Neural Networks

Perceptron Visualizer

A single-neuron model implementing linear classification boundaries.

What is Perceptron Visualizer?

The Perceptron is the fundamental building block of neural networks, modeling a single biological neuron. It is a linear binary classifier that takes a vector of inputs, calculates their weighted sum, adds a bias, and applies an activation function (like step function) to produce an output (Class A or Class B). It learns by iteratively updating its weights whenever it makes a classification error.

Key Characteristics:

  • First artificial single-layer neural network model
  • Calculates weighted sum: z = w1*x1 + w2*x2 + ... + bias
  • Step Activation: Output 1 if z >= 0, else 0
  • Learns only linearly separable datasets

Complexity Analysis

Avg Time Complexity: O(Epochs * N * D) training, O(D) prediction
Space Complexity: O(D) weight dimension storage
Best Case: O(N) (dataset classified correctly on epoch 1)
Worst Case: O(Epochs * N) (non-separable dataset loops infinitely)

How it Works Step-by-Step

  1. Compute Input Sum: w1*x1 + w2*x2 + ... + bias.
  2. Activation: Pass sum through step function; output prediction.
  3. Calculate Error: error = target_label - predicted_label.
  4. Update Weights: If error exists, update: w_new = w + rate * error * x.

Code Implementation

Worked Trace Example

Training Perceptron on AND gate with inputs (1,1) [Target 1]:
1. Initial weights: w1=0.2, w2=0.2, bias=-0.5
2. Sum = 0.2(1) + 0.2(1) - 0.5 = -0.1 -> Prediction = 0
3. Error = 1 - 0 = 1 (Misclassified)
4. Update weights: w1 = w1 + 0.1(1)(1) = 0.3. New bias = -0.4.