Critical points of the Sliced-Wasserstein objective are characterized via a barycentric equation, and any critical point containing a segment is shown to be unstable in dimension two.
Sliced and radon wasserstein barycenters of measures
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Towards Understanding Gradient Dynamics of the Sliced-Wasserstein Distance via Critical Point Analysis
Critical points of the Sliced-Wasserstein objective are characterized via a barycentric equation, and any critical point containing a segment is shown to be unstable in dimension two.