Logic Gates Perceptron

This repository implements perceptron models for logic gates using Java. It contains:

• SLP (Single-Layer Perceptron) for the AND gate
• Linear SLP for non-classification problems (e.g., regression: y = 2x + 1)
• MLP (Multi-Layer Perceptron) for the XOR gate

The project also includes tracking of the learning process and visualization of weights, biases, and outputs during training.

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Table of Contents

• SLP AND
• SLP Linear
• MLP XOR Model
• Usage

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SLP AND

Note: For the +2 threshold, the perceptron bias increases to help reach the activation threshold for producing output 1.

Note: For the -2 threshold, the perceptron bias decreases to adjust the weighted sum so that the neuron can still activate correctly.

• A single-layer perceptron for the AND gate.
• Learning rate: Can be increased to hasten learning but should be chosen cautiously; too high may prevent fine-tuning.
• Activation function: Step function return weightedSum >= threshold ? 1 : 0 for classification.

Key idea: For classification problems, the perceptron outputs discrete values using a step function.

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SLP Linear

Note: This is an unfinished training of the SLP for the regression function y = 2x + 1.
The network has a small learning rate and insufficient epochs, so the weights and bias have not yet reached their optimum values.

Note: This shows the finished training of the SLP for y = 2x + 1.
The network has now converged with appropriate weights and bias, closely approximating the target linear mapping.

• For non-classification / regression problems.
• Regression function used for testing: y = 2x + 1
• Activation function: Identity (linear), no step function required as it's a non-classification problem.

Notes:

• Step functions are avoided because the model must approximate a continuous mapping (y = 2x + 1).
• Using a nonlinear step function in regression would throw away useful information.

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MLP XOR Model

• Multi-layer perceptron (MLP) implemented to solve XOR, which cannot be solved by a single-layer perceptron.
• Tracks Mean Squared Error (MSE) loss and weight/bias changes during training.

Training Results:

Final Predictions:

Epoch 0, MSE Loss: 0.308586
Epoch 1000, MSE Loss: 0.252861

Input	Predicted	Target
[0, 0]	0.4733	0.0
[0, 1]	0.5152	1.0
[1, 0]	0.5043	1.0
[1, 1]	0.5232	0.0

Observations:

• Loss stabilizes around 0.25, not decreasing further due to the simplicity of the network.
• Weights like w2[1], w1[1][1], and output bias b2 decrease while balancing the increasing w2[0], w1[0][0], and w1[1][0].
• Network finds an approximate solution, showing the limitations of small MLPs for XOR with sigmoid activations.

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Usage

1. Clone the repository:

git clone https://github.com/your-username/logic-gates-perceptron.git

2. FXPlot plotting utility:

This project uses FXPlot

Local Installation:

Since FXPlot is not yet published to Maven Central, you can use JitPack to include FXPlot as a dependency.

Add this repository to your pom.xml:

<repositories>
  <repository>
    <id>jitpack.io</id>
    <url>https://jitpack.io</url>
  </repository>
</repositories>

Then add the dependency:

<dependencies>
  <dependency>
    <groupId>com.github.muichi-mon</groupId>
    <artifactId>fxplot</artifactId>
    <version>master-SNAPSHOT</version>
  </dependency>
</dependencies>

If using Java modules, add the following line to your module-info.java:

module your.module.name {
    requires io.github.rajveer.fxplot;
}