Deep Learning and Neural Networks

  Deep learning has revolutionized fields such as computer vision, natural language processing, and data generation. This module introduces key deep learning architectures and explains their unique strengths, structures, and applications. 🔹 Shallow vs. Deep Neural Networks A shallow neural network typically contains only one hidden layer between the input and output layers. It can model simple, linearly separable functions but struggles with complex patterns. A deep neural network (DNN) includes multiple hidden layers and a high number of neurons per layer. It can extract hierarchical representations from raw data and is more capable of handling non-linear relationships. ➤ Input Types: Shallow networks require pre-processed vector inputs (e.g., numerical features). Deep networks can directly process raw data such as images, audio, or text. ➤ Why the Boom in Deep Learning? Three key factors contributed: Algorithmic breakthroughs : e.g., ReLU activati...

  Activation functions are essential in deep learning as they enable neural networks to learn complex patterns by introducing non-linearity into the model. Without them, no matter how deep a network is, it would behave like a linear model . 🔁 Sigmoid Function (Logistic Function) The Sigmoid function , also known as the logistic function , is one of the earliest and most well-known activation functions in neural networks. 🧮 Definition: σ ( x ) = 1 1 + e − x \sigma(x) = \frac{1}{1 + e^{-x}} σ ( x ) = 1 + e − x 1 ​ ✅ Characteristics: Outputs values between 0 and 1 , ideal for binary classification Smooth and differentiable Interpreted as probability for a binary outcome ⚠️ Limitations: Vanishing Gradient Problem : For very large or small values of x x x , the gradient becomes very close to zero . This slows down or halts learning in deep networks during backpropagation. Non-zero-centered output : The function outputs only positive values , which...