Discrete neural nets

This repo 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 on the arXiv.

Git workflow

1) Fork main repo (https://github.com/caten2/Tripods2021UA). This is different than just cloning. There is a button on GitHub for this. 2) Clone your fork to your machine. 3) Make a branch on your machine. 4) At any time, you can push your changes to your personal fork of the repo. 5) On your machine, pull from the main repo's main branch. 6) On your machine, merge the main branch into your new branch. 7) Resolve any conflicts that arise, then merge your new branch into the main branch. 8) Push your work to your personal fork of the repo. 9) Make a pull request to pull your fork's main into the original repo's main.

Project structure

In the lists which follow, scripts marked with (ORGANIZE) are not part of the current, functioning implementation. These may be in the process of refactoring or being reorganized into another part of the repo.

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.
• binary_image_polymorphisms.py: Definitions of polymorphisms of the Hamming graph, as well as a neighbor function for the learning algorithm implemented in neural_net.py. (ORGANIZE)
• neural_net.py: Definition of the NeuralNet class, including feeding forward and learning.
• dominion.py: Tools for creating dominions, a combinatorial object used in the definition of the dominion polymorphisms in polymorphisms.py. (ORGANIZE)
• hyperoctohedral.py: Definitions of polymorphisms of the Hamming graph which come from the action of the hyperoctahedral group. (ORGANIZE)
• 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.
• 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 randomly-chosen architectures and activation functions.
• relations.py: Definitions pertaining to the Relation class, whose objects are relations in the sense of model theory.
• test.py: A test script which should be moved to the tests directory. (ORGANIZE)

The scripts that run various tests and example applications of the system are in the tests folder. These are:

• Those in the subdirectory binary_relation_polymorphisms: (Add description.)
• example_dominion.py: (Add description.) (ORGANIZE)
• test_binary_image_train_gAlpha.py: (Add description.) (ORGANIZE)
• test_binary_relation_polymorphisms: Examples of the basic functionality for the polymorphisms defined in polymorphisms.py when applied to binary relations.
• test_dominion.py: (Add description.) (ORGANIZE)
• test_gAlpha.py: (Add description.) (ORGANIZE)
• test_mnist_training_binary.py: Verification that MNIST training data is being loaded correctly from the training dataset.
• test_neural_net.py: Examples of creating NeuralNets using activation functions from arithmetic_operations.py and the RandomOperation from random_neural_net.py.
• test_polymorphism_relation.py: (Add description.) (ORGANIZE)
• test_relations.py: Examples of the basic functionality for the Relations defined in relations.py.

Environment

Make sure that the scripts in tests can import from scripts in src. In PyCharm this is accomplished most easily by going to Settings -> Project Structure and making sure that src is set as a "source" folder.