Competing conventions problem: Having more than one way to express a solution to a weight optimization problem with a neural network.
When two networks have have a solution to a (sub-)problem, but different encodings “conventions” for it, a resulting crossover is likely to produce damaged “offspring”.
The two networks compute the same exact function even though their hidden units appear in a different order and are represented by different chromosomes, making them incompatible for crossover. The figure shows that the two single-point recombinations are both missing one of the 3 main components of each solution. The depicted networks are only 2 of the 6 possible permutations of hidden unit orderings.
Similarily, taking the euclidian distance of the network’s parameters would wrongly indicate that they’re different.
Generally speaking, parameter/function mappings are usually not injective, because many different parameter configurations can lead to the same function.
NEAT addresses this problem by tracking the ancestry of edge genes with an innovation number.
map-elites addresses this problem by having different subpopulations, each specialized on a different part of the solution space, differentiated by behavior not genotype.