neural-semigroups

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Neural Semigroups

The project is abandoned.

If you want to reproduce results from the paper <https://arxiv.org/abs/2103.07388>, please use this notebook <https://colab.research.google.com/github/inpefess/neural-semigroups/blob/master/examples/train_a_model.ipynb>.

Here we try to model Cayley tables of semigroups using neural networks.

This work was inspired by a sudoku solver <https://github.com/Kyubyong/sudoku>__. A solved Sudoku puzzle is nothing more than a Cayley table of a quasigroup from 9 items with some well-known additional properties. So, one can imagine a puzzle made from a Cayley table of any other magma, e.g. a semigroup, by hiding part of its cells.

There are two major differences between sudoku and puzzles based on semigroups:

1. it’s easy to take a glance on a table to understand whether it is a sudoku or not. That’s why it was possible to encode numbers in a table cells as colour intensities. Sudoku is a picture, and a semigroup is not. It’s difficult to check a Cayley table’s associativity with a naked eye;

2. Sudoku puzzles are solved by humans for fun and thus catalogued. When solving a sudoku one knows for sure that there is a unique solution. On the contrary, nobody guesses values in a partially filled Cayley table of a semigroup as a form of amusement. As a result, one can create a puzzle from a full Cayley table of a semigroup but there may be many distinct solutions.

How to Install

The best way to install this package is to use pip:

.. code:: sh

pip install neural-semigroups

How to use

The simplest way to get started is to use Google Colaboratory <https://colab.research.google.com/github/inpefess/neural-semigroups/blob/master/examples/dae_4_colab.ipynb>__.

To look at more experimental results for different semigroups cardinalities, you can use Kaggle <https://kaggle.com>__:

• cardinality 4 <https://www.kaggle.com/inpefess/neural-semigroups-dae-dim-4>__
• cardinality 5 <https://www.kaggle.com/inpefess/neural-semigroups-dae-dim-5>__

There is also an experimental notebook <https://github.com/inpefess/neural-semigroups/blob/master/examples/ExperimentNotebook.ipynb>__ contributed by Žarko Bulić <https://github.com/zarebulic>__.

How to Contribute

Pull requests <https://github.com/inpefess/neural-semigroups/pulls>__ are welcome. To start:

.. code:: sh

git clone https://github.com/inpefess/neural-semigroups cd neural-semigroups

activate python virtual environment with Python 3.6+

pip install -U pip pip install -U setuptools wheel poetry poetry install

recommended but not necessary

pre-commit install

To check the code quality before creating a pull request, one might run the script show_report.sh <https://colab.research.google.com/github/inpefess/neural-semigroups/blob/master/show_report.sh>__. It locally does nearly the same as the CI pipeline after the PR is created.

Reporting issues or problems with the software

Questions and bug reports are welcome on the tracker <https://github.com/inpefess/neural-semigroups/issues>__.

More documentation

More documentation can be found here <https://neural-semigroups.readthedocs.io/en/latest>__.

.. |Open In Colab| image:: https://colab.research.google.com/assets/colab-badge.svg :target: https://colab.research.google.com/github/inpefess/neural-semigroups/blob/master/examples/dae_4_colab.ipynb .. |PyPI version| image:: https://badge.fury.io/py/neural-semigroups.svg :target: https://badge.fury.io/py/neural-semigroups .. |CircleCI| image:: https://circleci.com/gh/inpefess/neural-semigroups.svg?style=svg :target: https://circleci.com/gh/inpefess/neural-semigroups .. |Documentation Status| image:: https://readthedocs.org/projects/neural-semigroups/badge/?version=latest :target: https://neural-semigroups.readthedocs.io/en/latest/?badge=latest .. |codecov| image:: https://codecov.io/gh/inpefess/neural-semigroups/branch/master/graph/badge.svg :target: https://codecov.io/gh/inpefess/neural-semigroups