04·Multilayer network (MLP) and the forward pass step by step

Introduction

The Multi-Layer Perceptron (MLP) is the foundation of all modern feedforward networks. This lesson walks through the MLP forward pass step by step: the pre-activation z = Wx + b, the activation a = σ(z), layer composition, batch processing (X ∈ R^{B×n} rather than x ∈ R^n), tensor shapes at each stage, and conventions (row-major vs column-major, transposes, bias broadcasting). You will understand how to count parameter sizes, how to infer output shape, and why the transformer sequence (input → linear → activation → linear) is what it is.