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
The Need for Adaptive Learning Rates
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- Adaptive Subgradient Methods for Online Learning and Stochastic Optimization, John Duchi, Elad Hazan, and Yoram Singer, 2011 Journal of Machine Learning Research, Vol. 12 (Microtome Publishing) DOI: 10.5555/1953048.2078174 - Introduces AdaGrad, a foundational adaptive learning rate algorithm that scales parameter updates inversely proportional to the square root of the sum of past squared gradients. This paper helps understand the origin of per-parameter learning rate scaling.
- Adam: A Method for Stochastic Optimization, Diederik P. Kingma, Jimmy Ba, 2014 3rd International Conference for Learning Representations, San Diego, 2015 DOI: 10.48550/arXiv.1412.6980 - Presents Adam, a widely used adaptive optimization algorithm that combines the benefits of RMSprop and Momentum, offering individual adaptive learning rates for different parameters by estimating first and second moments of the gradients.
- Deep Learning, Ian Goodfellow, Yoshua Bengio, and Aaron Courville, 2016 (MIT Press) - Chapter 8, 'Optimization for Training Deep Models', provides a comprehensive overview of optimization algorithms, including the motivations for adaptive learning rates and detailed discussions of AdaGrad, RMSprop, and Adam.