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I have looked up what NEAT is on youtube and the internet, but I can only find projects using NEAT, but apart from the Wikipedia entry (which only says what it is in the introduction, and is very confusing), I still have no idea what it is, is it a library, is it a type of neural network, is it a method of training neural networks? Sorry if this is an obvious question.

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NEAT uses historical markings in its encoding process, this becomes easier in measuring. A function for deciding how to speciate is given in the paper, but the important part to note is that individuals in a population only have to compete with other individuals within that species. This allows for a new structure to be created and optimized without fear that it will be eliminated before it can be truly explored.

NEAT has a function name, explicit fitness sharing which means that individuals share how well they are doing across the species, boosting up higher performing species, though still allowing for other species to explore their structure optimization before being out-evolved.

NEAT works with the concept of species. That is simply a subdivision of the population into several groups of individuals, called species. This subdivision is based on the dissimilarity of the individuals that are computed based on the similar alignment of their genotypes as is used when doing a crossover. The probability of crossing over individuals from different species is then much smaller than crossover inside species. By promoting the mating of more similar parents, the children are less likely to be much worse than the parents because the parents just were compatible.

Within the species, the fitness value is shared among the individuals. This serves two purposes. 

It protects the individuals in the population from mutations that means when a mutation happens, the fitness would normally be low but because there is fitness sharing, the individual has the time to optimize its weights to adapt to this new structural change. 

It promotes diversity among the individuals because the bigger the species, the more is the fitness shared and the less fit are the members of the species.

If you wish to learn more about the NeuroEvolution of Augmenting Topologies the visit this Neural Network Tutorial.

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