Q16Machine Learning

A single Perceptron is a strictly linear classifier; it mathematically fails instantly when presented with a non-linear problem like the XOR logic gate. The Multilayer Perceptron (MLP) is the absolute foundational architecture of Deep Learning (a Feedforward Artificial Neural Network). It aggressively stacks thousands of perceptrons into highly structured mathematical layers.

The Architectural Layers

• 1. The Input Layer: A passive layer. It contains exactly one node for every single feature in the dataset (e.g., 784 nodes for a $28\times 28$ pixel image). It performs absolutely zero mathematical computation.
• 2. The Hidden Layers: The absolute computational core of the network. An MLP must have at least one hidden layer to be considered "Deep." It is a "Dense" (Fully Connected) architecture, meaning every single node in Layer 1 is mathematically wired via a unique Weight ($W$) to every single node in Layer 2.
• 3. The Output Layer: Represents the final prediction. For binary classification, it is 1 node utilizing a Sigmoid activation. For 10-class classification, it is 10 nodes utilizing a Softmax activation.

The Mathematical Execution (Forward Pass)

For a single node $j$ in a hidden layer, it receives the outputs from all $N$ nodes of the previous layer ($x_i$). It computes a massive linear algebra dot product: $$Z_j=\sum _{i=1}^N(w_{ij}\cdot x_i)+b_j$$

Crucially, $Z_j$ is then violently forced through a strict Non-Linear Activation Function (like ReLU or Tanh). If the activation function was removed, the entire massive 100-layer network would mathematically collapse back into a single, useless linear regression equation.