Has anyone thought about making a neural network ask questions, instead of only answering them? Most of the people is trying to answer question with a neural network. However, has anyone came up with some thoughts about how to make neural network ask questions, instead of answer questions? For example, if a CNN can decide which category an object belongs to, than can it ask some question to help the the classification?
Maybe neural networks are not the best tool for this.

It seems to me that an equivalent of the your notion of 'a question to help the classification' would be to use Machine Learning (ML) to obtain a human-readable ruleset which performs the classification. The idea is that, if you follow an applicable chain of rules all the way through to the end, you have a classifier, if you stop before that, you have an indicator of which features of the input give more coarse-grained classifications, which can be seen as a progressively detailed sequence of questions that 'help the classification'.



More detail on various options for using ML to create rulesets can be found in my answer to this question.