Together toward an AI plus ultra

AN AI 
NEAT PLUS ULTRA

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AN AI 
NEAT PLUS ULTRA
Good Afternoon everyone.
I am thrilled to be here with you on stage!

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Grégoire Hébert
Senior Developper — Trainer — Lecturer @ Les-Tilleuls.coop
@gheb_dev
@gregoirehebert
UNE IA 
NEAT PLUS ULTRA
Let me introduce myself :) 
My name is Grégoire Hébert, I am a senior developer, lecturer and speaker at Les-Tilleuls.coop . 
If you can’t pronounce it properly come at our booth, we’ll teach you :) 

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@gheb_dev @gregoirehebert

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Machine Learning
Image Recognition
Language Processing Autonomous Vehicules
Medical Diagnostics
Robotic
Recommender Systems
We are going to spend 40 minutes together, and the subject is the machine learning. 
Who, in this room, never worked with artificial intelligence before? Raise your hand.
For all the others, what I am about to say may sound trivial, or simplistic, but the goal here is to set a start. 
Because YES. Doing research about Machine learning is not, something trivial.
Machine learning is a subpart of the AI field, but is also part of the others.
Without mentioning them, I showed some fields of usage, we are going to focus on things the we want to set autonomous. Now, How complex can be an
AI? Does an AI has to be all powerful? 
Of course not,
we’ve got multiple levels of complexity. 
Starting from

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REACTIVE MACHINES (Scenarii reactive)
Reactive machine, this is the kind of AI, we have in video games.

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REACTIVE MACHINES (Senarii reactive)
LIMITED MEMORY (Environment reactive)
Limited Memory, where we begin to act according to time, location, extra knowledge surrounding you. 
For instance, my car gps knows I am leaving the office, it’s 6p.m. it shows me every known restaurant on my way home.

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THEORY OF MIND (People awareness)
For the Theory of mind, it’s not just a blind guess anymore.
The AI knows me ! I had a harsh day, It’ll show my favourite comforting restaurant.. 
. Mc Donald, KFC… and a little padthai restaurant.

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SELF AWARE
Self aware !! Beware ! It start to rule the world !

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SELF AWARE

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Ok before that, we need to grasp the subtleties of the ﬁrst level, ReactiveMachine. 
And don’t mistaken it’s simplicity for a lack of capabilities.
The goal now is, together, see how each one of you could leave this room and be able to write down a simple AI.
And then, be drown to the abyss of machine learning, even grow a passion to it :)

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INPUT
Alright, everything start from an input. 
An input can be a number, a set of numbers, an image, a string.
Well, If I want to treat everything the same way, I’ll need to normalise that input. 
For a picture of my cat, I need to transform that jpeg ﬁle into a matrix of values, each one between 0 and 255 of white
0 and 255 of red, of green and of blue. For each type of data I need to normalise it’s representation into something the system can read and exploit. The
larger is the set, the better is the result.

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INPUT
?
That input will be computed into a value. 
At the moment we don’t know how.

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INPUT
?
OUTPUT
And that value, will in the end be computed into a result. 
This result is the output we expect, the answer if you will.

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INPUT ? OUTPUT
PERCEPTRON
Well this simplest representation is called a perceptron.
Let’s put that into something representative shall we?

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?
Let’s say, according to my hunger, the machine should decide if I shall eat.

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?
Or not
Or not.

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?
Or not
0 - 10
To decide I need to normalise my stomach emptiness,
0 : I am not hungry
10: I am starving

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?
Or not
0 - 10
0 - 1
Activation
To get to the intermediate value I will use a weight. 
This weight is at start a random value between 0 and 1. 
This is arbitrary it could be between 1 and 10 or 100. It’s up to you. 
How to chose then, it’s by experience. By running through a lot of dataset, you start having a spider sense about where the ﬁnal value could be.

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?
Or not
0 - 10
0 - 1
Activation
We are going then to use the result of the weight multiplied by the input  
through an activation function. 
An activation function will help us to control the transformation of the input value into an output value according to their behaviour.

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0 - 10
?
Or not
0 - 1 0 - 1
Activation Activation

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What is an activation function? It’s a a function, 
A mathematical function. Well not really one function. 
There are few functions that are useful as an activation function.

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Binary Step
You’ve got the Binary step.

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Binary Step
The easiest, according to the input value it will return a 0, or a 1.

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Binary Step
Gaussian
The gaussian

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Binary Step
Gaussian
This one, if you do statistics you know it well :)  
It’s the same curve that represent the normal randomness distribution.

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Binary Step
Gaussian
Hyperbolic Tangent

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Binary Step
Gaussian
Hyperbolic Tangent
TanH

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Binary Step
Gaussian
Hyperbolic Tangent
Parametric Rectiﬁed Linear Unit
Relu

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Binary Step
Gaussian
Hyperbolic Tangent
Start a 0, and tends to inﬁnite

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Binary Step
Gaussian
Hyperbolic Tangent
Sigmoid
Sigmoid

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Binary Step
Gaussian
Hyperbolic Tangent
Sigmoid
Tends toward 0 and 1 but never touches them.

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Binary Step
Gaussian
Hyperbolic Tangent
Sigmoid
Thresholded Rectiﬁed Linear Unit

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Binary Step
Gaussian
Hyperbolic Tangent
Sigmoid
Like relu but with a threshold.

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Binary Step
Gaussian
Hyperbolic Tangent
Sigmoid
The most common one is Sigmoid, that’s the one we are going to use today.

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Sigmoid

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0 - 10
?
0 - 1 0 - 1

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Or not
0 - 10
0 - 1 0 - 1
And we are going to repeat the operation twice. 
A ﬁrst one to get the intermediary value,  
and a second one to get the output.

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?
Or not
0 - 10
0 - 1 0 - 1
Sigmoid Sigmoid
Ok, now we’ve got a coefficient (a weight) to multiply our value, and an activation function to obtains a contained value within a controlled range. Most of
the time this is not enough.
You need to see the ﬁrst calculus as a force. 
Imagine a second I am a Jedi. I want to pull a person from the audience to me. 
If I were to pull upward the stage in one direction you would probably end up stuck up above the screen, the face completely smashed. I need a second
force to direct the trajectory to me.

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?
Or not
0 - 10
0 - 1 0 - 1
Sigmoid Sigmoid
I need a bias to apply to the value.

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Or not
0 - 10
0 - 1 0 - 1
Sigmoid Sigmoid
Bias Bias
This bias will be a factor, another simple addition to run.
Their value, at start, are, like the weights, chosen at random, between 0 and 1. 
As before it could be to 10 or 100. 
Let’s change that into possible numbers for the example.

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?
Or not
8
0.2 0.3
Sigmoid Sigmoid
0.4 0.8
In this situation I am hungry. 
0.2 and 0.3 are the weight and 0.4 and 0.8 respectively the biases.
Note that I did not named the value in between the input and the output.
That intermediate representation.

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H
Or not
8
0.2 0.3
Sigmoid Sigmoid
0.4 0.8
I’ll write it H for Hidden. 
Each intermediate representation is called a node, and this we don’t really know in time what is the value and frankly don’t really care at the moment, we
will say that the node is hidden.
Now that we have established the system, let’s dive into the maths.

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0 - 10
?
0 - 1 0 - 1
Before going further I must confess. 
I am not a math guy. I got my degree with 3/20 in mathematics. 
But, as soon as I started to learn about AI, I discovered brilliant YouTube channels that gave me better ways to learn the math, and I started to realise that I
am a math guy. I love them. 
I just never had a proper way to learn that ﬁt me. 
Anyway the math we are going to do are simple even for me.

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H = sigmoid (Input x weight + bias)
To get the hidden value,  
We need calculate the input multiplied by the weight plus the bias. 
the result will be passed into sigmoid.

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H = sigmoid (8 x 0.2 + 0.4)
With our example numbers this gives us sigmoid(8 x 0.2 + 0.4)

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H = sigmoid (8 x 0.2 + 0.4)
H = 0.88078707797788
The result is 0.8807…
Is it good? We don’t know. We need to do every operation.

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H = sigmoid (8 x 0.2 + 0.4)
H = 0.88078707797788
O = sigmoid (H x W + B)
Now the output is the sigmoid(H x W + B)

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H = sigmoid (8 x 0.2 + 0.4)
H = 0.88078707797788
O = sigmoid (H x 0.3 + 0.8)
With our example value it’s sigmoid (0.8807 x 0.3 + 0.8)

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H = sigmoid (8 x 0.2 + 0.4)
H = 0.88078707797788
O = sigmoid (H x 0.3 + 0.8)
O = 0.74349981350761
It gives us 0.74.
Let’s agree that over 0.5 I eat, and under, I don’t.

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H = sigmoid (8 x 0.2 + 0.4)
H = 0.88078707797788
O = sigmoid (H x 0.3 + 0.8)
O = 0.74349981350761
I was hungry, And I eat :D

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H = sigmoid (8 x 0.2 + 0.4)
H = 0.88078707797788
O = sigmoid (H x 0.3 + 0.8)
O = 0.74349981350761
Is it good, ﬁrst run?
To know, I need to run all the math with a lower input.

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H = sigmoid (2 x 0.2 + 0.4)
H = 0.6897448112761
O = sigmoid (H x 0.3 + 0.8)
O = 0.73243113381927
Let’s say 2, I am not hungry. 
I can see that the output result is not that different…

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H = sigmoid (2 x 0.2 + 0.4)
H = 0.6897448112761
O = sigmoid (H x 0.3 + 0.8)
O = 0.73243113381927
I ate too much. I would have died like a ﬁlleted goose. 
We need to ﬁx the weights and biases until the numbers are right.

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H = sigmoid (2 x 0.2 + 0.4)
H = 0.6897448112761
O = sigmoid (H x 0.3 + 0.8)
O = 0.73243113381927
TRAINING
We need to train our system.

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H = sigmoid (2 x 0.2 + 0.4)
H = 0.6897448112761
O = sigmoid (H x 0.3 + 0.8)
O = 0.73243113381927

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H
Or not
8
0.2 0.3
Sigmoid Sigmoid
0.4 0.8
BACK PROPAGATION
The training system I am going to show you is called back propagation.
It’s purpose it to correct iteration after iteration each value of the weights and biases until the result satisfy our goal.

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H
Or not
8
0.2 0.3
Sigmoid Sigmoid
@gheb_dev 0.4 0.8
BACK PROPAGATION

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H
Or not
8
0.2 0.3
Sigmoid Sigmoid
@gheb_dev 0.4 0.8
BACK PROPAGATION
The way it works is by applying an operation, on each value from the output to the input by measuring the difference between the expected result and the
one we obtained.

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H
Or not
8
0.2 0.3
Sigmoid Sigmoid
@gheb_dev 0.4 0.8
BACK PROPAGATION
LINEAR GRADIENT DESCENT
Remember when I pictured the force used to pull someone here, and not up there? 
The same principle applies here. We need to change the values but the coefficient must not be too high nor too little.
We need to use a math principle called linear gradient descent. 
Ok I have the feeling that we should go through the maths, because so far it’s just words. 

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BACK PROPAGATION
ERROR
ok, we need to get the error. So the difference between the result and what’s expected.

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BACK PROPAGATION
It can be for a single point, or the median to a dataset.

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BACK PROPAGATION
ERROR EXPECTATION - OUTPUT
=
Grab and subtract the two values.
You’ve got the error. 
If I were to apply the difference directly into each value, the result might not be the one we expect.

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BACK PROPAGATION
=
Let’s say we are in a world where friction does not exists. 
If I continuously apply the same force through time to the train…well

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BACK PROPAGATION
=

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BACK PROPAGATION
=
Pfjrouu ! Yay roller coaster tycoon !

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BACK PROPAGATION
=
We need to adjust a few things to get it working.

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Imagine, we replace the rail track by this function representation. 
It’s quite similar. It’s a curve. 
My goal is to ﬁnd the lowest position on the curve.

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My starting point is arbitrary.  
As a human with two properly working eyes, I can easily eyeball that I need to reduce the value. 
I am too far. 
But on a computer perspective how do I know that?

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I need to ﬁnd the slope.
The slope will help us to ﬁnd whether the next value increase or decrease, same for the previous value. So I can apply the right operation, should I go forth
or go back.

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Thanks to the slope I know I can go back. 
In math to get the function’s slope, we need to use what’s called its derivative.

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The derivative or Slope 
 
For any function f, it’s derivative f’ 
calculate the direction 
 
S >= 0 then you must increase the value 
S <= 0 then you must decrease the value
The result of a derivative gives us the direction. 
If it’s over 0 we must increase the value,  
under 0, we must decrease the value.
Simple.

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BACK PROPAGATION
=
Let’s come back on the formula.

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BACK PROPAGATION
=
Sigmoid’ (OUTPUT)
We apply the derivative of sigmoid, with the output as entry value. 
We’ve got a result which is? 
The slope, thank you to follow!

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BACK PROPAGATION
=
Sigmoid’ (OUTPUT)
Multiplied by the error
We multiply this by the error.

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BACK PROPAGATION
=
Sigmoid’ (OUTPUT)
And a LEARNING RATE
And a learning rate. 
What is learning rate? 

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This is what I want.

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Going the closest to the red dot in the less attempts possible.

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But according to the error, I have a chance to miss my point. 
Greater the error, bigger are the chances.

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And I could swing around for a long moment.

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BACK PROPAGATION
=
Sigmoid’ (OUTPUT)
And the LEARNING RATE
I need a learning rate to temper this. 
Remember when I want to pull someone to stage,  
I can prevent him to ﬂy away to the sky, but if it is to break it’s spine to the ﬂoor…

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BACK PROPAGATION
=
GRADIENT Sigmoid’ (OUTPUT)
=
We call the result of this formula the gradient. And this, is the coefficient we want to apply to our different weight and biases. 
But I must warn you.
From the start we chose everything at random, expecting the values to be fixed through iterations. But the learning rate, you need to adjust it’s value. If it’s
too high, you might never reach your goal by always passing by it but never stop close enough. And if it’s too small, You’ve got two problems coming, first
one you will need way too many iterations to find the minimum value in the curb.
The second one is you can get trapped in a valley. Let me show you this:

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BACK PROPAGATION
Beware of the local minimum
If I am on the right part of the track, I’ll ﬁnd a local minimum. 
But I can see that I am not it the lowest part of the track. 
This is when the human is useful. You know or have the feeling that it’s not right. 
In addition to say, here is the objective, you can adjust the learning rate so you can go over hills. 
This is where it can be complex and you might need to use more advanced systems.

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BACK PROPAGATION
=
=
ΔWeights GRADIENT x H
=
Alright, by multiplying the gradient to the hidden value, we’ve got the delta for the weights.

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H
Or not
8
0.2 0.3
Sigmoid Sigmoid
@gheb_dev 0.4 0.8
BACK PROPAGATION
Remember pour little scheme ?
We are going to go back for every single one of the four values.

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BACK PROPAGATION
=
=
=
Weights ΔWeights + weights
=
The new weights values are now the delta (which might be negative) in addition to the previous weights values.

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BACK PROPAGATION
=
=
=
Weights ΔWeights + weights
=
Bias Bias + GRADIENT
=
For the bias we don’t need that much of a difference, just adding the gradient do the trick.

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H
Or not
8
0.2 0.3
Sigmoid Sigmoid
@gheb_dev
0.4 0.8
BACK PROPAGATION
Let’s see what it should look like after a few iterations.
We started from there and we end up with

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H
Or not
8
4.80 7.66
Sigmoid Sigmoid
@gheb_dev
-26.61 -3.75
BACK PROPAGATION
These results.

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H
8
4.80 7.66
Sigmoid Sigmoid
@gheb_dev
-26.61 -3.75
BACK PROPAGATION
0.97988
For this combination and a 8 over 10 hunger feeling, I got 0.97988 value.

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H
4.80 7.66
Sigmoid Sigmoid
@gheb_dev
-26.61 -3.75
BACK PROPAGATION
2
0.02295
And for a 2 over 10 hunger feeling, I’ve got a way more suitable number.

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H
4.80 7.66
Sigmoid Sigmoid
@gheb_dev
-26.61 -3.75
BACK PROPAGATION
2
0.02295

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CONGRATULATIONS !
Congratulation ! You are already capable of creating a small yet powerful machine learning system. 
Who feels that building this kind of system is at reach now? Raise your hand. 
Alright for the others, let me show you, that you under-estimate yourselves.

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CONGRATULATIONS !
Let’s play together :)
https://github.com/GregoireHebert/nn/
You can grab the code and play with it at home.
This is simple PHP, only one dependency to manipulate matrices of values, that’s it.
We are in a symfony conference so I could not resist I made a small toy with this  
and with 2 or 3 components from symfony I created a tamagotchi. An autonomous sheep :D 
It comes in an example branch, I installed a raspberry with an lcd screen, and asked a friend to print a box for me, that you have probably already seen on
the booth.

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CONGRATULATIONS !
Let’s play together :)
Now, that you have touched the most minimalistic system with the tip of the ﬁnger. 
What can we do to improve it and do things more complex?

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Hungry
EAT
Well with a perceptron I can do that.

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Hungry
EAT
But I can make it a little more complex, and have multiple hidden nodes each one with its own weights and biases.  
Maybe for each node you can use a different activation function.

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Hungry
EAT
MULTI LAYER PERCEPTRON
Hungry
EAT
Hungry
EAT
We can multiply this horizontally and vertically into a multi layer perceptron

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Hungry
EAT
Thirsty
DRINK
Sleepy
SLEEP

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Hungry
EAT
Thirsty
DRINK
Sleepy
SLEEP
Where each input has an impact on the others. 
Ok as far as we are now, we always have the control over the number of nodes and layers.
What if….

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Hungry
EAT
Thirsty
DRINK
Sleepy
SLEEP
We don’t.

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Hungry
EAT
Thirsty
DRINK
Sleepy
SLEEP
What if, any decision his made randomly? Number of layers, nodes, weights, biases, their values. 
And to check over different configurations which one is the best,  
 
Imagine we create hundreds of configurations randomly, put them all into competition and only keep the top 10. Then from the top ten we create a new
set of 90 configurations with some slight mutations. And we go over and over. Until the results is satisfying.

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Hungry
EAT
N.E.A.T.
Thirsty
DRINK
Sleepy
SLEEP
Neuro Evolution through Augmented Topology
This is called NEAT. Neuro evolution through augmented topology. 
This is really exciting !

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Hungry
EAT
N.E.A.T.
Thirsty
DRINK
Sleepy
SLEEP
Neuro Evolution through Augmented Topology
https://github.com/GregoireHebert/tamagotchi
I’ve started to play with it, you can ﬁnd examples by looking for MarI/O 
that is an implementation of this algorithm in LUA.

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Going Further
Data Normalization / Preparation 
 
Multiple Activation functions 
 
Mutations 
 
Unsupervised Learning 
So to summarise to go further,  
You can dig into data normalisation and preparation,  
multiple activation functions, applying mutations, and ﬁnish into the awesome vortex of unsupervised learning.

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I don’t leave you without sources, Here are some youtube channels you can follow  

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3blue1Brown which is an absolute goldmine for the math explanation of theorems and how neural networks works. 
The coding train is a teacher which has a tremendous amount of coding videos about machine learning. Even if in his case it’s more about drawings
recognition and approximation, he has a full serie about the fundamentals.
Computerphile is a concentrate of gold nuggets !

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Something More PHP related, In PHP there is a huge library which is PHP-ML. 
And since we have access to foreign function interfaces (FFI) in php, you can now use TensorFlow in PHP. It’s experimental but.

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There are two repositories, php-ffi and php-tensorﬂow.

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THANK YOU!
Thank you so much that’s it for me :)
I just have an ultimate question for you!

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THANK YOU!
How many sheeps did you see ?
How many sheeps did you see during the presentation ? :)

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Together toward an AI plus ultra

Together toward an AI plus ultra

Grégoire Hébert

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