The Perceptron, introduced by Frank Rosenblatt in 1957, is the fundamental unit of a neural network, inspired by the biological neuron. It's a binary linear classifier, meaning it can only classify data into two categories.

1. Inputs: A perceptron receives one or more binary (0 or 1) or real-valued inputs (x_1,x_2,dots,x_n). 2. Weights: Each input is multiplied by a corresponding weight (w_1,w_2,dots,w_n). These weights represent the strength or importance of each input. 3. Weighted Sum: All the weighted inputs are summed together: Z=(x_1w_1)+(x_2w_2)+dots+(x_nw_n). 4. Bias: An additional term called the bias (b) is added to the weighted sum. The bias allows the activation function to be shifted. So, Z=(x_1w_1)+(x_2w_2)+dots+(x_nw_n)+b. 5. Activation Function: The sum Z is then passed through an activation function. For the original Perceptron, this was a simple step function (also known as a Heaviside step function or threshold function). 6. Output: The output (0 or 1) is the perceptron's prediction.

Perceptrons learn by adjusting their weights and bias. If a prediction is incorrect, the weights are updated iteratively based on the error. The Perceptron learning rule would increase weights if the prediction was too low for a positive example, and decrease them if too high for a negative example.

The most significant limitation of a single perceptron is that it can only classify linearly separable data. This means it can only draw a single straight line (or hyperplane in higher dimensions) to separate two classes. It famously cannot solve the XOR problem, where the data points are not linearly separable. This limitation led to the development of multi-layer networks.

To overcome the linear separability limitation of a single perceptron, researchers connected multiple perceptrons in layers, leading to the Multi-Layer Perceptron (MLP), also known as a Feedforward Neural Network. MLPs are the foundational architecture for many deep learning concepts.

An MLP consists of at least three types of layers: 1. Input Layer: This layer receives the raw input features of your data. Each node in the input layer corresponds to one input feature. No computations (weights, biases, or activation functions) are performed in the input layer; it merely passes the input values to the next layer. 2. Hidden Layers: These are the intermediate layers between the input and output layers. An MLP must have at least one hidden layer, and deep learning refers to networks with many hidden layers. Each node (or 'neuron') in a hidden layer performs the same operation as a perceptron: it takes inputs from the previous layer, multiplies them by learned weights, sums them up, adds a bias, and then passes the result through an activation function. Hidden layers are crucial because they allow the network to learn complex, non-linear relationships and abstract representations of the input data. Each subsequent hidden layer can learn more intricate and higher-level features from the representations learned by the previous layer. The 'depth' in 'deep learning' refers to the number of hidden layers. 3. Output Layer: This is the final layer of the network, responsible for producing the model's prediction. The number of nodes in the output layer depends on the type of problem: Regression: Typically one node (for predicting a single numerical value). Binary Classification: One node (often with a Sigmoid activation to output a probability between 0 and 1). Multi-Class Classification: One node for each class (often with a Softmax activation to output probabilities for each class). Like hidden layers, nodes in the output layer also apply weights, biases, and an activation function.

The key to MLPs' power lies in the non-linear activation functions used in their hidden layers. While a single perceptron with a linear activation can only model linear relationships, stacking multiple layers with non-linear activation functions allows the MLP to approximate any continuous function. This means MLPs can learn highly complex, non-linear decision boundaries and discover intricate patterns in data that are not linearly separable (like the XOR problem). Each hidden layer learns increasingly abstract representations, effectively performing automatic feature engineering.