Can a neural network be used to find the genus of a 2-manifold given for instance as a CW complex?

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    $\begingroup$ I don't know. Why don't you try it and see? It seems hard to imagine that a neural network will be the right way to solve this problem, but the only way to find out is to try the experiment and see what happens. $\endgroup$ – D.W. Jun 10 '18 at 17:19
  • $\begingroup$ Depends on the structure you are allowing the network to have. In principle, nets with most reasonable activation functions can approximate any function arbitrarily closely, given enough units in the network. $\endgroup$ – András Salamon Jun 30 '18 at 14:05

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