Direct fixed-weight solver for free-support Wasserstein medians relocates atoms using OT barycentric projections and inverse-distance weights, achieving monotone descent on smoothed objectives with fewer subproblems than nested Weiszfeld baselines.
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CROSS replaces globally consistent metric maps with a pose-aware topological graph of RGB-D keyframes and maintains a bounded Gaussian-mixture belief over poses via sequential hypothesis testing in SE(3) to achieve change-robust spatial-semantic mapping and navigation.
A review reframing density estimation as 'density evolution' across scales, linking kernel smoothing to heat flow, mixtures to compression, and topology to level sets, while stating three structural results on modes, Gaussian semigroups, and log-concavity.
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