# Coreset selection for the Sinkhorn divergence and generic smooth divergences

arXiv: https://arxiv.org/abs/2504.20194 · HTML: https://mlsanity.com/paper/2504.20194/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Apr 2025.

## Built on by (most cited first, 4 of 4)

- [FlashSinkhorn: IO-Aware Entropic Optimal Transport on GPU](https://mlsanity.com/paper/2602.03067/) (2026)
- [Local EGOP for Continuous Index Learning](https://mlsanity.com/paper/2601.07061/) (2026)
- [Sinkhorn Treatment Effects: A Causal Optimal Transport Measure](https://mlsanity.com/paper/2605.08485/) (2026)
- [Low-Budget Active Learning through Entropic Optimal Transport](https://mlsanity.com/paper/2610.01199/) (2026)

## Abstract (arXiv)

We introduce CO2, an efficient algorithm to produce convexly-weighted coresets with respect to generic smooth divergences. By employing a functional Taylor expansion, we show a local equivalence between sufficiently regular losses and their second order approximations, reducing the coreset selection problem to maximum mean discrepancy minimization. We apply CO2 to the Sinkhorn divergence, providing a novel sampling procedure that requires poly-logarithmically many data points to match the approximation guarantees of random sampling. To show this, we additionally verify several new regularity properties for entropically regularized optimal transport of independent interest. Our approach leads to a new perspective linking coreset selection and kernel quadrature to classical statistical methods such as moment and score matching. We showcase this method with a practical application of subsampling image data, and highlight key directions to explore for improved algorithmic efficiency and theoretical guarantees.