Perceptron

A perceptron (or McCulloch–Pitts neuron) is a fundamental building block in neural networks and serves as a precursor to more complex neural network architectures.

A perceptron is a single-layer neural network. More complex neural networks with multiple layers are referred to as multi-layer perceptrons or simply neural networks.

flowchart TD
    %% Define styles
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    classDef weight fill:#ccccff,stroke:#000,stroke-width:2px;
    classDef sum fill:#ffffcc,stroke:#000,stroke-width:2px;
    classDef activation fill:#ccffcc,stroke:#000,stroke-width:2px;
    classDef output fill:#ffcce0,stroke:#000,stroke-width:2px;

    %% Define nodes
    A1(("Input 1")):::input
    A2(("Input 2")):::input
    A3(("Input 3")):::input

    B["Weights & Bias"]:::weight

    C>"Net Sum"]:::sum

    D{"Activation Function"}:::activation

    E(("Output")):::output

    %% Define connections
    A1 --> B
    A2 --> B
    A3 --> B
    B --> C
    C --> D
    D --> E

Legend

Color Coding

Component	Color
Input
Weights & Bias
Net Sum
Activation Function
Output

Components of a Perceptron

The perceptron consists of four main parts:

1. Input Values:

   • Also known as the input layer, these are the raw data or features fed into the perceptron. Each input value represents a feature of the data.

2. Weights and Bias:

   • Weights: Parameters associated with each input value. They determine the importance of each input feature. During training, the weights are adjusted to minimize the error in predictions.
   • Bias: An additional parameter that allows the model to fit the data better by shifting the activation function. It helps in adjusting the output independently of the input values.

3. Net Sum:

   • The perceptron calculates a net sum by taking the weighted sum of the inputs and adding the bias. Mathematically, this can be represented as: [ \text{Net Sum} = \sum (w_i \cdot x_i) + b ] where ( w_i ) represents the weights, ( x_i ) represents the input values, and ( b ) represents the bias.

4. Activation Function:

   • The net sum is passed through an activation function to produce the final output of the perceptron. Common activation functions include:
     • Step Function: Outputs a binary result (0 or 1) based on whether the net sum exceeds a certain threshold.
     • Sigmoid Function: Provides a smooth gradient and maps the output to a range between 0 and 1.

Working of a Perceptron

1. Compute Net Sum: Calculate the weighted sum of the inputs and add the bias.

2. Apply Activation Function: Pass the net sum through the activation function to obtain the output.

The perceptron is a simple yet powerful model that forms the basis for more advanced neural networks. It demonstrates how weights, bias, and activation functions work together to make predictions based on input data.