NNexpy (A bunch of python script and classes to experiment with homology, knot theory and neural networks)

Introduction

This repository is a compilation of my work during my master course at Kyushu Institute of Technology. A clone of the repository is also available on KIT Honda Lab's github. The purpose of this repository is to provide with some python code to get started with homology and knot theory as a mean to evaluate neural networks' expressiveness.

Requirement

To run this code you need python3 as well as some libraries. They can be installed using Conda and I personally used a conda environment which environment file is available in this repository.

To setup a functional conda environment with conda cli you simply need to use the following command:

conda env create -f environment.yml
conda activate nexpy

For more information refer to conda documentation and in particular the section about managing environment

Usage

To use this code, copy the nnexpy folder in your python project and import nnexpy

import nnexpy

NNexpy contains the following classes:

• Bounds
• DataDescriptor
• DataInstance
• DataPoint
• KnotDescriptor
• NetworkGenerator
• RandomNetwork

Examples

The examples folder is a collection of the various scripts I have been creating during my research. Here follows a short description of all of them.

• ai_playground.py: Generates a few DataInstance with different homology and then call rasScript to train batch of networks on these different datasets.
• analyse_network.py: Computes betti numbers and makes the PCA to obtain a trajectory from Keras + Tensorflow neural network.
• bettiScript.py: Computes Betti numbers of Keras + Tensorflow neural networks on a DataDescriptor
• oldBottleneckScript.py: Computes Betti numbers of Keras + Tensorflow neural networks on a DataDescriptor
• compare_results.py: Script to use bettiScript, oldBettiScript and oldBottleneckScript as subprocesses
• oldBettiScript.py: Another version of betti number computation of Keras + Tensorflow neural networks on a DataDescriptor
• rasScript.py: Trains a Keras + Tensorflow neural network on a given DataInstance
• test_random_networks.py: Generate PCA of random networks with an input trajectory
• visualize_results.py: Plot the predicted data of Keras + Tensorflow networks on a DataInstance