Detecting If A Number Is Even With Neural Networks

@mattzeunert

http://neuralnetworksanddeeplearning.com/chap1.html

5

1

110b (6)

isEven?

Neurons

Array => Number

http://playground.tensorflow.org/

Neurons

Input Layer: NOT Neurons

Neurons

Array => Number

???

5

2

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

    return sum
}

var neuron = new Neuron([4, -2, 6])
var output = neuron.process([1, 0, 1])
// output = 10

2

2.5

1

0

-3

1.5

Is 01b (1) even?

Training Data

   Number    => isEven
[0, 0, 0] => [1]
[0, 0, 1] => [0]
[0, 1, 0] => [1]
[0, 1, 1] => [0]
[1, 0, 0] => [1]
...

Hidden

Layer

5

9

4

0

2

generateTestData(0, 4)

[
    {
        "input":  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
        "output": [1]
    },
    {
        "input":  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1],
        "output": [0]
    },
    {
        "input":  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0],
        "output": [1]
    },
    {
        "input":  [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1],
        "output": [0]
    }
]

var trainingSet = generateTestData(0, 100);

var testSet = generateTestData(10000, 11000);

predictIsEven(number, weights)
==> e.g. 0.17
==> 0.17 < 0.5, prediction is "not even"

correctness([0.2, 2.9, ...], tE) = 60%
correctness([1.2, 1.5, ...], tE) = 74%
correctness([2.1, 0.3, ...], tE) = 23%
correctness([1.3, 0.4, ...], tE) = 54%

const ITERATIONS = 20000

var weights, bestWeights
var bestCorrectness = -1

for (var i=0; i<ITERATIONS; i++){
    weights = getRandomWeights()
    var correctness = getCorrectness(weights, trainingSet)

    if (correctness > bestCorrectness) {
        bestCorrectness = correctness
        bestWeights = cloneObject(weights)
    }
}

$ node is-even.js 

New best correctness in training set: 47%
Correctness in test set:  45%

New best correctness in training set: 50%
Correctness in test set:  50%

...

New best correctness in training set: 90%
Correctness in test set:  75%

New best correctness in training set: 95%
Correctness in test set:  54%

New best correctness in training set: 96%
Correctness in test set:  80%

Improvements

0

1

1

1.5

1

0

1.5

Is 01b (1) even?

YES

1.5 > 0.5

http://neuralnetworksanddeeplearning.com/chap1.html

Using neural nets to recognize handwritten digits

neuralnetworksanddeeplearning.com/chap1.html

Slides

bit.ly/leeds-nn​

@mattzeunert

Full Code

bit.ly/simple-nn