AI based on a neural network

In the transfer function the inputs of the neuron are prepared for the activation function. Usually the sum of all inputs multiplied by their weights is calculated and transferred to the activation function.

There are many different activation functions. A class of functions frequently used here are the sigmoid functions. These functions are characterized by the fact that they are limited and differentiable on both sides. The differentiability is later very important for the training of the network.
The function in the figure above maps each input to a value between 1 and -1.

The weight change of the current neuron (i) to a neuron (j) on the preceding layer is the product of the learning rate, the value of the error of the current neuron from the derivation of the activation function and the activation value of the considered neuron of the preceding layer. The learning rate should be kept very close to zero, but must not be zero, otherwise no changes will occur. For the error of the current neuron a case distinction must be performed. If the neuron is on the output layer, the error is calculated from the difference between the target activation value from the training data and the actual activation value of the neuron. If the neuron is on a hidden layer, the error of the current neuron is calculated as the sum of the product of all errors of the neurons on the next layer with the weight of this neuron to the current one. The sum of the already existing weight and the weight change now forms the new weight.t.

Training through evolution is not really about training, because there is not only one net from which the weights are adjusted. Training data creates a survival situation in which the net has to assert itself. Ideally, it is defined when a net has failed in a scenario. In addition, a “fitness” is assigned, which makes the net comparable. The goal is to maximize the fitness.
It starts with a single, randomly generated net that clones itself at certain fixed points. The idea behind this is that this net has already made it to a point and therefore has a certain acceptable basic configuration. The new cloned net is only randomly changed slightly and starts over again with the training data. The variant of the training is often also modified into a turn-based training. It is started with several random nets at the same time and only the best nets of this round are used as a basis for the generation of new nets for the next round.

After the net has been constructed, the training data must be created manually. This is the most work, because for each input the target output has to be defined manually. In this example it is relatively manageable, because there is a maximum of 4*2 = 8 different paths. For example, a training data record could contain the input (x1, x2, x3, x4, y1, y2) = (1, 0, 0, 0, 0, 1) and the target output (s1, s2, s3) = (-0.5, 0, -0.5).

It would make sense to use the training about backpropagation instead of evolution.

Due to the very simple construction for illustration and the perfection of the training data, it is not possible to use this net for another task with four start positions, two target positions and 3 switches. The training would be obsolete, as the connections can be completely different. A net that recognizes cat photos, for example, can very well be used outside the training data. However, this is because there are almost infinitely many potential training data sets and you train the net with only a fraction of them. It would be transferable to create only six instead of eight training data sets to see if it decides correctly for the other two cases.