What is a Perceptron?

A perceptron is a simple model of an artificial neuron that outputs either 0 or 1 based on the input signals.

1. Structure of a Perceptron

Like other artificial neurons, a perceptron consists of input, weights, bias, activation function, and output.

The perceptron calculates the output value by applying the activation function to the sum of the product of input values and weights, added to the bias.

The operation of a perceptron can be expressed by the following equation:

$$y = f\left(\sum w_i x_i + b\right)$$

Where each symbol represents the following:

• $x_i$: Input value
• $w_i$: Weight
• $b$: Bias
• $f$: Activation function
• $y$: Output value

2. Operation of a Perceptron

The perceptron outputs 1 (true, activated) if the sum of the product of the given input values and weights exceeds a certain threshold, otherwise it outputs 0 (false, deactivated).

This method of producing one of two possible values (e.g., true/false, 0/1) is called Binary Classification, and a perceptron that performs binary classification in a single layer is called a single-layer perceptron.

Using a single-layer perceptron, you can create simple rules to compare two input values.

For example, the perceptron below outputs 1 only when both input values are 1 (true), and 0 in all other cases.

Input Value 1 ($x_1$)	Input Value 2 ($x_2$)	Output ($y$)
0	0	0
0	1	0
1	0	0
1	1	1

This rule, where the output is 1 only when all input values are 1, is known as the AND operation.

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Now, consider a perceptron where the result is 1 if at least one input value is 1.

Input Value 1 ($x_1$)	Input Value 2 ($x_2$)	Output ($y$)
0	0	0
0	1	1
1	0	1
1	1	1

This rule, where the output is 1 if at least one input value is 1, is known as the OR operation.

In the next lesson, we will explore the limitations of single-layer perceptrons and delve into multi-layer perceptrons that overcome these limitations.

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