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

arXiv: https://arxiv.org/abs/2607.28755 · HTML: https://mlsanity.com/paper/2607.28755/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 40 references that are in the map.
- First posted on arXiv 30 Jul 2026.

## Builds on (most cited first, 21 of 21)

- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [Git Re-Basin: Merging Models modulo Permutation Symmetries](https://mlsanity.com/paper/2209.04836/) (2022)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [Frame Averaging for Invariant and Equivariant Network Design](https://mlsanity.com/paper/2110.03336/) (2021)
- [Similarity of Neural Network Models: A Survey of Functional and Representational Measures](https://mlsanity.com/paper/2305.06329/) (2023)
- [Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances](https://mlsanity.com/paper/2105.12221/) (2021)
- [Geoopt: Riemannian Optimization in PyTorch](https://mlsanity.com/paper/2005.02819/) (2020)
- [Residual Pathway Priors for Soft Equivariance Constraints](https://mlsanity.com/paper/2112.01388/) (2021)
- [geomstats: a Python Package for Riemannian Geometry in Machine Learning](https://mlsanity.com/paper/1805.08308/) (2018)
- [On the Symmetries of Deep Learning Models and their Internal Representations](https://mlsanity.com/paper/2205.14258/) (2022)
- [NNsight and NDIF: Democratizing Access to Open-Weight Foundation Model Internals](https://mlsanity.com/paper/2407.14561/) (2024)
- [The Topology ToolKit](https://mlsanity.com/paper/1805.09110/) (2018)
- [A Canonicalization Perspective on Invariant and Equivariant Learning](https://mlsanity.com/paper/2405.18378/) (2024)
- [The Topology and Geometry of Neural Representations](https://mlsanity.com/paper/2309.11028/) (2023)
- [Geometry of Decision Making in Language Models](https://mlsanity.com/paper/2511.20315/) (2025)
- [Parametric information geometry with the package Geomstats](https://mlsanity.com/paper/2211.11643/) (2022)
- [Learning from landmarks, curves, surfaces, and shapes in Geomstats](https://mlsanity.com/paper/2406.10437/) (2024)

## Abstract (arXiv)

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.