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Artificial neural networks revolutionized many areas of computer science inrecent years since they provide solutions to a number of previously unsolvedproblems. On the other hand, for many problems, classic algorithms exist, whichtypically exceed the accuracy and stability of neural networks. To combinethese two concepts, we present a new kind of neural networks$-$algorithmicneural networks (AlgoNets). These networks integrate smooth versions of classicalgorithms into the topology of neural networks. A forward AlgoNet includesalgorithmic layers into existing architectures while a backward AlgoNet cansolve inverse problems without or with only weak supervision. In addition, wepresent the $\texttt{algonet}$ package, a PyTorch based library that includes,inter alia, a smoothly evaluated programming language, a smooth 3D meshrenderer, and smooth sorting algorithms.

AlgoNet: $C^\infty$ Smooth Algorithmic Neural Networks