JavaScript : Simple perceptron predicting wrong for XOR gate

Question

This JavaScript code represents the concept of simple perceptron in a neural network. Below code is predicting fine with all truth table except XOR table . please run this code in your browser's console window and find what is wrong.

Since this is a simple single neuron, I didn't give much importance to hidden layers. I'am training this up to 10,000 iteration for better result.

//AND GATE
var X1 = [0,1,1,0];
var X2 = [0,1,0,1];
var OUT = [0,1,0,0];

/*

//AND GATE
var X1 = [0,1,1,0];
var X2 = [0,1,0,1];
var OUT = [0,1,0,0];

//OR GATE
var X1 = [0,1,1,0];
var X2 = [0,1,0,1];
var OUT = [0,1,1,1];

//NAND GATE
var X1 = [0,1,1,0];
var X2 = [0,1,0,1];
var OUT = [1,0,1,1];

//NOR GATE
var X1 = [0,1,1,0];
var X2 = [0,1,0,1];
var OUT = [1,0,0,0];

//XOR GATE
var X1 = [0,1,1,0];
var X2 = [0,1,0,1];
var OUT = [0,0,1,1];

*/

var LR = 0.01; //Learning rate to speedup learning process.
var BIAS = 1; // Avoid sum become zero.
var TRAIN = 10000; //Epochs we need to run for accurate result
var WEIGHTS = [Math.random(),Math.random(),Math.random()]; //3 Random weights 2 for input & 1 for bias 

//console.log("Initial Weights : "+WEIGHTS);

function neuron(x1,x2,out){

var sum = 0;
var error = 0;

//Sum of weighted x1,x2 and bias
sum = x1*WEIGHTS[0] + x2*WEIGHTS[1] + BIAS*WEIGHTS[2];

//Heaviside step function as activation function
if(sum>1){
    sum = 1;
}else{
    sum = 0;
}

//Calculate the error
error = out - sum;

//Adjust weights
WEIGHTS[0] = WEIGHTS[0] + error * x1 * LR;  
WEIGHTS[1] = WEIGHTS[1] + error * x2 * LR;
WEIGHTS[2] = WEIGHTS[2] + error * BIAS * LR;

//console.log("Weights adjust : "+WEIGHTS);

}

function Train(){
//Epoch iteration eg- 10000 is good
for(var k=1;k<=TRAIN;k++){
//Train Four sets of truth table
for(var i=0;i<X1.length;i++){
neuron(X1[i],X2[i],OUT[i]);
}
}
}

function Predict(x1,x2){
var predict = 0;
predict = x1*WEIGHTS[0] + x2*WEIGHTS[1] + BIAS*WEIGHTS[2];

if(predict>1){
    predict = 1;
}else{
    predict = 0;
}
//Predict for given input
console.log("The prediction for "+(x1+","+x2)+" is "+predict);

}

//First train the perceptron 
Train();
//Predict for given input
Predict(1,1);
Predict(0,0);
Predict(1,0);
Predict(0,1);

The output for XOR gate is

The prediction for 1,1 is 1
The prediction for 0,0 is 1
The prediction for 1,0 is 1
The prediction for 0,1 is 1

Answer 1

Some sources state that is not possible to solve the XOR gate with a single perceptron.

Other sources let you know that you need higher order perceptrons to solve the XOR with a single Perceptron.

I quote from the second link:

Everyone who has ever studied about neural networks has probably already read that a single perceptron can't represent the boolean XOR function. The book Artificial Intelligence: A Modern Approach, the leading textbook in AI, says: “[XOR] is not linearly separable so the perceptron cannot learn it” (p.730).

I hope this points you in the right direction. This kind of question is not new here.