Some neural networks compute, others don't

I address whether neural networks perform computations in the sense of computability theory and computer science. I explicate and defend the following theses. (1) Many neural networks compute--they perform computations. (2) Some neural networks compute in a classical way. Ordinary digital computers, which are very large networks of logic gates, belong in this class of neural networks. (3) Other neural networks compute in a non-classical way. (4) Yet other neural networks do not perform computations. Brains may well fall into this last class.