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A single neuron neural network (perceptron) written entirely in Swift with only Foundation
import Foundation
//Swift version of
//In Swift you can't easily add, multiply arrays/matrices etc, so I had write it manually and some of them are kinda ugly
//Used for my 2020 Marin Academy Math Night Presentation: "Neural Networks and Their Applications in Text Generation"
//Pattern to the data: output = column 2 of input
var inputs = [[0,0,1], [1,1,1], [1,0,1], [0,1,1]] as [[Double]]
var outputs = [[0], [1], [0], [1]] as [[Double]]
//3x1 matrix of weights randomly initialized to be between -1 and 1
var weights = ((0..<3).map( {_ in Double.random(in: -1...1)})).map({[$0]})
func trainNeuron(trainingInputs: [[Double]], trainingOutputs: [[Double]], i:Int) {
for _ in 0..<i {
//get output - sigmoid(inputs • weights)
let outputs = getOutput(inputs: trainingInputs, weights: weights)
//calculate error (correct output - actual outputs)
let errors: [[Double]] = (0..<trainingOutputs.count).map { i in
let error = trainingOutputs[i][0] - outputs[i][0]
return [error]
//multiply errors and siggrad of outputs
let grad = sigGrad(input: outputs)
let multiplied: [[Double]] = (0..<grad.count).map { i in
let x = (grad[i][0])*(errors[i][0])
return [x]
//calculate how much to adjust each weight by
let adjustments = dot(m1: transpose(input: trainingInputs), m2: multiplied)
//adjust each weight by that
let newWeights: [[Double]] = (0..<weights.count).map { i in
let x = weights[i][0] + adjustments[i][0]
return [x]
weights = newWeights
//sigmoid(inputs • weights)
func getOutput(inputs: [[Double]], weights: [[Double]]) -> [[Double]] {
return sigmoidArray(input: dot(m1: inputs, m2: weights))
//swift doesnt really have a dot product function so lets write our own. m1 = AxN, m2 = Nx1
func dot(m1: [[Double]], m2: [[Double]]) -> [[Double]] {
var dotted = [[Double]]()
for i in 0..<m1.count { //for each frow of m1 multiply each value by the weights
var sum = 0.0
for i2 in 0..<m1[0].count {
sum += m1[i][i2] * m2[i2][0]
return dotted
//sigmoid 1/(1+e^x)
func sigmoid(input: Double) -> Double {
return 1 / (1 + pow(Darwin.M_E, -1*input))
//derivative of sigmoid (x*(1-x)
func sigGrad(input: [[Double]]) -> [[Double]] {
return{[($0[0]) * (1-($0[0]))]})
//applys sigmoid to every element in Nx1 array
func sigmoidArray(input: [[Double]]) -> [[Double]] {
return{[sigmoid(input: $0[0])]})
//transpose array -
func transpose<T>(input: [[T]]) -> [[T]] {
if input.isEmpty{
return [[T]]()
let count = input[0].count
var out = [[T]](repeating: [T](), count: count)
for outer in input {
for (index, inner) in outer.enumerated() {
return out
//starting weights
print("Starting weights: \(weights)")
trainNeuron(trainingInputs: inputs, trainingOutputs: outputs, i: 10000)
//trained weights
print("Trained weights: \(weights)")
let validatingOutput = getOutput(inputs: [[1,1,0]], weights: weights)
print(validatingOutput) //should be 1 (column 2 is 1 and that was the pattern
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