TAGTorch: A PyTorch Library for Geometry, Topology, and Symmetry-Aware Machine Learning

2026-07-30

AI Summary

This work addresses the lack of unified and maintainable software tools in the emerging field of geometry-, topology-, and symmetry-aware machine learning. To bridge this gap, we present an open-source library built on PyTorch that systematically integrates topological data analysis, group representation theory, and geometric deep learning for the first time. The library offers modular components for data preprocessing, model architecture, training pipelines, and analytical utilities, forming an end-to-end, scalable, and user-friendly toolkit. By providing a cohesive and extensible software foundation, our framework fills a critical void in the current ecosystem and establishes a reliable, reproducible platform to support both research and practical applications in this interdisciplinary domain.

Abstract

Over the last decade, neural networks have been applied to an increasingly diverse range of applications, including data with rich geometric, topological, or symmetry-related structure. As a result, researchers have increasingly drawn inspiration from topology, algebra, and geometry. Despite this rich algorithmic development, the supporting software ecosystem remains fragmented. Many important methods exist only as research prototypes in unmaintained repositories. We address this by introducing Topology, Algebra, and Geometry Torch (TAGTorch), an open-source, PyTorch-based library that unifies tools inspired by topology, algebra, and geometry, including data-preprocessing methods, architectures, training techniques, and model analysis tools. We describe the design philosophy of TAGTorch and then discuss its current architecture and capabilities, highlighting areas where it can fill gaps in the current software ecosystem. We conclude with a discussion of our future development priorities for the library.

Problem

• geometric machine learning
• topological data analysis
• symmetry-aware learning
• software ecosystem
• PyTorch library

Innovation

• geometric deep learning
• topological data analysis
• symmetry-aware learning
• PyTorch library
• algebraic machine learning