Perceptron

A perceptron is an algorithm used in machine-learning. It's the simplest of all neural networks, consisting of only one neuron, and is typically used for pattern recognition.

A perceptron attempts to separate input into a positive and a negative class with the aid of a linear function. The inputs are each multiplied by weights, random weights at first, and then summed. Based on the sign of the sum a decision is made.

In order for the perceptron to make the right decision, it needs to train with input for which the correct outcome is known, so that the weights can slowly be adjusted until they start producing the desired results.

Task

The website The Nature of Code demonstrates a perceptron by making it perform a very simple task : determine if a randomly chosen point (x, y) is above or below a line:

 y = mx + b

Implement this perceptron and display an image (or some other visualization) of the result.

See also

Forth

Works with: GNU Forth

Where it says [email protected] it should say f@. <lang Forth>require random.fs here seed !

warnings off

( THE PERCEPTRON )

randomWeight 2000 random 1000 - s>f 1000e f/ ;

createPerceptron create dup , 0 ?DO randomWeight f, LOOP ;

variable arity variable ^weights variable ^inputs

perceptron! dup @ arity ! cell+ ^weights ! ;

inputs! ^inputs ! ;

0.0001e fconstant learningConstant

activate 0e f> IF 1e ELSE -1e THEN ;

feedForward

   ^weights @  ^inputs @  0e
   arity @  0  ?DO
       dup f@  float + swap
       dup f@  float + swap
       f* f+
   LOOP 2drop activate ;

train

   feedForward f- learningConstant f*
   ^weights @  ^inputs @
   arity @  0  ?DO
       fdup  dup f@ f*  float + swap
       dup f@ f+  dup f!  float + swap
   LOOP 2drop fdrop ;

( THE TRAINER )

create point 0e f, 0e f, 1e f, \ x y bias

x point ;

y point float + ;

randomX 640 random s>f ;

randomY 360 random s>f ;

\ y = Ax + B 2e fconstant A 1e fconstant B

randomizePoint

   randomY fdup y f!
   randomX fdup x f!
   A f* B f+ f<  IF -1e ELSE 1e THEN ;

3 createPerceptron myPerceptron variable trainings 10000 constant #rounds

setup 0 ; \ success counter

calculate s>f #rounds s>f f/ 100e f* ;

report ." After " trainings @ . ." trainings: "

               calculate f. ." % accurate" cr ;

check learningConstant f~ IF 1+ THEN ;

evaluate randomizePoint feedForward check ;

evaluate setup #rounds 0 ?DO evaluate LOOP report ;

tally 1 trainings +! ;

timesTrain 0 ?DO randomizePoint train tally LOOP ;

initialize

   myPerceptron perceptron!
   point inputs!
   0 trainings ! ;

go

       initialize evaluate
     1 timesTrain evaluate
     1 timesTrain evaluate
     1 timesTrain evaluate
     1 timesTrain evaluate
     1 timesTrain evaluate
     5 timesTrain evaluate
    10 timesTrain evaluate
    30 timesTrain evaluate
    50 timesTrain evaluate
   100 timesTrain evaluate
   300 timesTrain evaluate
   500 timesTrain evaluate ;

go bye</lang> Example output:

After 0 trainings: 10.16 % accurate
After 1 trainings: 7.43 % accurate
After 2 trainings: 7.71 % accurate
After 3 trainings: 4.93 % accurate
After 4 trainings: 3.11 % accurate
After 5 trainings: 0.6 % accurate
After 10 trainings: 48.72 % accurate
After 20 trainings: 85.55 % accurate
After 50 trainings: 86.36 % accurate
After 100 trainings: 98.59 % accurate
After 200 trainings: 98.84 % accurate
After 500 trainings: 95.86 % accurate
After 1000 trainings: 99.8 % accurate

Go

Library: Go Graphics

This is based on the Java entry but just outputs the final image (as a .png file) rather than displaying its gradual build up. It also uses a different color scheme - blue and red circles with a black dividing line. <lang go>package main

import (

   "github.com/fogleman/gg"
   "math/rand"
   "time"

)

const c = 0.00001

func linear(x float64) float64 {

   return x*0.7 + 40

}

type trainer struct {

   inputs []float64
   answer int

}

func newTrainer(x, y float64, a int) *trainer {

   return &trainer{[]float64{x, y, 1}, a}

}

type perceptron struct {

   weights  []float64
   training []*trainer

}

func newPerceptron(n, w, h int) *perceptron {

   weights := make([]float64, n)
   for i := 0; i < n; i++ {
       weights[i] = rand.Float64()*2 - 1
   }

   training := make([]*trainer, 2000)
   for i := 0; i < 2000; i++ {
       x := rand.Float64() * float64(w)
       y := rand.Float64() * float64(h)
       answer := 1
       if y < linear(x) {
           answer = -1
       }
       training[i] = newTrainer(x, y, answer)
   }
   return &perceptron{weights, training}

}

func (p *perceptron) feedForward(inputs []float64) int {

   if len(inputs) != len(p.weights) {
       panic("weights and input length mismatch, program terminated")
   }
   sum := 0.0
   for i, w := range p.weights {
       sum += inputs[i] * w
   }
   if sum > 0 {
       return 1
   }
   return -1

}

func (p *perceptron) train(inputs []float64, desired int) {

   guess := p.feedForward(inputs)
   err := float64(desired - guess)
   for i := range p.weights {
       p.weights[i] += c * err * inputs[i]
   }

}

func (p *perceptron) draw(dc *gg.Context, iterations int) {

   le := len(p.training)
   for i, count := 0, 0; i < iterations; i, count = i+1, (count+1)%le {
       p.train(p.training[count].inputs, p.training[count].answer)
   }
   x := float64(dc.Width())
   y := linear(x)
   dc.SetLineWidth(2)
   dc.SetRGB255(0, 0, 0) // black line
   dc.DrawLine(0, linear(0), x, y)
   dc.Stroke()
   dc.SetLineWidth(1)
   for i := 0; i < le; i++ {
       guess := p.feedForward(p.training[i].inputs)
       x := p.training[i].inputs[0] - 4
       y := p.training[i].inputs[1] - 4
       if guess > 0 {
           dc.SetRGB(0, 0, 1) // blue circle
       } else {
           dc.SetRGB(1, 0, 0) // red circle
       }
       dc.DrawCircle(x, y, 8)
       dc.Stroke()
   }

}

func main() {

   rand.Seed(time.Now().UnixNano())
   w, h := 640, 360
   perc := newPerceptron(3, w, h)
   dc := gg.NewContext(w, h)
   dc.SetRGB(1, 1, 1) // white background
   dc.Clear()
   perc.draw(dc, 2000)
   dc.SavePNG("perceptron.png")

}</lang>

Java

Works with: Java version 8

<lang java>import java.awt.*; import java.awt.event.ActionEvent; import java.util.*; import javax.swing.*; import javax.swing.Timer;

public class Perceptron extends JPanel {

   class Trainer {
       double[] inputs;
       int answer;

       Trainer(double x, double y, int a) {
           inputs = new double[]{x, y, 1};
           answer = a;
       }
   }

   Trainer[] training = new Trainer[2000];
   double[] weights;
   double c = 0.00001;
   int count;

   public Perceptron(int n) {
       Random r = new Random();
       Dimension dim = new Dimension(640, 360);
       setPreferredSize(dim);
       setBackground(Color.white);

       weights = new double[n];
       for (int i = 0; i < weights.length; i++) {
           weights[i] = r.nextDouble() * 2 - 1;
       }

       for (int i = 0; i < training.length; i++) {
           double x = r.nextDouble() * dim.width;
           double y = r.nextDouble() * dim.height;

           int answer = y < f(x) ? -1 : 1;

           training[i] = new Trainer(x, y, answer);
       }

       new Timer(10, (ActionEvent e) -> {
           repaint();
       }).start();
   }

   private double f(double x) {
       return x * 0.7 + 40;
   }

   int feedForward(double[] inputs) {
       assert inputs.length == weights.length : "weights and input length mismatch";

       double sum = 0;
       for (int i = 0; i < weights.length; i++) {
           sum += inputs[i] * weights[i];
       }
       return activate(sum);
   }

   int activate(double s) {
       return s > 0 ? 1 : -1;
   }

   void train(double[] inputs, int desired) {
       int guess = feedForward(inputs);
       double error = desired - guess;
       for (int i = 0; i < weights.length; i++) {
           weights[i] += c * error * inputs[i];
       }
   }

   @Override
   public void paintComponent(Graphics gg) {
       super.paintComponent(gg);
       Graphics2D g = (Graphics2D) gg;
       g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
               RenderingHints.VALUE_ANTIALIAS_ON);

       // we're drawing upside down
       int x = getWidth();
       int y = (int) f(x);
       g.setStroke(new BasicStroke(2));
       g.setColor(Color.orange);
       g.drawLine(0, (int) f(0), x, y);

       train(training[count].inputs, training[count].answer);
       count = (count + 1) % training.length;

       g.setStroke(new BasicStroke(1));
       g.setColor(Color.black);
       for (int i = 0; i < count; i++) {
           int guess = feedForward(training[i].inputs);

           x = (int) training[i].inputs[0] - 4;
           y = (int) training[i].inputs[1] - 4;

           if (guess > 0)
               g.drawOval(x, y, 8, 8);
           else
               g.fillOval(x, y, 8, 8);
       }
   }

   public static void main(String[] args) {
       SwingUtilities.invokeLater(() -> {
           JFrame f = new JFrame();
           f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
           f.setTitle("Perceptron");
           f.setResizable(false);
           f.add(new Perceptron(3), BorderLayout.CENTER);
           f.pack();
           f.setLocationRelativeTo(null);
           f.setVisible(true);
       });
   }

}</lang>

JavaScript

Uses P5 lib. <lang javascript> const EPOCH = 1500, TRAINING = 1, TRANSITION = 2, SHOW = 3;

var perceptron; var counter = 0; var learnRate = 0.02; var state = TRAINING;

function setup() {

   createCanvas( 800, 600 );
   clearBack();
   perceptron = new Perceptron( 2 );

}

function draw() {

   switch( state ) {
       case TRAINING: training(); break;
       case TRANSITION: transition(); break;
       case SHOW: show(); break;
   }

}

function clearBack() {

   background( 0 );
   stroke( 255 );
   strokeWeight( 4 );

   var x = width;
   line( 0, 0, x, lineDef( x ) );

}

function transition() {

   clearBack();
   state = SHOW;

}

function lineDef( x ) {

   return .75 * x;

}

function training() {

   var a = random( width ),
       b = random( height );

   lDef = lineDef( a ) > b ? -1 : 1;

   perceptron.setInput( [a, b] );
   perceptron.feedForward();
   var pRes = perceptron.getOutput();
   var match = (pRes == lDef);
   var clr;

   if( !match ) {
       var err = ( pRes - lDef ) * learnRate;
       perceptron.adjustWeights( err );

       clr = color( 255, 0, 0 );

   } else {
       clr = color( 0, 255, 0 );
   }

   noStroke();
   fill( clr );
   ellipse( a, b, 4, 4 );

   if( ++counter == EPOCH ) state = TRANSITION;

}

function show() {

   var a = random( width ),
       b = random( height ),
       clr;

   perceptron.setInput( [a, b] );
   perceptron.feedForward();
   var pRes = perceptron.getOutput();

   if( pRes < 0 )
       clr = color( 255, 0, 0 );
   else 
       clr = color( 0, 255, 0 );

   noStroke();
   fill( clr );
   ellipse( a, b, 4, 4 );

}

function Perceptron( inNumber ) {

   this.inputs = [];
   this.weights = [];
   this.output;
   this.bias = 1;
   
   // one more weight for bias
   for( var i = 0; i < inNumber + 1; i++ ) {
       this.weights.push( Math.random() );
   };

   this.activation = function( a ) {
       return( Math.tanh( a ) < .5 ? 1 : -1 );
   }

   this.feedForward = function() {
       var sum = 0;
       for( var i = 0; i < this.inputs.length; i++ ) {
           sum += this.inputs[i] * this.weights[i];
       }

       sum += this.bias * this.weights[this.weights.length - 1];

       this.output = this.activation( sum );
   }

   this.getOutput = function() {
       return this.output;
   }

   this.setInput= function( inputs ) {
       this.inputs = [];
       for( var i = 0; i < inputs.length; i++ ) {
           this.inputs.push( inputs[i] );
       }
   }

   this.adjustWeights = function( err ) {
       for( var i = 0; i < this.weights.length - 1; i++ ) {
           this.weights[i] += err * this.inputs[i];
       }
   }

} </lang> File:PerceptronJS.png

Well, it seems I cannot upload an image :(

Julia

<lang julia># file module.jl

module SimplePerceptrons

default activation function

step(x) = x > 0 ? 1 : -1

mutable struct Perceptron{T, F}

   weights::Vector{T}
   lr::T
   activate::F

end

Perceptron{T}(n::Integer, lr = 0.01, f::Function = step) where T =

   Perceptron{T, typeof(f)}(2 .* rand(n + 1) .- 1, lr, f)

Perceptron(args...) = Perceptron{Float64}(args...)

@views predict(p::Perceptron, x::AbstractVector) = p.activate(p.weights[1] + x' * p.weights[2:end]) @views predict(p::Perceptron, X::AbstractMatrix) = p.activate.(p.weights[1] .+ X * p.weights[2:end])

function train!(p::Perceptron, X::AbstractMatrix, y::AbstractVector; epochs::Integer = 100)

   for _ in Base.OneTo(epochs)
       yhat = predict(p, X)
       err = y .- yhat
       ΔX = p.lr .* err .* X
       for ind in axes(ΔX, 1)
           p.weights[1] += err[ind]
           p.weights[2:end] .+= ΔX[ind, :]
       end
   end
   return p

end

accuracy(p, X::AbstractMatrix, y::AbstractVector) = count(y .== predict(p, X)) / length(y)

end # module SimplePerceptrons </lang>

<lang julia># file _.jl

const SP = include("module.jl")

p = SP.Perceptron(2, 0.1)

a, b = 0.5, 1 X = rand(1000, 2) y = map(x -> x[2] > a + b * x[1] ? 1 : -1, eachrow(X))

Accuracy

@show SP.accuracy(p, X, y)

Train

SP.train!(p, X, y, epochs = 1000)

ahat, bhat = p.weights[1] / p.weights[2], -p.weights[3] / p.weights[2]

using Plots

scatter(X[:, 1], X[:, 2], markercolor = map(x -> x == 1 ? :red : :blue, y)) Plots.abline!(b, a, label = "real line", linecolor = :red, linewidth = 2)

SP.train!(p, X, y, epochs = 1000) ahat, bhat = p.weights[1] / p.weights[2], -p.weights[3] / p.weights[2] Plots.abline!(bhat, ahat, label = "predicted line") </lang>

Kotlin

Translation of: Java

<lang scala>// version 1.1.4-3

import java.awt.* import java.awt.event.ActionEvent import java.util.Random import javax.swing.JPanel import javax.swing.JFrame import javax.swing.Timer import javax.swing.SwingUtilities

class Perceptron(n: Int) : JPanel() {

   class Trainer(x: Double, y: Double, val answer: Int) {
       val inputs = doubleArrayOf(x, y, 1.0)
   }

   val weights: DoubleArray
   val training: Array<Trainer>
   val c = 0.00001
   var count = 0

   init {
       val r = Random()
       val dim = Dimension(640, 360)
       preferredSize = dim
       background = Color.white
       weights = DoubleArray(n) { r.nextDouble() * 2.0 - 1.0 }
       training = Array(2000) {
           val x = r.nextDouble() * dim.width
           val y = r.nextDouble() * dim.height
           val answer = if (y < f(x)) -1 else 1
           Trainer(x, y, answer)
       }
       Timer(10) { repaint() }.start()
   }

   private fun f(x: Double) = x * 0.7 + 40.0

   fun feedForward(inputs: DoubleArray): Int {
       if (inputs.size != weights.size)
           throw IllegalArgumentException("Weights and input length mismatch")
       val sum = weights.zip(inputs) { w, i -> w * i }.sum()
       return activate(sum)
   }

   fun activate(s: Double) = if (s > 0.0) 1 else -1

   fun train(inputs: DoubleArray, desired: Int) {
       val guess = feedForward(inputs)
       val error = desired - guess
       for (i in 0 until weights.size) weights[i] += c * error * inputs[i]
   }

   public override fun paintComponent(gg: Graphics) {
       super.paintComponent(gg)
       val g = gg as Graphics2D
       g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
                          RenderingHints.VALUE_ANTIALIAS_ON)

       // we're drawing upside down
       var x = width
       var y = f(x.toDouble()).toInt()
       g.stroke = BasicStroke(2.0f)
       g.color = Color.orange
       g.drawLine(0, f(0.0).toInt(), x, y)

       train(training[count].inputs, training[count].answer)
       count = (count + 1) % training.size

       g.stroke = BasicStroke(1.0f)
       g.color = Color.black
       for (i in 0 until count) {
           val guess = feedForward(training[i].inputs)
           x = training[i].inputs[0].toInt() - 4
           y = training[i].inputs[1].toInt() - 4 
           if (guess > 0) g.drawOval(x, y, 8, 8)
           else g.fillOval(x, y, 8, 8)
       }
   }

}

fun main(args: Array<String>) {

   SwingUtilities.invokeLater {
       val f = JFrame()
       with(f) {
           defaultCloseOperation = JFrame.EXIT_ON_CLOSE
           title = "Perceptron"
           isResizable = false
           add(Perceptron(3), BorderLayout.CENTER)
           pack()
           setLocationRelativeTo(null)
           isVisible = true
       }
   }

}</lang>

Lua

Simple implementation allowing for any number of inputs (in this case, just 1), testing of the Perceptron, and training. <lang lua>local Perceptron = {} Perceptron.__index = Perceptron

function Perceptron.new(numInputs)

   local cell = {}
   setmetatable(cell, Perceptron)

   cell.weights = {}
   cell.bias = math.random()
   cell.output = 0

   for i = 1, numInputs do
       cell.weights[i] = math.random()
   end

   return cell

end

--used in both training and testing, calculates the output from inputs and weights function Perceptron:update(inputs)

   local sum = self.bias
   for i = 1, #inputs do
       sum = sum + self.weights[i] * inputs[i]
   end
   self.output = sum

end

--returns the output from a given table of inputs function Perceptron:test(inputs)

   self:update(inputs)
   return self.output

end

--used in training to adjust the weights and bias function Perceptron:optimize(stepSize)

   local gradient = self.delta * self.output
   for i = 1, #self.weights do
       self.weights[i] = self.weights[i] + (stepSize*gradient)
   end
   self.bias = self.bias + (stepSize*self.delta)

end

--takes a table of training data, the number of iterations (or epochs) to train over, and the step size for training function Perceptron:train(data, iterations, stepSize)

   for i = 1, iterations do
       for j = 1, #data do
           local datum = data[j]
           self:update(datum[1])
           self.delta = datum[2] - self.output
           self:optimize(stepSize)
       end
   end

end

local node = Perceptron.new(1) --creates a new Perceptron that takes in 1 input local trainingData = {} --this Perceptron will be trained on the function y=2x+1 print("Untrained results:") for i = -2, 2, 1 do

   print(i..":", node:test({i}))
   trainingData[i+3] = {{i},2*i+1} --the training data is a table, where each element is another table that has a table of inputs and one output

end node:train(trainingData, 100, .1) --trains on the set for 100 epochs with a step size of 0.1 print("\nTrained results:") for i = -2, 2, 1 do

   print(i..":", node:test({i}))

end </lang>

Output:

Untrained results:
-2: -0.55767321178784
-1: 0.1898736124016
0: 0.93742043659104
1: 1.6849672607805
2: 2.4325140849699

Trained results:
-2: -3
-1: -1
0: 1
1: 3
2: 5

Pascal

This is a text-based implementation, using a 20x20 grid (just like the original Mark 1 Perceptron had). The rate of improvement drops quite markedly as you increase the number of training runs. <lang pascal>program Perceptron;

(*

* implements a version of the algorithm set out at
* http://natureofcode.com/book/chapter-10-neural-networks/ ,
* but without graphics
*)

function targetOutput( a, b : integer ) : integer; (* the function the perceptron will be learning is f(x) = 2x + 1 *) begin

   if a * 2 + 1 < b then
       targetOutput := 1
   else
       targetOutput := -1

end;

procedure showTargetOutput; var x, y : integer; begin

   for y := 10 downto -9 do
   begin
       for x := -9 to 10 do
           if targetOutput( x, y ) = 1 then
               write( '#' )
           else
               write( 'O' );
       writeln
   end;
   writeln

end;

procedure randomWeights( var ws : array of real ); (* start with random weights -- NB pass by reference *) var i : integer; begin

   randomize; (* seed random-number generator *)
   for i := 0 to 2 do
       ws[i] := random * 2 - 1

end;

function feedForward( ins : array of integer; ws : array of real ) : integer; (* the perceptron outputs 1 if the sum of its inputs multiplied by its input weights is positive, otherwise -1 *) var sum : real;

   i : integer;

begin

   sum := 0;
   for i := 0 to 2 do
       sum := sum + ins[i] * ws[i];
   if sum > 0 then
       feedForward := 1
   else
       feedForward := -1

end;

procedure showOutput( ws : array of real ); var inputs : array[0..2] of integer;

   x, y : integer;

begin

   inputs[2] := 1; (* bias *)
   for y := 10 downto -9 do
   begin
       for x := -9 to 10 do
       begin
           inputs[0] := x;
           inputs[1] := y;
           if feedForward( inputs, ws ) = 1 then
               write( '#' )
           else
               write( 'O' )
       end;
       writeln
   end;
   writeln

end;

procedure train( var ws : array of real; runs : integer ); (* pass the array of weights by reference so it can be modified *) var inputs : array[0..2] of integer;

   error : real;
   x, y, i, j : integer;

begin

   inputs[2] := 1; (* bias *)
   for i := 1 to runs do
   begin
       for y := 10 downto -9 do
       begin
           for x := -9 to 10 do
           begin
               inputs[0] := x;
               inputs[1] := y;
               error := targetOutput( x, y ) - feedForward( inputs, ws );
               for j := 0 to 2 do
                   ws[j] := ws[j] + error * inputs[j] * 0.01;
                   (* 0.01 is the learning constant *)
           end;
       end;
   end;

end;

var weights : array[0..2] of real;

begin

   writeln( 'Target output for the function f(x) = 2x + 1:' );
   showTargetOutput;
   randomWeights( weights );
   writeln( 'Output from untrained perceptron:' );
   showOutput( weights );
   train( weights, 1 );
   writeln( 'Output from perceptron after 1 training run:' );
   showOutput( weights );
   train( weights, 4 );
   writeln( 'Output from perceptron after 5 training runs:' );
   showOutput( weights )

end.</lang>

Output:

Target output for the function f(x) = 2x + 1:
##############OOOOOO
#############OOOOOOO
#############OOOOOOO
############OOOOOOOO
############OOOOOOOO
###########OOOOOOOOO
###########OOOOOOOOO
##########OOOOOOOOOO
##########OOOOOOOOOO
#########OOOOOOOOOOO
#########OOOOOOOOOOO
########OOOOOOOOOOOO
########OOOOOOOOOOOO
#######OOOOOOOOOOOOO
#######OOOOOOOOOOOOO
######OOOOOOOOOOOOOO
######OOOOOOOOOOOOOO
#####OOOOOOOOOOOOOOO
#####OOOOOOOOOOOOOOO
####OOOOOOOOOOOOOOOO

Output from untrained perceptron:
OOO#################
OOOO################
OOOOO###############
OOOOO###############
OOOOOO##############
OOOOOO##############
OOOOOOO#############
OOOOOOOO############
OOOOOOOO############
OOOOOOOOO###########
OOOOOOOOO###########
OOOOOOOOOO##########
OOOOOOOOOOO#########
OOOOOOOOOOO#########
OOOOOOOOOOOO########
OOOOOOOOOOOOO#######
OOOOOOOOOOOOO#######
OOOOOOOOOOOOOO######
OOOOOOOOOOOOOO######
OOOOOOOOOOOOOOO#####

Output from perceptron after 1 training run:
###############OOOOO
###############OOOOO
##############OOOOOO
#############OOOOOOO
#############OOOOOOO
############OOOOOOOO
############OOOOOOOO
###########OOOOOOOOO
##########OOOOOOOOOO
##########OOOOOOOOOO
#########OOOOOOOOOOO
#########OOOOOOOOOOO
########OOOOOOOOOOOO
#######OOOOOOOOOOOOO
#######OOOOOOOOOOOOO
######OOOOOOOOOOOOOO
######OOOOOOOOOOOOOO
#####OOOOOOOOOOOOOOO
####OOOOOOOOOOOOOOOO
####OOOOOOOOOOOOOOOO

Output from perceptron after 5 training runs:
##############OOOOOO
#############OOOOOOO
#############OOOOOOO
############OOOOOOOO
############OOOOOOOO
###########OOOOOOOOO
###########OOOOOOOOO
##########OOOOOOOOOO
##########OOOOOOOOOO
#########OOOOOOOOOOO
#########OOOOOOOOOOO
########OOOOOOOOOOOO
########OOOOOOOOOOOO
#######OOOOOOOOOOOOO
#######OOOOOOOOOOOOO
######OOOOOOOOOOOOOO
######OOOOOOOOOOOOOO
#####OOOOOOOOOOOOOOO
#####OOOOOOOOOOOOOOO
####OOOOOOOOOOOOOOOO

Phix

Library: pGUI

Interactive GUI version. Select one of five lines, set the number of points, learning constant, learning rate, and max iterations. Plots accuracy vs. iterations and displays the training data in blue/black=above/incorrect and green/red=below/incorrect [all blue/green = 100% accurate]. <lang Phix>-- demo\rosetta\Perceptron.exw -- -- The learning curve turned out more haphazard than I imagined, and adding a -- non-linear line to f() (case 5) was perhaps not such a great idea given how -- much it sometimes struggles with some of the other straight lines anyway. -- include pGUI.e --#withtype Ihandle --#withtype Ihandles --#withtype cdCanvas

constant help_txt = """ A perceptron is the simplest possible neural network, consisting of just one neuron that we train to recognise whether a point is above or below a given straight line. NB: It would probably be unwise to overly assume that this could easily be adapted to anything more complex, or actually useful. It is just a basic introduction, but you have to start somewhere. What is interesting is that ultimately the neuron is just three numbers, plus a bucket-load of training gumpf.

The left hand panel allows settings to be changed, in the middle we plot the rate of learning, and on the right we show the training data colour coded as above/below and correct/incorrect (blue/black=above/incorrect, green/red=below/incorrect). What you want to see is all blue/green, with no black/red.

You can change the line algorithm (four straight and one curved that it is not meant to be able to cope with), the number of points (size of training data), the learning constant, learning rate (iterations/second) and the maximum number of iterations. Note that training automatically stops once 100% accuracy is reached (since the error is then always zero, no further changes would ever occur). Also note that a restart is triggered when any setting is changed, not just when the restart button is pressed.

The learning curve was expected to start at 50% (random chance of being right) and gradually improve towards 100%, except when the non-linear line was selected. It turned out far more haphazard than I thought it would. Originally it allowed up to 10,000,000 iterations, but it rarely improved much beyond 1,000,000."""

function help_cb(Ihandln /*help*/)

   IupMessage("Perceptron",help_txt)
   return IUP_DEFAULT

end function

Ihandle dlg, plot, canvas, timer,

       iteration, accuracy, w1, w2, w3

cdCanvas cddbuffer, cdcanvas

integer line_alg = 1 integer points = 2000,

       learning_rate = 10000,
       max_iterations = 1_000_000,
       total_iterations = 0

atom learning_constant = 0.00001

enum WEIGHTS, -- The actual neuron (just 3 numbers)

    TRAINING   -- training data/results, variable length

enum INPUTS, ANSWER -- contents of [TRAINING]

    -- note that length(inputs[i]) must = length(weights)

sequence perceptron = {},

        last_wh -- (recreate "" on resize)

function activate(atom t)

   return iff(t>0?+1:-1)

end function

function f(atom x)

   switch line_alg
       case 1: return x*0.7+40
       case 2: return 300-0.3*x
       case 3: return x*0.75
       case 4: return 2*x+1
       case 5: return x/2+sin(x/100)*100+100 -- (fail)
   end switch

end function

procedure new_perceptron(integer n)

   sequence weights := repeat(0, n)
   for i=1 to n do
       weights[i] = rnd()*2 - 1
   end for
   sequence training := repeat(0,points)
   integer {w,h} = last_wh
   for i=1 to points do
       integer x := rand(w),
               y := rand(h),
               answer := activate(y-f(x))
       sequence inputs = {x, y, 1}
       -- aside: inputs is {x,y,1}, rather than {x,y} because an
       --        input of {0,0} could only ever yield 0, whereas
       --        {0,0,1} can yield a non-zero guess: weights[3].
       training[i] = {inputs, answer}  -- {INPUTS, ANSWER}
   end for
   perceptron = {weights, training}  -- {WEIGHTS, TRAINING}

end procedure

function feed_forward(sequence inputs)

   if length(inputs)!=length(perceptron[WEIGHTS]) then
       throw("weights and input length mismatch, program terminated")
   end if
   atom total := 0.0
   for i=1 to length(inputs) do
       total += inputs[i] * perceptron[WEIGHTS][i]
   end for
   return activate(total)

end function

procedure train(sequence inputs, integer desired)

   integer guess := feed_forward(inputs),
           error := desired - guess
   for i=1 to length(perceptron[WEIGHTS]) do
       perceptron[WEIGHTS][i] += learning_constant * error * inputs[i]
   end for

end procedure

--DEV add to pGUI/doc procedure cdCanvasCircle(cdCanvas cddbuffer, atom x, y, r)

   cdCanvasArc(cddbuffer,x,y,r,r,0,360)

end procedure

function draw(bool bDraw=true) -- (if bDraw is false, we just want the "correct" count)

   integer correct = 0
   atom x, y
   for i=1 to points do
       {sequence inputs, integer answer} = perceptron[TRAINING][i]
       integer guess := feed_forward(inputs)
       correct += (guess=answer)
       if bDraw then
           {x,y} = inputs
           -- blue/black=above/incorrect, green/red=below/incorrect
           integer clr = iff(guess=answer?iff(guess>0?CD_BLUE:CD_GREEN)
                                         :iff(guess>0?CD_BLACK:CD_RED))
           cdCanvasSetForeground(cddbuffer, clr)
           cdCanvasCircle(cddbuffer, x, y, 8)
       end if
   end for
   if bDraw then
       cdCanvasSetForeground(cddbuffer, CD_BLACK)
       x := last_wh[1]
       y := f(x)
       if line_alg=5 then
           -- non-linear so (crudely) draw in little segments
           for i=0 to x by 20 do
               cdCanvasLine(cddbuffer,i,f(i),i+20,f(i+20))
           end for
       else
           cdCanvasLine(cddbuffer,0,f(0),x,y)
       end if
   end if
   return correct

end function

bool re_plot = true atom plot0 sequence plotx = repeat(0,19),

        ploty = repeat(0,19)

integer imod = 1, -- keep every 1, then 10, then 100, ...

       pidx = 1

function restart_cb(Ihandln /*restart*/)

   last_wh = IupGetIntInt(canvas, "DRAWSIZE")
   new_perceptron(3)
   imod = 1
   pidx = 1
   total_iterations = 0
   plot0 = (draw(false)/points)*100
   re_plot = true
   IupSetInt(timer,"RUN",1)
   return IUP_DEFAULT

end function

function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/)

   if perceptron={}
   or last_wh!=IupGetIntInt(canvas, "DRAWSIZE") then
       {} = restart_cb(NULL)
   end if
   cdCanvasActivate(cddbuffer)
   cdCanvasClear(cddbuffer)
   integer correct = draw()
   cdCanvasFlush(cddbuffer)

   if re_plot then
       re_plot = false
       IupSetAttribute(plot, "CLEAR", NULL)
       IupPlotBegin(plot)
       IupPlotAdd(plot, 0, plot0)
       for i=1 to pidx-1 do
           IupPlotAdd(plot, plotx[i], ploty[i])
       end for
       {} = IupPlotEnd(plot)
       IupSetAttribute(plot, "REDRAW", NULL)
   end if
   
   IupSetStrAttribute(iteration,"TITLE","iteration: %d",{total_iterations})
   IupSetStrAttribute(w1,"TITLE","%+f",{perceptron[WEIGHTS][1]})
   IupSetStrAttribute(w2,"TITLE","%+f",{perceptron[WEIGHTS][2]})
   IupSetStrAttribute(w3,"TITLE","%+f",{perceptron[WEIGHTS][3]})
   IupSetStrAttribute(accuracy,"TITLE","accuracy: %.4g%%",{(correct/points)*100})
   IupRefresh({iteration,w1,w2,w3,accuracy})   -- (force label resize)
   if correct=points then
       IupSetInt(timer,"RUN",0)                -- stop at 100%
   end if
   return IUP_DEFAULT

end function

function map_cb(Ihandle ih)

   cdcanvas = cdCreateCanvas(CD_IUP, ih)
   cddbuffer = cdCreateCanvas(CD_DBUFFER, cdcanvas)
   cdCanvasSetBackground(cddbuffer, CD_PARCHMENT)
   return IUP_DEFAULT

end function

function valuechanged_cb(Ihandle ih)

   string name = IupGetAttribute(ih, "NAME")
   integer v = IupGetInt(ih, "VALUE")
   switch name
       case "line":    line_alg = v
       case "points":  points = power(10,v)
       case "learn":   learning_constant = power(10,-v)
       case "rate":    learning_rate = power(10,v-1)
       case "max":     max_iterations = power(10,v)
   end switch
   {} = restart_cb(NULL)
   return IUP_DEFAULT

end function

function timer_cb(Ihandle /*timer*/)

   for i=1 to min(learning_rate,max_iterations) do
       total_iterations += 1
       integer c = mod(total_iterations,points)+1
       train(perceptron[TRAINING][c][INPUTS], perceptron[TRAINING][c][ANSWER])
       if mod(total_iterations,imod)=0 then
           -- save 1,2..10, then 20,30,..100, then 200,300,..1000, etc
           re_plot = true
           plotx[pidx] = total_iterations
           ploty[pidx] = (draw(false)/points)*100
           if pidx=10 or pidx=19 then
               if pidx=19 then
                   -- drop (eg) 1,2,..9, replace with 10,20,..90,
                   -- next time replace 10,20..90 with 100,200..900, etc
                   plotx[1..10] = plotx[10..19]
                   ploty[1..10] = ploty[10..19]
               end if
               imod *= 10
               pidx = 11
           else
               pidx += 1
           end if
       end if      
   end for
   if total_iterations>=max_iterations then
       IupSetInt(timer,"RUN",0)
   end if
   IupUpdate(canvas)
   return IUP_IGNORE

end function

function esc_close(Ihandle /*ih*/, atom c)

   if c=K_ESC then return IUP_CLOSE end if
   if c=K_F1 then return help_cb(NULL) end if
   if c=K_F5 then return restart_cb(NULL) end if
   return IUP_CONTINUE

end function

function settings(string lname, name, sequence opts, integer v=1)

   Ihandle lbl = IupLabel(lname,"PADDING=0x4"),
           list = IupList("NAME=%s, DROPDOWN=YES",{name}),
           hbox = IupHbox({lbl,IupFill(),list})
   for i=1 to length(opts) do
       IupSetAttributeId(list,"",i,opts[i])
   end for
   IupSetInt(list,"VISIBLEITEMS",length(opts)+1)
   IupSetInt(list,"VALUE",v)
   IupSetCallback(list, "VALUECHANGED_CB", Icallback("valuechanged_cb"));
   return hbox

end function

function sep()

   return IupLabel("","SEPARATOR=HORIZONTAL")

end function

procedure main()

   IupOpen()
   IupControlsOpen()

   Ihandle settings_lbl = IupHbox({IupFill(),IupLabel("Settings"),IupFill()}),
           line = settings("line","line",{"x*0.7 + 40","300 - 0.3*x","x*0.75","2*x + 1","x/2+sin(x/100)*100+100"}),
           points = settings("number of points","points",{"10","100","1000","10000"},3),
           learn = settings("learning constant","learn",{"0.1","0.01","0.001","0.0001","0.00001"},5),
           rate = settings("learning rate","rate",{"1/s","10/s","100/s","1000/s","10000/s"},5),
           maxiter = settings("max iterations","max",{"10","100","1000","10,000","100,000","1,000,000"},6),
           restart = IupButton("Restart (F5)", "ACTION", Icallback("restart_cb")),
           helpbtn = IupButton("Help (F1)", "ACTION", Icallback("help_cb")),
           buttons = IupHbox({restart,IupFill(),helpbtn})

   iteration = IupLabel("iteration: 1")
   w1 = IupLabel("1")
   w2 = IupLabel("2")
   w3 = IupLabel("3")
   Ihandle weights = IupHbox({IupLabel("weights: ","PADDING=0x4"),IupVbox({w1,w2,w3})})
   accuracy = IupLabel("accuracy: 12.34%")

   Ihandle vbox = IupVbox({settings_lbl, sep(),
                           line, sep(), points, sep(), learn, sep(), 
                           rate, sep(), maxiter, sep(), buttons, sep(),
                           IupHbox({iteration}), weights, IupHbox({accuracy})})
   IupSetAttribute(vbox, "GAP", "4");

   plot = IupPlot("MENUITEMPROPERTIES=Yes")
   IupSetAttribute(plot, "TITLE", "Learning Curve");
   IupSetAttribute(plot, "TITLEFONTSIZE", "10");
   IupSetAttribute(plot, "TITLEFONTSTYLE", "ITALIC");
   IupSetAttribute(plot, "GRIDLINESTYLE", "DOTTED");
   IupSetAttribute(plot, "GRID", "YES");
   IupSetAttribute(plot, "AXS_XLABEL", "iterations");
   IupSetAttribute(plot, "AXS_YLABEL", "% correct");
   IupSetAttribute(plot, "AXS_XFONTSTYLE", "ITALIC");
   IupSetAttribute(plot, "AXS_YFONTSTYLE", "ITALIC");
   IupSetAttribute(plot, "AXS_XTICKNUMBER", "No");
   IupSetAttribute(plot, "AXS_YAUTOMIN", "No");
   IupSetAttribute(plot, "AXS_YAUTOMAX", "No");
   IupSetInt(plot, "AXS_YMIN", 0)
   IupSetInt(plot, "AXS_YMAX", 100)

   canvas = IupCanvas(NULL)
   IupSetAttribute(canvas, "RASTERSIZE", "640x360") -- initial size
   IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))
   IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))

   Ihandle hbox = IupHbox({vbox, plot, canvas},"MARGIN=4x4, GAP=10")
   dlg = IupDialog(hbox);
   IupSetCallback(dlg, "K_ANY", Icallback("esc_close"))
   IupSetAttribute(dlg, "TITLE", "Perceptron")
   IupMap(dlg)
   IupSetAttribute(canvas, "RASTERSIZE", NULL) -- release limitation
   IupShowXY(dlg,IUP_CENTER,IUP_CENTER)
   timer = IupTimer(Icallback("timer_cb"), 100) -- (was 1 sec, now 0.1s)
   IupMainLoop()
   IupClose()

end procedure main()</lang>

Racket

Translation of: Java

<lang racket>#lang racket (require 2htdp/universe

        2htdp/image)

(define (activate s) (if (positive? s) 1 -1))

(define perceptron%

 (class object%
   (super-new)
   (init-field n)
   
   (field [weights (build-vector n (λ (i) (- (* (random) 2) 1)))])
   
   (define c 0.001)

   (define/public (feed-forward inputs)
     (unless (= (vector-length inputs) (vector-length weights))
       (error 'feed-forward "weights and inputs lengths mismatch"))
     (activate (for/sum ((i (in-vector inputs)) (w (in-vector weights))) (* i w))))

   (define/public (train! inputs desired)
     (let ((error (- desired (feed-forward inputs))))
       (set! weights (vector-map (λ (w i) (+ w (* c error i))) weights inputs))))))

(struct training-data (inputs answer))

(define (make-training-data x y f)

 (training-data (vector x y 1) (activate (- (f x) y))))

(define (demo)

 (struct demonstration (p w h f i))

 (define (draw-classification-space p w h scl n)
   (for/fold ((scn (place-image (text (~a (get-field weights p)) 12 "red")
                                (* scl (/ w 2))
                                (* scl (/ h 2))
                                (empty-scene (* w scl) (* h scl)))))
             ((_ (in-range n)))
     (let* ((x (* (random) w))
            (y (* (random) h))
            (guess+? (positive? (send p feed-forward (vector x y 1)))))          
       (place-image (rectangle 4 4 (if guess+? 'solid 'outline) (if guess+? 'red 'black))
                    (- (* scl x) 2) (- (* scl (- h y)) 2)
                    scn))))

 (define the-demo
   (let ((w 640/100) (h 360/100) (f (λ (x) (+ (* x 0.7) 0.8))))
     (demonstration (new perceptron% [n 3]) w h f 0)))

 (define (demo-train p w h f)
   (let ((td (make-training-data (* (random) w) (* (random) h) f)))
     (send p train! (training-data-inputs td) (training-data-answer td))))

 (define tick-handler
   (match-lambda
     [(and d (demonstration p w h f i))
      (for ((_ (in-range 100))) (demo-train p w h f))
      (struct-copy demonstration d [i (+ 100 i)])]))

 (define draw-demo (match-lambda
                     [(demonstration p w h f i)
                      (let ((scl 100))
                        (scene+line (place-image (text (~a i) 24 "magenta")
                                                 (* scl (/ w 2))
                                                 (* scl (/ h 3))
                                                 (draw-classification-space p w h scl 1000))
                                    0 (* scl (- h (f 0))) (* scl w) (* scl (- h (f w))) "red"))]))
 
 (big-bang the-demo (to-draw draw-demo) (on-tick tick-handler)))

(module+ main (demo))</lang>

Run it and see the image for yourself, I can't get it onto RC!

REXX

Translation of: Java

<lang rexx>/* REXX */ Call init Call time 'R' try=0 Call show 0 Do d=1 To dots

 x=x.d
 y=y.d
 Parse Value x y 1 with inputs.0 inputs.1 inputs.2
 answer.d=sign(y-f(x))
 Select
   When f(x)<y Then r='<'
   When f(x)>y Then r='>'
   Otherwise        r='='
   End
 training.d=x y 1 answer.d
 End

Do try=1 To tries

 Call time 'R'
 zz=0
 Do d=1 To dots
   Parse Var training.d inputs.0 inputs.1 inputs.2 answer.d
   Call train d
   Do ii=1 To d
     Parse Var training.ii inputs.0 inputs.1 inputs.2 answer.d
     guess = feedForward(d)
     End
   End
 Call show try
 End

Exit

show:

 Parse Arg run
 show=wordpos(run,'0 1' tries)>0
 If run>0 Then Say ' '
 If show Then  Say 'Point    x f(x) r    y ff ok   zz'
 zz=0
 Do d=1 To dots
   x=x.d
   y=y.d
   Parse Value x.d y.d 1 with inputs.0 inputs.1 inputs.2
   ff=format(feedForward(),2)
   Select
     When f(x)<y Then r='<'
     When f(x)>y Then r='>'
     Otherwise        r='='
     End
   If r='<' & ff=1 |,
      r='>' & ff=-1 Then Do; tag='ok'; zz=zz+1; End
                    Else tag='--'
   If show Then
    Say format(d,5) format(x,4,0) format(f(x),4,0) r format(y,4,0) right(ff,2),
                                                                   tag format(zz,4)
   End
 If show Then Say copies('-',33)
 weights=format(weights.0,2,5) format(weights.1,2,5) format(weights.2,2,5)
 Select
   When run=0 Then txt='Initial pattern'
   When run=1 Then txt='After one loop '
   Otherwise       txt='After' run 'loops'
   End
 Say left(txt,15) format(zz,4) 'points fire. weights='weights
 Return

train: Procedure Expose inputs. weights.

 desired=sign(inputs.1-f(inputs.0))
 guess  = feedForward()
 error  = desired-guess
 Do i=0 To 2
   weights.i=weights.i+0.00001*error*inputs.i
   End
 Return

f: Return arg(1)*0.7+40

nextDouble: /* random number between -1 and +1 */

 Return random(100000)/100000

feedforward: Procedure Expose inputs. weights.

 sum=0
 Do i=0 To 2
   sum=sum+inputs.i*weights.i
   End
 Return activate(sum)

activate:

 If arg(1)>0 Then Return 1
             Else Return -1

init:

 Call random 10000,10000,333 /* seed the random function */
 dots=30
 width=640
 height=360
 tries=10
 Do i=0 To 2
   weights.i=nextDouble()
   End
 Do i=1 To dots
   x.i=nextDouble()*width
   y.i=nextDouble()*height
   End
 Return</lang>

Output:

Point    x f(x) r    y ff ok   zz
    1  100  110 <  204  1 ok    1
    2  613  469 >  117  1 --    1
    3  528  409 >  125  1 --    1
    4  141  139 >  119  1 --    1
    5   32   62 <  245  1 ok    2
    6   11   48 <  336  1 ok    3
    7  435  344 >  270  1 --    3
    8  572  440 >  280  1 --    3
    9  442  350 >  141  1 --    3
   10  410  327 >  209  1 --    3
   11  290  243 <  355  1 ok    4
   12  257  220 <  260  1 ok    5
   13  235  205 >   51  1 --    5
   14  600  460 >   66  1 --    5
   15   21   55 <  182  1 ok    6
   16  197  178 >   42  1 --    6
   17  444  351 >  150  1 --    6
   18  393  315 >   87  1 --    6
   19  622  475 >  280  1 --    6
   20  436  345 >  292  1 --    6
   21  553  427 >  261  1 --    6
   22  478  374 >  264  1 --    6
   23  373  301 >  120  1 --    6
   24  527  409 >   94  1 --    6
   25  558  431 >   49  1 --    6
   26  616  471 >  358  1 --    6
   27  241  209 >   68  1 --    6
   28  365  295 >  164  1 --    6
   29  371  299 >  155  1 --    6
   30  102  112 <  220  1 ok    7
---------------------------------
Initial pattern    7 points fire. weights= 0.28732  0.50931  0.45298

Point    x f(x) r    y ff ok   zz
    1  100  110 <  204  1 ok    1
    2  613  469 >  117  1 --    1
    3  528  409 >  125  1 --    1
    4  141  139 >  119  1 --    1
    5   32   62 <  245  1 ok    2
    6   11   48 <  336  1 ok    3
    7  435  344 >  270  1 --    3
    8  572  440 >  280  1 --    3
    9  442  350 >  141  1 --    3
   10  410  327 >  209  1 --    3
   11  290  243 <  355  1 ok    4
   12  257  220 <  260  1 ok    5
   13  235  205 >   51  1 --    5
   14  600  460 >   66  1 --    5
   15   21   55 <  182  1 ok    6
   16  197  178 >   42  1 --    6
   17  444  351 >  150  1 --    6
   18  393  315 >   87  1 --    6
   19  622  475 >  280  1 --    6
   20  436  345 >  292  1 --    6
   21  553  427 >  261  1 --    6
   22  478  374 >  264  1 --    6
   23  373  301 >  120  1 --    6
   24  527  409 >   94  1 --    6
   25  558  431 >   49  1 --    6
   26  616  471 >  358  1 --    6
   27  241  209 >   68  1 --    6
   28  365  295 >  164  1 --    6
   29  371  299 >  155  1 --    6
   30  102  112 <  220  1 ok    7
---------------------------------
After one loop     7 points fire. weights= 0.08433  0.43412  0.45252

After 2 loops     16 points fire. weights=-0.10749  0.35991  0.45208

After 3 loops     26 points fire. weights=-0.18168  0.31845  0.45192

After 4 loops     28 points fire. weights=-0.20192  0.30482  0.45186

After 5 loops     29 points fire. weights=-0.20473  0.30245  0.45184

After 6 loops     29 points fire. weights=-0.20755  0.30007  0.45182

After 7 loops     29 points fire. weights=-0.21037  0.29769  0.45180

After 8 loops     29 points fire. weights=-0.21319  0.29532  0.45178

After 9 loops     29 points fire. weights=-0.21601  0.29294  0.45176

Point    x f(x) r    y ff ok   zz
    1  100  110 <  204  1 ok    1
    2  613  469 >  117 -1 ok    2
    3  528  409 >  125 -1 ok    3
    4  141  139 >  119  1 --    3
    5   32   62 <  245  1 ok    4
    6   11   48 <  336  1 ok    5
    7  435  344 >  270 -1 ok    6
    8  572  440 >  280 -1 ok    7
    9  442  350 >  141 -1 ok    8
   10  410  327 >  209 -1 ok    9
   11  290  243 <  355  1 ok   10
   12  257  220 <  260  1 ok   11
   13  235  205 >   51 -1 ok   12
   14  600  460 >   66 -1 ok   13
   15   21   55 <  182  1 ok   14
   16  197  178 >   42 -1 ok   15
   17  444  351 >  150 -1 ok   16
   18  393  315 >   87 -1 ok   17
   19  622  475 >  280 -1 ok   18
   20  436  345 >  292 -1 ok   19
   21  553  427 >  261 -1 ok   20
   22  478  374 >  264 -1 ok   21
   23  373  301 >  120 -1 ok   22
   24  527  409 >   94 -1 ok   23
   25  558  431 >   49 -1 ok   24
   26  616  471 >  358 -1 ok   25
   27  241  209 >   68 -1 ok   26
   28  365  295 >  164 -1 ok   27
   29  371  299 >  155 -1 ok   28
   30  102  112 <  220  1 ok   29
---------------------------------
After 10 loops    29 points fire. weights=-0.21883  0.29057  0.45174

Scala

Java Swing Interoperability

<lang Scala>import java.awt._ import java.awt.event.ActionEvent

import javax.swing._

import scala.util.Random

object Perceptron extends App {

 SwingUtilities.invokeLater(() =>

   new JFrame("Perceptron") {

     class Perceptron(val n: Int) extends JPanel {
       private val (c, dim) = (0.00001, new Dimension(640, 360))
       private val (random, training) = (new Random, Array.ofDim[Trainer](2000))
       private val weights = Array.fill(n)(random.nextDouble * 2 - 1)
       private var count = 0

       override def paintComponent(gg: Graphics): Unit = {
         var x = getWidth
         var y = f(x).toInt

         def train(inputs: Array[Double], desired: Int): Unit = {
           val guess = feedForward(inputs)
           for (i <- weights.indices) weights(i) += c * (desired - guess) * inputs(i)
         }

         def feedForward(inputs: Array[Double]) = {
           assert(inputs.length == weights.length, "weights and input length mismatch")
           var sum = 0.0
           for (i <- weights.indices) {
             sum += inputs(i) * weights(i)
           }
           if (sum > 0) 1 else -1
         }

         super.paintComponent(gg)
         val g = gg.asInstanceOf[Graphics2D]
         g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON)
         // we're drawing upside down
         g.setStroke(new BasicStroke(2))
         g.setColor(Color.orange)
         g.drawLine(0, f(0).toInt, x, y)
         train(training(count).inputs, training(count).answer)
         count = (count + 1) % training.length
         g.setStroke(new BasicStroke(1))
         g.setColor(Color.black)
         for (i <- 0 until count) {
           val guess = feedForward(training(i).inputs)
           x = training(i).inputs(0).toInt - 4
           y = training(i).inputs(1).toInt - 4
           if (guess > 0) g.drawOval(x, y, 8, 8)
           else g.fillOval(x, y, 8, 8)
         }
       }

       private def f(x: Double) = x * 0.7 + 40

       class Trainer(val x: Double, val y: Double, var answer: Int) {
         val inputs = Array[Double](x, y, 1)
       }

       for (j <- training.indices;
            x = random.nextDouble * dim.width;
            y = random.nextDouble * dim.height;
            answer = if (y < f(x)) -1 else 1
       ) training(j) = new Trainer(x, y, answer)

       new Timer(10, (e: ActionEvent) => repaint()).start()

       setBackground(Color.white)
       setPreferredSize(dim)
     }

     add(new Perceptron(3), BorderLayout.CENTER)
     pack()
     setDefaultCloseOperation(WindowConstants.EXIT_ON_CLOSE)
     setLocationRelativeTo(null)
     setResizable(false)
     setVisible(true)
   })

}</lang>

Scheme

<lang scheme>(import (scheme base)

       (scheme case-lambda)
       (scheme write)
       (srfi 27))      ; for random numbers

(random-source-randomize! default-random-source)

num-inputs

size of input data
learning-rate: small number, to give rate of learning
returns perceptron as a function
accepting 'train data -> trains on given list of data
'test data -> returns percent correct on given list of data
'show -> displays the perceptron weights
classes assumed to be 1, -1

(define (create-perceptron num-inputs learning-rate)

 (define (make-rnd-vector n) ; rnd vector, values in [-1,1]
   (let ((result (make-vector n)))
     (do ((i 0 (+ 1 i)))
       ((= i n) result)
       (vector-set! result i (- (* 2 (random-real)) 1)))))
 (define (extended input) ; add a 1 to end of vector
   (let* ((n (vector-length input))
          (result (make-vector (+ 1 n))))
     (do ((i 0 (+ 1 i)))
       ((= i n) (vector-set! result i 1)
                result)
       (vector-set! result i (vector-ref input i)))))
 (define (predict weights extended-input)
   (let ((sum 0))
     (vector-for-each (lambda (w i) (set! sum (+ sum (* w i))))
                      weights extended-input)
     (if (positive? sum) 1 -1)))
 ;
 (let ((weights (make-rnd-vector (+ 1 num-inputs))))
   (case-lambda ; defines a function for the perceptron
     ((key)
      (when (eq? key 'show)
        (display weights) (newline)))
     ((action data) 
      (case action
        ((train) 
         (for-each 
           (lambda (datum)
             (let* ((extended-input (extended (car datum)))
                    (error (- (cdr datum) (predict weights extended-input))))
               (set! weights (vector-map (lambda (w i) (+ w (* learning-rate error i)))
                                         weights
                                         extended-input))))
           data))
        ((test) 
         (let ((count 0))
           (for-each 
             (lambda (datum) (when (= (cdr datum) (predict weights (extended (car datum))))
                               (set! count (+ 1 count))))
             data)
           (inexact (* 100 (/ count (length data)))))))))))

create data

list of n ( #(input values) . target ) pairs
using formula y = mx + b, target based on if input above / below line

(define (create-data m b n)

 (define (target x y)
   (let ((fx (+ b (* m x)))) 
     (if (< fx y) 1 -1)))
 (define (create-datum)
   (let ((x (random-real))
         (y (random-real)))
     (cons (vector x y) (target x y))))
 ;
 (do ((data '() (cons (create-datum) data)))
   ((= n (length data)) data)))

(let* ((m 0.7)

      (b 0.2)
      (perceptron (create-perceptron 2 0.001)))
 (perceptron 'train (create-data m b 5000))
 (perceptron 'show)
 (display "Percent correct on test set: ")
 (display (perceptron 'test (create-data m b 1000)))
 (newline))

(let* ((m 0.7) ; gradient of target line

      (b 0.2) ; y-intercept of target line
      (train-step 1000)  ; step in training set size
      (train-stop 20000) ; largest training set size
      (test-set (create-data m b 1000)) ; create a fixed test set
      (perceptron (create-perceptron 2 0.001)))
 (do ((i train-step (+ i train-step)))
   ((> i train-stop) )
   (perceptron 'train (create-data m b train-step))
   (display (string-append "Trained on " (number->string i)
                           ", percent correct is " 
                           (number->string (perceptron 'test test-set))
                           "\n"))))</lang>

Output:

#(-0.5914540100624854 1.073343782042039 -0.29780862758499393)
Percent correct on test set: 95.4
Trained on 1000, percent correct is 18.1
Trained on 2000, percent correct is 91.1
Trained on 3000, percent correct is 98.0
Trained on 4000, percent correct is 92.5
Trained on 5000, percent correct is 98.6
Trained on 6000, percent correct is 98.6
Trained on 7000, percent correct is 98.8
Trained on 8000, percent correct is 97.8
Trained on 9000, percent correct is 99.1
Trained on 10000, percent correct is 96.0
Trained on 11000, percent correct is 98.6
Trained on 12000, percent correct is 98.2
Trained on 13000, percent correct is 99.2
Trained on 14000, percent correct is 99.4
Trained on 15000, percent correct is 99.0
Trained on 16000, percent correct is 98.8
Trained on 17000, percent correct is 97.5
Trained on 18000, percent correct is 99.8
Trained on 19000, percent correct is 99.2
Trained on 20000, percent correct is 100.0

Smalltalk

Works with: GNU Smalltalk

<lang Smalltalk>Number extend [

   activate
       [^self > 0 ifTrue: [1] ifFalse: [-1]]

]

Object subclass: Perceptron [

   | weights |

   feedForward: inputArray
       [^(self sumOfWeighted: inputArray) activate]

   train: inputArray desire: expected
       [| actual error |
       actual := self feedForward: inputArray.
       error := 0.0001 * (expected - actual).
       weights := weights
           with: inputArray
           collect: [:weight :input | weight + (error * input)]]

   sumOfWeighted: inputArray
       [^(self weighted: inputArray)
           inject: 0
           into: [:each :sum | each + sum]]

   weighted: inputArray
       [^weights
           with: inputArray
           collect: [:weight :input | weight * input]]

   Perceptron class >> new: arity
       [^self basicNew
           initialize: arity;
           yourself]

   initialize: arity
       [weights := 1
           to: arity
           collect: [:x | self randomWeight]]

   randomWeight
       [^(Random between: -1000 and: 1000) / 1000]

]

Perceptron class extend [

   | perceptron trainings input expected actual |

   evaluationSamples := 100000.

   initializeTest
       [perceptron := self new: 3.
       input := Array new: 3.
       trainings := 0.
       input at: 1 put: 1. "Bias"]

   randomizeSample
       [| x y |
       x := Random between: 0 and: 640-1.
       y := Random between: 0 and: 360-1.
       expected := (y >= (2*x+1)) ifTrue: [1] ifFalse: [-1].
       input at: 2 put: x.
       input at: 3 put: y]

   test
       [self
           initializeTest; evaluate;
           train: 1; evaluate;
           train: 1; evaluate;
           train: 1; evaluate;
           train: 1; evaluate;
           train: 1; evaluate;
           train: 5; evaluate;
           train: 10; evaluate;
           train: 30; evaluate;
           train: 50; evaluate;
           train: 100; evaluate;
           train: 300; evaluate;
           train: 500; evaluate]

   evaluate
       [| hits |
       hits := 0.
       evaluationSamples timesRepeat:
           [self randomizeSample.
           expected = (perceptron feedForward: input)
               ifTrue: [hits := hits + 1]].
       Transcript
           display: 'After ';
           display: trainings;
           display: ' trainings: ';
           display: (hits / evaluationSamples * 100) asFloat;
           display: ' % accuracy';
           nl]

   train: anInteger
       [anInteger timesRepeat:
           [self randomizeSample.
           perceptron
               train: input
               desire: expected.
           trainings := trainings + 1]]

]

Perceptron test.</lang> Example output:

After 0 trainings: 14.158 % accuracy
After 1 trainings: 14.018 % accuracy
After 2 trainings: 14.19 % accuracy
After 3 trainings: 14.049 % accuracy
After 4 trainings: 14.029 % accuracy
After 5 trainings: 14.105 % accuracy
After 10 trainings: 20.39 % accuracy
After 20 trainings: 57.08 % accuracy
After 50 trainings: 92.998 % accuracy
After 100 trainings: 98.988 % accuracy
After 200 trainings: 98.055 % accuracy
After 500 trainings: 99.777 % accuracy
After 1000 trainings: 98.523 % accuracy

XLISP

Like the Pascal example, this is a text-based program using a 20x20 grid. It is slightly more general, however, because it allows the function that is to be learnt and the perceptron's bias and learning constant to be passed as arguments to the trainer and perceptron objects. <lang scheme>(define-class perceptron

   (instance-variables weights bias learning-constant) )

(define-method (perceptron 'initialize b lc)

   (defun random-weights (n)
       (if (> n 0)
           (cons (- (/ (random 20000) 10000) 1) (random-weights (- n 1))) ) )
   (setq weights (random-weights 3))
   (setq bias b)
   (setq learning-constant lc)
   self )

(define-method (perceptron 'value x y)

   (if (> (+ (* x (car weights)) (* y (cadr weights)) (* bias (caddr weights))) 0)
   1
   -1 ) )

(define-method (perceptron 'print-grid)

   (print-row self 10) )

(define-method (perceptron 'learn source runs)

   (defun learn-row (row)
       (defun learn-cell (cell)
           (define inputs `(,cell ,row ,bias))
           (define error (- (source 'value cell row) (self 'value cell row)))
           (defun reweight (ins ws)
               (if (car ins)
                   (cons (+ (car ws) (* error (car ins) learning-constant)) (reweight (cdr ins) (cdr ws))) ) )
           (setq weights (reweight inputs weights))
           (if (< cell 10)
               (learn-cell (+ cell 1)) ) )
       (learn-cell -9)
       (if (> row -9)
           (learn-row (- row 1)) ) )
   (do ((i 1 (+ i 1))) ((> i runs))
       (learn-row 10) ) )

(define-class trainer

   (instance-variables fn) )

(define-method (trainer 'initialize function)

   (setq fn function)
   self )

(define-method (trainer 'print-grid)

   (print-row self 10) )

(define-method (trainer 'value x y)

   (if (apply fn `(,x ,y))
       1
       -1 ) )

(defun print-row (obj row)

   (defun print-cell (cell)
       (if (= (obj 'value cell row) 1)
           (display "#")
           (display "O") )
       (if (< cell 10)
           (print-cell (+ cell 1))
           (newline) ) )
   (print-cell -9)
   (if (> row -9)
       (print-row obj (- row 1))
       (newline) ) )

(define ptron (perceptron 'new 1 0.01))

(define training (trainer 'new

   (lambda (x y) (> y (+ (* x 2) 1))) ) )

(newline) (display "Target output for y = 2x + 1:") (newline) (training 'print-grid) (display "Output from untrained perceptron:") (newline) (ptron 'print-grid) (display "Output from perceptron after 1 training run:") (newline) (ptron 'learn training 1) (ptron 'print-grid) (display "Output from perceptron after 5 training runs:") (newline) (ptron 'learn training 4) (ptron 'print-grid)</lang>

Output:

Target output for y = 2x + 1:
##############OOOOOO
#############OOOOOOO
#############OOOOOOO
############OOOOOOOO
############OOOOOOOO
###########OOOOOOOOO
###########OOOOOOOOO
##########OOOOOOOOOO
##########OOOOOOOOOO
#########OOOOOOOOOOO
#########OOOOOOOOOOO
########OOOOOOOOOOOO
########OOOOOOOOOOOO
#######OOOOOOOOOOOOO
#######OOOOOOOOOOOOO
######OOOOOOOOOOOOOO
######OOOOOOOOOOOOOO
#####OOOOOOOOOOOOOOO
#####OOOOOOOOOOOOOOO
####OOOOOOOOOOOOOOOO

Output from untrained perceptron:
######OOOOOOOOOOOOOO
######OOOOOOOOOOOOOO
#######OOOOOOOOOOOOO
#######OOOOOOOOOOOOO
#######OOOOOOOOOOOOO
########OOOOOOOOOOOO
########OOOOOOOOOOOO
########OOOOOOOOOOOO
#########OOOOOOOOOOO
#########OOOOOOOOOOO
#########OOOOOOOOOOO
##########OOOOOOOOOO
##########OOOOOOOOOO
##########OOOOOOOOOO
###########OOOOOOOOO
###########OOOOOOOOO
###########OOOOOOOOO
############OOOOOOOO
############OOOOOOOO
############OOOOOOOO

Output from perceptron after 1 training run:
###############OOOOO
###############OOOOO
##############OOOOOO
##############OOOOOO
#############OOOOOOO
############OOOOOOOO
############OOOOOOOO
###########OOOOOOOOO
##########OOOOOOOOOO
##########OOOOOOOOOO
#########OOOOOOOOOOO
#########OOOOOOOOOOO
########OOOOOOOOOOOO
#######OOOOOOOOOOOOO
#######OOOOOOOOOOOOO
######OOOOOOOOOOOOOO
#####OOOOOOOOOOOOOOO
#####OOOOOOOOOOOOOOO
####OOOOOOOOOOOOOOOO
####OOOOOOOOOOOOOOOO

Output from perceptron after 5 training runs:
##############OOOOOO
#############OOOOOOO
#############OOOOOOO
############OOOOOOOO
############OOOOOOOO
###########OOOOOOOOO
###########OOOOOOOOO
##########OOOOOOOOOO
##########OOOOOOOOOO
#########OOOOOOOOOOO
#########OOOOOOOOOOO
########OOOOOOOOOOOO
########OOOOOOOOOOOO
#######OOOOOOOOOOOOO
#######OOOOOOOOOOOOO
######OOOOOOOOOOOOOO
######OOOOOOOOOOOOOO
#####OOOOOOOOOOOOOOO
#####OOOOOOOOOOOOOOO
####OOOOOOOOOOOOOOOO

zkl

Translation of: Java

Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl <lang zkl>class Perceptron{

  const c=0.00001;
  var [const] W=640, H=350;

  fcn init(n){
     r:=(0.0).random.fp(1); // r()-->[0..1)
     var weights=n.pump(List(),'wrap(){ r()*2 - 1 }), // Float[n]
         training=(2000).pump(List,'wrap(){         // (x,y,1,answer)[2000]
            x,y,answer:=r()*W, r()*H, (if(y<f(x)) -1 or 1);

return(x,y,1,answer) });

  }
  fcn f(x){ 0.7*x + 40 }    // a line
  fcn feedForward(xy1a){
     sum:=0.0;
     foreach i in (weights.len()){ sum+=xy1a[i]*weights[i] }
     (sum<0) and -1 or 1   // activate(sum)
  }
  fcn train(xy1a){ 
     guess,error:=feedForward(xy1a), xy1a[-1] - guess;
     foreach i in (weights.len()){ weights[i]+=c*error*xy1a[i] }
  }

}</lang> <lang zkl>p:=Perceptron(3); p.training.apply2(p.train);

PPM:=Import("ppm.zkl").PPM; pixmap:=PPM(p.W+20,p.H+20,0xFF|FF|FF);

foreach xy1a in (p.training){

  guess,x,y:=p.feedForward(xy1a), 8 + xy1a[0], 8 + xy1a[1];
  color:=(if(guess>0) 0 else 0xFF|00|00);  // black or red
  pixmap.circle(x,y,8,color);

} pixmap.writeJPGFile("perceptron.zkl.jpg");</lang>

Output: