Having defined the structure of a neural network and prepared the input data, we now examine how the network processes information to arrive at a result. This process, known as forward propagation (or the forward pass), involves feeding input data through the network, layer by layer, to compute an output.

In this chapter, you will learn the mechanics of this information flow. We will cover:

• Calculating the weighted sum within a neuron ($z = \sum_{i} w_i x_i + b$).
• Applying activation functions ($a = g(z)$) to introduce non-linearity.
• Performing these calculations efficiently across layers using matrix operations ($Z = WX + b$, $A = g(Z)$).
• Tracing the data path from the input layer to the final output layer to generate a prediction.

We'll see how these steps combine to transform input features into a meaningful network output. By the end of this chapter, you will be able to implement the complete forward pass for a simple neural network using Python and NumPy.