Neural nets don't generalize much, they interpolate between training examples. But if you couple them with search (MCTS) then you can do logic and reasoning with them, like AlphaGo.

You can also put any algorithm you want inside a neural net as long as you have a mechanism to pass gradients back - for example in the final layer you could have a complex graph-matching algorithm to map the predictions to the target, or you could put an ODE solver as a layer, or a logic engine, or a database.