Synoros-io

Synoros-io / holonomy_lib

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Research-grade PyTorch math: differential geometry, spectral graph theory, discrete Ricci flow, simplicial topology, persistent homology, cellular sheaves, SO(3) Lie primitives, information geometry, tensor decompositions, content-addressable provenance. GPU-native, batched-first, audit-clean, cited.

doi.org10.5281zenodo.20451005 cellular-sheaves differential-geometry directed-graphs geometric-deep-learning gpu-computing
14
1
94% credibility
Found Jun 02, 2026 at 14 stars -- GitGems finds repos before they trend. Get early access to the next one.
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AI Analysis
Python
AI Summary

holonomy_lib is a comprehensive research-grade PyTorch library that unifies advanced mathematical tools for machine learning: Riemannian manifolds (hyperbolic, spherical, Euclidean, and mixed-curvature spaces), spectral graph theory, discrete geometry (Ricci curvature, Ricci flow), persistent homology, information geometry, and content-addressable provenance tracking. It is GPU-native, batched-first, audit-clean (no undocumented constants), and every primitive is cited to the original research paper. The library is designed for researchers working at the intersection of differential geometry, spectral graph theory, computational topology, and mechanistic interpretability.

How It Works

1
💼 You need advanced math for your AI project

You discover that your machine learning project requires Riemannian geometry, hyperbolic embeddings, and spectral graph analysis -- math that existing libraries handle in pieces.

2
📈 You find one library that does everything

You discover holonomy_lib, which brings together differential geometry, spectral graph theory, persistent homology, and content-addressable provenance in a single, well-cited library.

3
🚀 You install it with one command

You run a simple installation command, and within seconds the library is ready on your GPU with all 12 modules available.

4
You choose your path
🏫
Work with curved spaces

You embed your data in hyperbolic space using the Lorentz manifold, or use the kappa-stereographic model that smoothly interpolates between spherical, flat, and hyperbolic geometries.

📌
Analyze graph structure

You compute Ollivier-Ricci curvature to find community boundaries, or run persistent homology to detect holes and connected components in your data.

5
💡 Your operations stay numerically clean

Every calculation is automatically checked for undocumented numerical constants, and all mathematical primitives cite the original research papers.

6
📝 You track where every result comes from

The built-in provenance system automatically records a complete history of every computation, so you can trace any result back through its entire chain of operations.

✨ Your research is rigorous and reproducible

You have GPU-accelerated access to research-grade mathematical primitives with full audit trails, making your work both powerful and trustworthy.

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AI-Generated Review

What is holonomy_lib?

Holonomy_lib is a research-grade Python library for advanced mathematical operations built on PyTorch. It bundles together differential geometry, spectral graph theory, computational topology, and mechanistic interpretability tools under one roof. The library gives you GPU-accelerated Riemannian geometry on manifolds like SPD matrices and hyperbolic spaces, spectral graph operations including multiple Laplacian variants, discrete Ricci curvature and flow, batched persistent homology, cellular sheaves, and SO(3) Lie group primitives. Every operation takes a leading batch dimension and runs on CUDA, ROCm, MPS, or CPU. The library also tracks content-addressable provenance for every computation, enabling TransformerLens-style activation patching and SAELens-style dataset emission for mathematical primitives.

Why is it gaining traction?

The library solves a real fragmentation problem. Researchers implementing hyperbolic embeddings, graph neural networks with spectral convolutions, or topological data analysis end up stitching together geoopt, geomstats, gudhi, ripser, and custom code. Holonomy_lib consolidates these domains with consistent API conventions and GPU-first design. The audit discipline is unusual: every numerical constant must be derived, a universal invariant, or experimentally tuned with documented scale-of-validity. The provenance system is the other hook. For mechanistic interpretability researchers, having a Merkle DAG of every math primitive enables substitution and replay experiments that were previously only possible on neural network internals.

Who should use this?

This is for ML researchers working at the intersection of geometry and learning. If you're implementing hyperbolic graph embeddings, training on SPD manifolds, or using topological features in your pipeline, this library replaces several dependencies with one consistent option. Researchers doing mechanistic interpretability work will find the provenance system directly useful. The AGPL license and small team mean enterprises should contact the copyright holder for commercial terms before embedding this in proprietary products.

Verdict

Holonomy_lib is a serious, well-tested library with 1187 passing tests and a rigorous approach to numerical correctness. The credibility score of 0.949999988079071% reflects a small but active project with thorough documentation and testing. The 14 stars indicate early-stage traction. If your research involves Riemannian optimization, spectral graph theory, or topological data analysis, this library is worth evaluating. The learning curve is steep for researchers outside these domains, but the cited primitives and audit discipline make it trustworthy for production research. Watch the roadmap for the v0.6 GPU persistent homology kernel if batched topological analysis is your bottleneck.

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