What is perceptron? Explain.

A perceptron is a fundamental building block of artificial neural networks, specifically a type of single-layer neural network used for binary classification tasks. It was introduced by Frank Rosenblatt in the late 1950s and is based on the concept of a simplified model of a biological neuron.

A perceptron consists of:

• Input Layer: The perceptron takes input features (x1, x2, …, xn) and applies weights (w1, w2, …, wn) to each input. These weighted inputs are summed up along with a bias term (b).
• Activation Function: The weighted sum (z) is then passed through an activation function (often a threshold function like the step function or the sigmoid function) to produce the perceptron's output (y).

Mathematically, the output (y) of a perceptron can be expressed as:
[ y = \text{activation_function}(z) = \text{activation_function}(w_1x_1 + w_2x_2 + \ldots + w_nx_n + b) ]

The perceptron learning process involves:

• Initialization: Assigning random weights and biases to the perceptron.
• Training: Adjusting the weights and biases based on the difference between the predicted output and the actual output (error). This is typically done using the perceptron learning rule, which updates the weights and biases to minimize the error over multiple iterations (epochs) of training.

The perceptron learning rule updates the weights and bias as follows:
[ w_i \leftarrow wi + \alpha \times (y{\text{true}} – y_{\text{pred}}) \times xi ]
[ b \leftarrow b + \alpha \times (y{\text{true}} – y_{\text{pred}}) ]

Where:

• ( w_i ) is the weight associated with input ( x_i ),
• ( \alpha ) is the learning rate,
• ( y_{\text{true}} ) is the true output (target label),
• ( y_{\text{pred}} ) is the predicted output (computed by the perceptron).

Perceptrons are limited to linear decision boundaries and are only capable of learning linearly separable patterns. However, they laid the groundwork for more complex neural network architectures, such as multi-layer perceptrons (MLPs), which can learn non-linear patterns and are used extensively in modern machine learning applications for tasks like image recognition, natural language processing, and more complex classifications.