Iso-Riemannian Optimization on Learned Data Manifolds

[1] W. Diepeveen, M. Weber.  
Iso-Riemannian Optimization on Learned Data Manifolds.
arXiv preprint arXiv:2510.21033. 2025 Oct 23.

Setup

The recommended (and tested) setup is based on Python 3.13. Install the following dependencies with anaconda:

# Create conda environment
conda create --name iso-riem-opt python=3.13
conda activate iso-riem-opt

# Clone source code and install
git clone https://github.com/Weber-GeoML/Iso-Riem-Opt.git
cd "Iso-Riem-Opt"
pip install -r requirements.txt

Reproducing the experiments in [1]

To produce the results in [1].

• For the iso-barycentre and iso-K-means experiments run:
  • r2_river_bary.ipynb for the river data set experiments under modeled pullback geometry,
  • r2_spiral_bary.ipynb for the spiral data set experiments under modeled pullback geometry,
  • mnist_additive_nflow_bary.ipynb for the MNIST data set experiments under learned pullback geometry.
• For iso-convex optimization over geodesic submanifold experiments run:
  • r2_banana_least_squares.ipynb for the modeled banana manifold experiments,
  • mnist_additive_nflow_least_squares.ipynb for the learned MNIST manifold experiments.