JavaScript - artificial neuron model

In this short article, we would like to show an example of Artificial Neuron implementation in JavaScript.

Hint: the article describes McCulloch–Pitts (MCP) neuron that is commonly used in AI.

Quick solution:

// ONLINE-RUNNER:browser;

const activationFunction = (sum) => sum;

const inputs  = [ 1,   2,   3 ];  // x(1) x(2) x(3)
const bias    =   1;              // w(0)
const weights = [ 0,  0.5,  1 ];  // w(1) w(2) w(3)

const sum = weights.reduce((sum, weight, index) => sum + inputs[index] * weight, bias); // Σ
const output = activationFunction(sum);                                                 // y = f(Σ)

console.log(output);              // y = 5

Where:

Using equation notation

So, the above neuron uses formula.

Using matrix notation

The above model can be calculated using matrixes.

Where:

• w is a column vector (array) of neuron weight values (from w(0) to w(n)),
• x is a column vector (array) of neuron input values (from 1 to x(n)),
• f is neuron activation function,
• y is neuron output value.

Note: go to the following articles to know more about vectors and matrixes:

• https://en.wikipedia.org/wiki/Row_and_column_vectors
• https://en.wikipedia.org/wiki/Matrix_(mathematics)

Simple JavaScript implementation

In this section, you can see simple step-by-step calculations made by artificial neurons.

// ONLINE-RUNNER:browser;

// Calculates sum using:
//    Σ = 1*w(0) + x(1)*w(1) + ... + x(n-1)*w(n-1) + x(n)*w(n)
//
const caclulateSum = (bias, weights, inputs) => {
    let sum = bias;
    for (let i = 0; i < weights.length; ++i) {
        sum += inputs[i] * weights[i];
    }
  	return sum;
};

// Used activation function
//
//   We use simple linear activation function (called Identity Function)
//   https://en.wikipedia.org/wiki/Activation_function
//
const activationFunction = (sum) => sum;


// Neuron calculation:

const inputs  = [ 1,   2,   3 ];  // x(1) x(2) x(3)

const bias    =   1;              // w(0)
const weights = [ 0,  0.5,  1 ];  // w(1) w(2) w(3)

const sum = caclulateSum(bias, weights, inputs);
const output = activationFunction(sum);

console.log(output);  // 5

Reusable code example

In this section, you will find simple Neuron class implementation that can be combined into layers.

// ONLINE-RUNNER:browser;

function Neuron(bias, weights, activationFunction) {
  	this.bias = bias;
  	this.weights = weights;
	this.calculate = function(inputs) {
    	var sum = this.bias;
        for (var i = 0; i < this.weights.length; ++i) {
            sum += inputs[i] * this.weights[i];
        }
      	return activationFunction(sum);
    };
}


// Usage example:

var identityFunction = function(sum) {
  	return sum;
};

var neuron = new Neuron(1,  [0, 0.5, 1], identityFunction);
var output = neuron.calculate([1, 2, 3]);

console.log(output);  // 5

References

1. Artificial neuron - Wikipedia
2. Activation function - Wikipedia