On the Optimisation Landscape of Overparameterised Weighted MMD
We study the optimisation landscape of the maximum mean discrepancy (MMD) over weighted atomic measures. For the one-dimensional Gaussian kernel, we show that, for any compactly supported target distribution, sufficiently many particles ensure that every local minimum has arbitrarily small MMD. Moreover, any stationary point whose MMD remains bounded away from zero is unstable under an unweighted gradient flow over the particle locations. These results hold both when the weights are constrained to the simplex, and when they are unconstrained but optimised at each step. When the target is itself finitely supported, we further strengthen this result: beyond an explicit particle threshold, t...
| Authors | Tharrshann Jayan Logarajah, Jeremias Knoblauch, Louis Sharrock |
|---|---|
| Primary category | stat.ML |
| Published | 14 October 2026 |
| Last updated at source | 14 October 2026 |
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 15 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.