Artificial neural networks revolutionized many areas of computer science in recent years since they provide solutions to a number of previously unsolved problems.
 On the other hand, for many problems, classic algorithms exist, which typically exceed the accuracy and stability of neural networks.
 To combine these two concepts, we present a new kind of neural networks—algorithmic neural networks (AlgoNets).
 These networks integrate smooth versions of classic algorithms into the topology of neural networks.
 Our novel reconstructive adversarial network (RAN) enables solving inverse problems without or with only weak supervision.
Solving inverse problems by using smooth approximations of the forward algorithms to train the inverse models.