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

## TL;DR

AlgoNet introduces a novel neural network framework that integrates smooth versions of classic algorithms into neural architectures, enabling improved stability and inverse problem solving.

## Contribution

This paper presents AlgoNet, a new class of neural networks that embed smooth algorithmic layers, along with a PyTorch library for practical implementation.

## Key findings

- Enhanced stability and accuracy in neural networks with algorithmic layers
- Ability to solve inverse problems with weak supervision
- Provision of a PyTorch library for smooth algorithmic components

## Abstract

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. A forward AlgoNet includes algorithmic layers into existing architectures while a backward AlgoNet can solve inverse problems without or with only weak supervision. In addition, we present the $\texttt{algonet}$ package, a PyTorch based library that includes, inter alia, a smoothly evaluated programming language, a smooth 3D mesh renderer, and smooth sorting algorithms.