This library provides approximate implementations of popcount and popcount-compare circuits. Moreover, it provides a sketch of how to use it to approximate a TNN neural network. The library consists of hardware and software models of approximate circuits that are designed to be easily used in arbitrary applications.

This library is licensed under MIT license. If you use the library in your research, please refer to the following paper:

MRAZEK Vojtech, KOKKINIS Argyrios, PAPANIKOLAOU Panagiotis, VASICEK Zdeněk, SIOZIOS Kostas, TZIMPRAGOS Georgios, TAHOORI Mehdi and ZERVAKIS Georgios. Evolutionary Approximation of Ternary Neurons for On-sensor Printed Neural Networks. In: 2024 IEEE/ACM International Conference on Computer Aided Design (ICCAD). New Jersey, 2024, p. 9. doi: 10.1145/3676536.3676728

@INPROCEEDINGS{tnns:iccad19,
   author = "Vojtech Mrazek and Argyrios Kokkinis and Panagiotis Papanikolaou and Zdenek Vasicek and Kostas Siozios and Georgios Tzimpragos and Mehdi Tahoori and Georgios Zervakis",
   title = "Evolutionary Approximation of Ternary Neurons for On-sensor Printed Neural Networks",
   pages = 9,
   booktitle = "2024 IEEE/ACM International Conference on Computer Aided Design (ICCAD)",
   year = 2024,
   location = "New Jersey, US",
   doi = "10.1145/3676536.3676728",
   }

This repository shows the Verilog approximate implementations of two mathematic operations: popcount ($pc(a) = \sum_{\forall x \in A} {x}$) and binary relation operator popcount-compare ( $pc(a) \geq pc(b)$ ).

For more details, please see the original paper.

See the following folders with the results:

• pc-circuits approximate implementation of circuits realizing popcount operation used in PCCs and in the neurons in the output layer
• pcc-circuits approximate implementation of circuits realizing popcount-compare used in the neurons of hidden layer
• moo multiobjective optimization of TNNs by assignment of the components to the TNNs