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A Neural Network for Semigroups

Abstract : Tasks like image reconstruction in computer vision, matrix completion in recommender systems and link prediction in graph theory, are well studied in machine learning literature. In this work, we apply a denoising autoencoder-based neural network architecture to the task of completing partial multiplication (Cayley) tables of finite semigroups. We suggest a novel loss function for that task based on the algebraic nature of the semigroup data. We also provide a software package for conducting experiments similar to those carried out in this work. Our experiments showed that with only about 10% of the available data, it is possible to build a model capable of reconstructing a full Cayley from only half of it in about 80% of cases.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03175811
Contributor : Boris Shminke <>
Submitted on : Sunday, March 21, 2021 - 1:49:59 PM
Last modification on : Thursday, June 3, 2021 - 10:30:02 AM

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Distributed under a Creative Commons Attribution 4.0 International License

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  • HAL Id : hal-03175811, version 1
  • ARXIV : 2103.07388

Citation

Edouard Balzin, Boris Shminke. A Neural Network for Semigroups. 2021. ⟨hal-03175811⟩

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