Initial commit

.gitignore

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+# Byte-compiled / optimized / DLL files
+__pycache__/
+*.py[cod]
+*$py.class
+
+# C extensions
+*.so
+
+# Distribution / packaging
+.Python
+build/
+develop-eggs/
+dist/
+downloads/
+eggs/
+.eggs/
+lib/
+lib64/
+parts/
+sdist/
+var/
+wheels/
+pip-wheel-metadata/
+share/python-wheels/
+*.egg-info/
+.installed.cfg
+*.egg
+MANIFEST
+
+# PyInstaller
+#  Usually these files are written by a python script from a template
+#  before PyInstaller builds the exe, so as to inject date/other infos into it.
+*.manifest
+*.spec
+
+# Installer logs
+pip-log.txt
+pip-delete-this-directory.txt
+
+# Unit test / coverage reports
+htmlcov/
+.tox/
+.nox/
+.coverage
+.coverage.*
+.cache
+nosetests.xml
+coverage.xml
+*.cover
+*.py,cover
+.hypothesis/
+.pytest_cache/
+
+# Translations
+*.mo
+*.pot
+
+# Django stuff:
+*.log
+local_settings.py
+db.sqlite3
+db.sqlite3-journal
+
+# Flask stuff:
+instance/
+.webassets-cache
+
+# Scrapy stuff:
+.scrapy
+
+# Sphinx documentation
+docs/_build/
+
+# PyBuilder
+target/
+
+# Jupyter Notebook
+.ipynb_checkpoints
+
+# IPython
+profile_default/
+ipython_config.py
+
+# pyenv
+.python-version
+
+# pipenv
+#   According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control.
+#   However, in case of collaboration, if having platform-specific dependencies or dependencies
+#   having no cross-platform support, pipenv may install dependencies that don't work, or not
+#   install all needed dependencies.
+#Pipfile.lock
+
+# PEP 582; used by e.g. github.com/David-OConnor/pyflow
+__pypackages__/
+
+# Celery stuff
+celerybeat-schedule
+celerybeat.pid
+
+# SageMath parsed files
+*.sage.py
+
+# Environments
+.env
+.venv
+env/
+venv/
+ENV/
+env.bak/
+venv.bak/
+
+# Spyder project settings
+.spyderproject
+.spyproject
+
+# Rope project settings
+.ropeproject
+
+# mkdocs documentation
+/site
+
+# mypy
+.mypy_cache/
+.dmypy.json
+dmypy.json
+
+# Pyre type checker
+.pyre/
+
+# Emacs
+.dir-locals.el
+.dir-locals.el~
+
+# PyCharm
+.idea/
+
+# Mac OS
+.DS_Store
+
+# Stored Trees, Dominions, and Homomorphisms
+Tree0/
+Tree1/
+Tree2/
+Tree3/
+test2.py
+
+# Stored trees and dominions
+output/

LICENSE

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+MIT License
+
+Copyright (c) 2025 Charlotte Aten
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

README.md

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+# Discrete neural nets
+This repository contains code and examples of implementing the notion of a
+discrete neural net and polymorphic learning in Python. For more information on
+these notions, see
+[the corresponding preprint](https://arxiv.org/abs/2308.00677) on the arXiv.
+
+### Project structure
+The scripts that define basic components of the system are in the `src` folder.
+These are:
+
+* `arithmetic_operations.py`: Definitions of arithmetic operations modulo some
+    positive integer. These are used to test the basic functionality of the
+    `NeuralNet` class.
+* `dominion.py`: Tools for creating dominions, a combinatorial object used in
+    the definition of the dominion polymorphisms in `polymorphisms.py`.
+* `dominion_setup.py`: Utilities for creating files of trees, dominions with
+    those trees as constraint graphs, and the data for the corresponding
+    polymorphisms.
+* `graphs.py`: Utilities for creating and storing simple graphs, including
+    randomly-generated trees.
+* `mnist_training_binary.py`: Describes how to manufacture binary relations
+    from the MNIST dataset which can be passed as arguments into the
+    polymorphisms in `polymorphisms.py`.
+* `neural_net.py`: Definition of the `NeuralNet` class, including feeding
+    forward and learning.
+* `operations.py`: Definitions pertaining to the `Operation` class, whose
+    objects are to be thought of as operations in the sense of universal
+    algebra/model theory.
+* `polymorphisms.py`: Definitions of polymorphisms of the Hamming graph, as
+    well as a neighbor function for the learning algorithm implemented in
+    `neural_net.py`.
+* `random_neural_net.py`: Tools for making `NeuralNet` objects with