Neural networks

Introduction

First, let's define a neural network : It's a group of neurons connected to one another that takes one or more input and returns one or more outputs.
You can model a neural network as some kind of function.
The neural network that we will study here are made out of layers. Each layer contains neurons. The neurons inside a layer are not connected.
Each layer is a smaller network that is processing the information in it's own way. The first layer applies a first simple process, the second layer makes a more complex analysis and so on.

The purpose of neural networks

Usually, neural network are used to accomplish complex task that are not suited for a computer : Image recognition, Voice analysis ...
The strengh of neural network is their ability to "evolve" : You can modify a neural network so that it give slightly different answer. Then, you can test if your neural network is more efficient than previously and repeat. That way, the neural network will be improving itself over time. Given enough time to train and a good "teacher" (a function that evaluates the performances of the network), this kind of program can do anything.
Let's dive in and see precisely how they work.

How a neuron works ?

A quick explanation of what is happening :

We initialize the network (With 1 and 3 for example):

We reset the value of all neurons
The neuron L1N1 (The first neuron of the first layer) contains 3.
L1N2 (The second neuron of the first layer) contains 1.
The weight of L1N1 and L1N2 are set to 1
The connection weights of L1N1 and L1N2 are set to 0.5

So the result of the networks is :

 
					(1*1*0.25) + (3*1*0.75) = 0.25 + 2.25 = 2.5

General formula to compute the value of the first neuron of a layer based on the entering connections :

 
					StartValue + (n1_value * n1_weight * n1_connection_1) + (n2_value * n2_weight * n2_connection_1) + (n3_value * n3_weight * n3_connection_1) + ...

The code used to generate the network :

A more complex network example

Networks can be a lot more complex than what we've just seen : This network take 5 inputs and gives back 4 answers.
Here, the weight of each neuron and the weights of his connections are random to make things even more interesting.
The code used to generate the network :

The behaviour of a simple neuron given 2 outputs

We will now draw the results of a neural network given 2 outputs to show how powerfull a neuron is.

The 2 inputs will be render as coordinates in a plane
The output will be the color of the point at thoses coordinates
The properties of the network will be customizable

The result : (The coordinates goes from bottom (0) to top (100) and from left (0) to right (100))

Value of the first weight :

Value of the second weight :

We can see that just by changing 2 parameters, the neural network can process quite complex patterns.
Here are some remarquable cases :

1 ; 1 is a+b
1 ; -1 is a-b
-1 ; 1 is b-a
1 ; 0 is only a
0 ; 1 is only b
2 ; -2 is (a-b)*2

That's already quite a lot of models that our network can simulate.
With more neurons, even more patterns can be analysed.
The code as usual :

A robot trying to grab apples

Let's try to train our network with a simple task : collecting apples in a field (green dots)
Ok, let's define the problem more precisely :

The robot (red dots) is wandering through a field of apples (green dots)
Each time the robot is near an apple he collects it
To makes things harder, the robot can only see the world as one line (robot vision is displayed below the 2d view)
At each tick, the robot makes a decision (forward / turn left / turn right) based only on what he is currenlty seeing
After 1000 ticks, the robot stops. His score (fitness) is how much apples he collected

Now, we need to figure out a way to generate a network that is adapted to this task. We'll test 3 different networks :

A simple randomly generated network
The best network among a hundred randomly generated networks
The best network of a generation of neural networks generated from a modify version of previous network (evolutionary algorithm)

Above, a visualization of what the robot sees and the 2d world. Below, the brain of the robot

Results :

The random networks have usualy bad scores, which make sense
The second network is better
The third is generally the best

The code is more complicated because we need to render the world. The neural network part is at the bottom.

A basic introduction to neural networks