Neural Networks Fundamentals

Master the foundations of neural networks from mathematical principles to practical implementations. 8 comprehensive chapters covering feedforward networks, backpropagation, activation functions, CNNs, RNNs, and LSTMs with detailed explanations, formulas, and code examples.

Chapter 1: Introduction to Neural Networks

From Biological Neurons to Artificial Networks

  • Biological inspiration and neuron model
  • Perceptron and linear classification
  • Multi-layer perceptrons (MLPs)
  • Universal approximation theorem
  • Neural network architecture basics
Foundation Theory Mathematics

Chapter 2: Feedforward Networks & Forward Propagation

Understanding Information Flow

  • Layer-by-layer computation
  • Matrix operations in neural networks
  • Weight initialization strategies
  • Bias terms and their role
  • Forward propagation implementation
Forward Pass Linear Algebra Implementation

Chapter 3: Activation Functions

Non-Linearity and Network Capacity

  • Sigmoid, Tanh, ReLU, and variants
  • Activation function properties
  • Vanishing gradient problem
  • Choosing the right activation
  • Leaky ReLU, ELU, Swish functions
Activation Non-Linearity Gradients

Chapter 4: Backpropagation Algorithm

The Learning Mechanism

  • Chain rule and gradient computation
  • Backward pass step-by-step
  • Computational graph understanding
  • Gradient flow and vanishing/exploding gradients
  • Backpropagation implementation from scratch
Backpropagation Gradients Calculus

Chapter 5: Optimization & Training

Learning from Data

  • Loss functions (MSE, Cross-entropy)
  • Gradient descent variants (SGD, Adam, RMSprop)
  • Learning rate scheduling
  • Batch normalization
  • Regularization techniques (L1, L2, Dropout)
Optimization Training Regularization

Chapter 6: Convolutional Neural Networks (CNNs)

Processing Spatial Data

  • Convolution operation and filters
  • Pooling layers (Max, Average)
  • CNN architecture patterns
  • Image classification examples
  • Transfer learning with CNNs
CNNs Computer Vision Convolution

Chapter 7: Recurrent Neural Networks (RNNs)

Processing Sequential Data

  • RNN architecture and hidden states
  • Unfolding RNNs through time
  • Backpropagation through time (BPTT)
  • Vanishing gradient in RNNs
  • RNN applications and limitations
RNNs Sequences Time Series

Chapter 8: Long Short-Term Memory (LSTM)

Solving the Vanishing Gradient Problem

  • LSTM cell architecture
  • Forget, input, and output gates
  • Cell state and hidden state
  • LSTM vs RNN comparison
  • GRU (Gated Recurrent Unit) introduction
LSTM Memory Gates