Deep Learning and Neural Networks

  1. Deepening the Network
    1. The Rise of Deep Learning
      1. Historical Context
        1. Key Breakthroughs and Milestones
          1. Computational Advances
            1. Data Availability
            2. Challenges with Deep Networks
              1. The Vanishing Gradient Problem
                1. Causes and Mathematical Explanation
                  1. Effects on Training Deep Networks
                    1. Impact on Early Layers
                    2. The Exploding Gradient Problem
                      1. Causes and Mathematical Explanation
                        1. Effects on Training Stability
                          1. Gradient Clipping Solutions
                          2. Overfitting in Deep Networks
                            1. Increased Model Complexity
                              1. Memorization vs. Generalization
                              2. Training Instability
                                1. Computational Complexity
                                2. Solutions and Modern Practices
                                  1. Improved Activation Functions
                                    1. ReLU and its Variants
                                      1. Addressing Vanishing Gradients
                                      2. Weight Initialization Schemes
                                        1. Importance of Proper Initialization
                                          1. Random Initialization Problems
                                            1. Xavier/Glorot Initialization
                                              1. Mathematical Formulation
                                                1. Variance Preservation
                                                  1. Use Cases
                                                  2. He Initialization
                                                    1. Mathematical Formulation
                                                      1. ReLU-Specific Design
                                                        1. Use Cases
                                                      2. Normalization Techniques
                                                        1. Batch Normalization
                                                          1. Normalizing Activations
                                                            1. Internal Covariate Shift
                                                              1. Impact on Training Speed and Stability
                                                                1. Implementation Details
                                                                2. Layer Normalization
                                                                  1. Per-Sample Normalization
                                                                    1. Comparison to Batch Normalization
                                                                    2. Group Normalization
                                                                      1. Instance Normalization
                                                                      2. Residual Connections
                                                                        1. Skip Connections
                                                                          1. Identity Mappings
                                                                            1. Benefits for Deep Networks
                                                                              1. ResNet Architecture

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                                                                          2. Training Shallow Neural Networks

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                                                                          4. Practical Considerations for Training