout Implementation
Dropout Rate as a Hyperparameter
Considerations for Convolutional and Recurrent Layers
Implementing Dropout in Practice
Hands-on Practical: Adding Dropout Layers
Quiz for Chapter 3
Chapter 4: Normalization Techniques for Training Stability
The Problem of Internal Covariate Shift
Introduction to Batch Normalization
Batch Normalization: Forward Pass Calculation
Batch Normalization: Backward Pass Calculation
Benefits of Batch Normalization
Batch Normalization at Test Time
Considerations and Placement in Networks
Introduction to Layer Normalization
Implementing Batch Normalization
Hands-on Practical: Integrating Batch Normalization
Quiz for Chapter 4
Chapter 5: Foundational Optimization Algorithms
Revisiting Gradient Descent
Challenges with Standard Gradient Descent
Stochastic Gradient Descent (SGD)
Mini-batch Gradient Descent
SGD Challenges: Noise and Local Minima
SGD with Momentum: Accelerating Convergence
Nesterov Accelerated Gradient (NAG)
Implementing SGD and Momentum
Practice: Comparing GD, SGD, and Momentum
Quiz for Chapter 5
Chapter 6: Adaptive Optimization Algorithms
The Need for Adaptive Learning Rates
AdaGrad: Adapting Learning Rates per Parameter
AdaGrad Limitations: Diminishing Learning Rates
RMSprop: Addressing AdaGrad's Limitations
Adam: Adaptive Moment Estimation
Adam Algorithm Breakdown
Adamax and Nadam Variants (Brief Overview)
Choosing Between Optimizers: Guidelines
Implementing Adam and RMSprop
Hands-on Practical: Optimizer Comparison Experiment
Quiz for Chapter 6
Chapter 7: Optimization Refinements and Hyperparameter Tuning
Importance of Parameter Initialization
Common Initialization Strategies (Xavier, He)
Learning Rate Schedules: Motivation
Step Decay Schedules
Exponential Decay and Other Scheduling Methods
Warmup Strategies
Tuning Hyperparameters: Learning Rate, Regularization Strength, Batch Size
Relationship Between Batch Size and Learning Rate
Grid Search vs. Random Search for Hyperparameters
Implementing Learning Rate Scheduling
Practice: Tuning Hyperparameters for a Model
Quiz for Chapter 7
Chapter 8: Combining Techniques and Practical Considerations
Interaction Between Regularization and Optimization
Typical Deep Learning Training Workflow
Monitoring Training: Loss Curves and Metrics
Early Stopping as Regularization
Combining Dropout and Batch Normalization
Data Augmentation as Implicit Regularization
Choosing the Right Combination of Techniques
Debugging Training Issues Related to Optimization/Regularization
Hands-on Practical: Building and Tuning a Regularized/Optimized Model
Quiz for Chapter 8
Stochastic Gradient Descent (SGD)
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- Deep Learning, Ian Goodfellow, Yoshua Bengio, and Aaron Courville, 2016 (MIT Press) - Comprehensive textbook covering fundamental concepts of deep learning, including a detailed explanation of Stochastic Gradient Descent and its variants.
- A Stochastic Approximation Method, Herbert Robbins, Sutton Monro, 1951 The Annals of Mathematical Statistics, Vol. 22 (Institute of Mathematical Statistics) DOI: 10.1214/aoms/1177729586 - The foundational paper that introduced the stochastic approximation method, which provides the mathematical basis for Stochastic Gradient Descent.
- Optimization Methods for Large-Scale Machine Learning, Léon Bottou, Frank E. Curtis, and Jorge Nocedal, 2018 SIAM Review, Vol. 60 (Society for Industrial and Applied Mathematics) DOI: 10.1137/16M1080173 - A comprehensive survey on optimization methods for large-scale machine learning, with a significant focus on Stochastic Gradient Descent and its theoretical properties and practical applications.