Multi-Layer Perceptrons (MLPs): Architecture and Backpropagation

Learning Objectives Diagram the architecture of a Multi-Layer Perceptron, identifying input, hidden, and output layers. Explain the role of weights, biases, and activation functions within a neuron. Trace the flow of data through an MLP during a forward pass to generate a prediction. Define the purpose of a loss function and its role in measuring model error. Describe the process of backpropagation, including the calculation of gradients and the weight update rule. Articulate how an MLP 'learns' by iteratively adjusting its parameters to minimize error. How does your phone instantly recognize your face or a photo app categorize pictures of your cat? 🤖 It's not magic; it's the power of neural networks learning from data! This tutorial demystifies the Mul...

TermDefinitionExample Neuron (or Perceptron)The basic computational unit of a neural network. It receives one or more inputs, applies a weighted sum, adds a bias, and then passes the result through an activation function to produce an output.A neuron in the first layer might take two inputs, x1=0.5 and x2=0.8. With weights w1=0.2 and w2=0.9, and bias b= -0.1, the initial sum is (0.5*0.2) + (0.8*0.9) - 0.1 = 0.72. This sum is then fed into an activation function. Activation FunctionA mathematical function applied to the output of a neuron that introduces non-linearity into the network. This allows the MLP to learn complex patterns that a simple linear model cannot.The Sigmoid function, σ(z) = 1 / (1 + e^-z), squashes any input value 'z' to a range between 0 and 1. If a neuron&#03...

Forward Pass Calculation (Per Neuron) z = (w₁x₁ + w₂x₂ + ... + wₙxₙ) + b a = f(z) For each neuron, calculate the weighted sum 'z' of its inputs 'x' and weights 'w', plus a bias 'b'. Then, apply the activation function 'f' to 'z' to get the neuron's output 'a'. This process is repeated for every neuron, layer by layer, from input to output. Loss Calculation (Mean Squared Error) Loss = (1/n) * Σ(y_true - y_pred)² Used to quantify the model's error. For each data point, find the square of the difference between the true value (y_true) and the predicted value (y_pred). The average of these squared differences across all 'n' data points is the Mean Squared Error (MSE). Weight Update Rule...