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Presumably the neural network was trained on a dataset where all planes had two wings, so it will predict planes with two wings.

Yeah, there's definitely some previous knowledge of the kinds of objects it's inferring, which is used to deduce the parts.

Look at the chairs' legs, where it's transforming the flat base of the rotating chair into something that looks as wheels, and where it's completely missing the bars connecting the legs in the second tall chair.

Maybe it involves machine learning also and it is able to tell that it's looking at an aeroplane?

It looks like the algorithm expects symmetry.