Introduction to Deep Learning
Chapter 1: Neural Network Foundations
From Machine Learning to Deep Learning
Biological Inspiration: The Neuron
The Artificial Neuron: A Mathematical Model
The Perceptron: The Simplest Neural Network
Limitations of Single-Layer Perceptrons
Multi-Layer Perceptrons (MLPs): Adding Depth
Hands-on Practical: Building a Simple Perceptron Model
Quiz for Chapter 1
Chapter 2: Activation Functions and Network Architecture
The Role of Activation Functions
Sigmoid Activation
Hyperbolic Tangent (Tanh) Activation
Rectified Linear Unit (ReLU)
Variants of ReLU (Leaky ReLU, PReLU, ELU)
Choosing the Right Activation Function
Understanding Network Layers: Input, Hidden, Output
Designing Feedforward Network Architectures
Hands-on Practical: Implementing Different Activations
Quiz for Chapter 2
Chapter 3: Training Neural Networks: Loss and Optimization
Measuring Performance: Loss Functions
Common Loss Functions for Regression (MSE, MAE)
Common Loss Functions for Classification (Cross-Entropy)
Optimization: Finding the Best Weights
Gradient Descent Algorithm
Learning Rate
Stochastic Gradient Descent (SGD)
Challenges with Gradient Descent
Hands-on Practical: Visualizing Gradient Descent
Quiz for Chapter 3
Chapter 4: Backpropagation and Advanced Optimization
Calculating Gradients: The Chain Rule
Computational Graphs
The Backpropagation Algorithm Explained
Forward Pass vs. Backward Pass
Gradient Descent with Momentum
RMSprop Optimizer
Adam Optimizer
Choosing an Optimization Algorithm
Hands-on Practical: Backpropagation Step-by-Step
Quiz for Chapter 4
Chapter 5: Building and Training Deep Neural Networks
Introduction to Deep Learning Frameworks (TensorFlow/Keras, PyTorch)
Setting up the Development Environment
Preparing Data for Neural Networks
Defining a Feedforward Network Model
Weight Initialization Strategies
Compiling the Model: Loss and Optimizer Selection
Training the Model: The fit Method
Monitoring Training Progress (Loss and Metrics)
Evaluating Model Performance
Hands-on Practical: Training a Classifier on MNIST
Quiz for Chapter 5
Chapter 6: Regularization and Improving Performance
The Problem of Overfitting
Regularization Techniques Overview
L1 and L2 Regularization
Dropout Regularization
Early Stopping
Batch Normalization
Hyperparameter Tuning Fundamentals
Strategies for Hyperparameter Search (Grid Search, Random Search)
Hands-on Practical: Applying Dropout and Early Stopping
Quiz for Chapter 6
Chapter 7: Introduction to Specialized Architectures
Limitations of Feedforward Networks
Convolutional Neural Networks (CNNs): Motivation
Core CNN Operations: Convolution
Core CNN Operations: Pooling
Typical CNN Architecture
Recurrent Neural Networks (RNNs): Motivation
The Concept of Recurrence and Hidden State
Basic RNN Architecture
Challenges with Simple RNNs (Vanishing/Exploding Gradients)
Overview: LSTMs and GRUs
Quiz for Chapter 7
Challenges with Gradient Descent
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- Deep Learning, Ian Goodfellow, Yoshua Bengio, Aaron Courville, 2016 (MIT Press) - This textbook provides a detailed explanation of optimization challenges in deep learning, including local minima, saddle points, slow convergence in ravines, and the impact of learning rate.
- The Loss Surfaces of Multilayer Networks, Anna Choromanska, Mikael Henaff, Michael Mathieu, Gérard Ben Arous, Yann LeCun, 2015 Proceedings of Machine Learning Research, Vol. 38 (PMLR) - This paper provides theoretical insights into the geometry of loss surfaces for deep neural networks, arguing that in high dimensions, most local minima are empirically good and the primary challenge comes from saddle points.
- Identifying and attacking the saddle point problem in high-dimensional non-convex optimization, Yann N. Dauphin, Razvan Pascanu, Caglar Gulcehre, Kyunghyun Cho, Surya Ganguli, Yoshua Bengio, 2014 Advances in Neural Information Processing Systems (NIPS 27) (MIT Press) - This paper discusses the prevalence of saddle points over local minima in high-dimensional non-convex optimization, explaining how they can impede gradient-based optimization algorithms.
- Optimization Methods for Large-Scale Machine Learning, Léon Bottou, Frank E. Curtis, Jorge Nocedal, 2018 SIAM Review, Vol. 60 (Society for Industrial and Applied Mathematics) DOI: 10.1137/16M1080173 - This review article offers a comprehensive survey of optimization algorithms used in large-scale machine learning, discussing the theoretical foundations and practical aspects relevant to deep learning.