kappakit 0.1.0

Estimating the curvature of a manifold from data

KappaKit: Curvature Estimation on Data Manifolds with Diffusion-Augmented Sampling

kappakit is a Python library for estimating the curvature of a data manifold.

Curvature is the fundamental descriptor of local geometry—useful in shape analysis, learning theory, and non-Euclidean algorithms—yet it proves elusive to estimate on sparse, noisy data.

KappaKit offers a modular base framework for various curvature estimation methods. In particular, it supports training diffusion models via the HuggingFace API to increase the sample density for downstream estimation methods.

Installation

From pip:

pip install kappakit

From source:

git clone https://github.com/Weber-GeoML/kappakit.git
pip install -e .

Usage

This repository contains the experiment scripts to reproduce the paper Curvature Estimation on Data Manifolds with Diffusion-Augmented Sampling. If you use this repository, please use this paper as the citation.

You can reproduce the experiments by running scripts/experiments/all.sh. The figures in the paper were generated with scripts/experiments/generate_figures.ipynb.

A curvature estimation experiment may invoke the following routines in order:

1. kappakit.routines.create_dataset
2. kappakit.routines.train_diffusion_model
3. kappakit.routines.estimate_curvature

Please refer to the documentation for the API reference as well as tutorials on how to use or expand this codebase.