Machine learning modularity

This repository provides the official implementation for the paper "Machine learning modularity". The project explores the application of machine learning architectures to identify and simplify complex mathematical structures, specifically focusing on Möbius transformations, $q-\theta$ functions, and elliptic $\Gamma$ functions.

Project Architecture

The codebase is organized into three primary modules, each corresponding to a specific section of the research:

1. Domain Reduction

Focus: Machine Learning Möbius Transformations.

• Objective: Given a complex point located outside the fundamental domain, the model predicts a matrix such that the modular action maps the point back into the fundamental domain.
• Location: /domain_reduction

2. $q-\theta$ Simplification

Focus: Machine Learning for $q-\theta$ Functions.

• Objective: The model identifies patterns within symbolic expressions of - products and reduces them to their minimal, simplified forms.
• Location: /q_theta_simplify

3. Elliptic Gamma Simplification

Focus: Machine Learning the Elliptic Gamma Function.

• Objective: This module handles elliptic gamma expressions following specific identities, training the model to transform them into a canonical or simplified representation.
• Location: /elliptic_gamma_simplify

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Quick Start Guide

1. Environment Setup

Install the necessary dependencies using pip:

pip install -r requirements.txt

2. Model Weights

To run the inference or evaluation scripts, you must download the pre-trained model weights:

1. Download: Access the weight files via Google Drive.
2. Extraction: After downloading, extract the archives.
3. Placement: Move the extracted model files into their respective directory structures.

3. Execution

Navigate to the desired module folder to begin:

• quick start: Open and run the demo.ipynb notebooks for interactive demonstrations.