Accepted to ICML 2026
ITSPACE is a certified few-step Gaussian optimal transport method for low-rank covariance alignment, with closed-form Bures-Wasserstein updates, PSD/rank preservation, and monotone descent guarantees.
Covariance matrices serve as compact descriptors of feature distributions in many machine-learning pipelines, including domain adaptation and Gaussian embeddings. Under a centered Gaussian approximation, the unregularized Wasserstein-2 optimal-transport discrepancy admits a closed form on covariances given by the Bures-Wasserstein objective. ITSPACE directly optimizes this exact objective through closed-form updates in a square-root factorization, preserving PSD structure and supporting rank-restricted factors.
The Bures-Wasserstein covariance objective becomes a quadratic term minus a nuclear norm under a low-rank square-root factorization. A polar/Procrustes certificate gives a tight linear minorization, leading to a closed-form proximal majorization-minimization update.
ITSPACE targets settings where covariance states must be updated in only a few valid steps under strict compute budgets, such as domain adaptation, representation drift correction, whitening-recoloring modules, normalization, Gaussian embeddings, and covariance-aware model adaptation.
The repository contains a clean reusable implementation, a minimal example, and the ICML paper reproduction scripts.
git clone https://github.com/itsmeuniverse/itspace.git
cd itspace
pip install -e .
python examples/minimal.py@inproceedings{na2026itspace,
title = {ITSPACE: Monotone Gaussian Optimal Transport Updates},
author = {Na, Woojoo and Dy, Jennifer},
booktitle = {Proceedings of the 43rd International Conference on Machine Learning},
year = {2026}
}