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name: barycenters description: "Fixed-support, free-support, entropic, debiased, convolutional, and sample-cloud Wasserstein barycenter workflows." disable-model-invocation: true metadata: disco-role: operating license: MIT

POT barycenters

Use this sub-skill when a task asks for a Wasserstein barycenter on a fixed grid, a moving/free support barycenter, a debiased or convolutional image barycenter, or a sample-cloud barycenter with POT.

Read references/api-reference.md when choosing the correct barycenter API, checking signatures, or validating shapes and return fields.

Read references/workflows.md when deciding between fixed-support histograms, free-support point clouds, convolutional images, and solve_bary_sample workflows.

Read references/troubleshooting.md when barycenters have unexpected mass, convergence warnings, shape errors, LP solver issues, or confusing sample-cloud behavior.

Run scripts/barycenter_smoke.py to check a local POT install against deterministic tiny barycenter fixtures before adapting a workflow.

Route quickly

• Shared histogram grid: use ot.bregman.barycenter for entropic barycenters, ot.bregman.barycenter_debiased when entropic blur is a concern, or ot.lp.barycenter for tiny exact LP barycenters.
• Moving support with explicit point-cloud measures: use ot.lp.free_support_barycenter for exact 2-Wasserstein support updates or ot.bregman.free_support_sinkhorn_barycenter for entropic support updates.
• Unequal-size sample clouds where the barycenter support itself must be optimized: use ot.solvers.solve_bary_sample and inspect its BaryResult.
• Image stacks on a regular grid: use ot.bregman.convolutional_barycenter2d or ot.bregman.convolutional_barycenter2d_debiased.
• Graph/structured GW or FGW barycenters belong in the gromov sub-skill. Gaussian and GMM barycenters belong primarily in the sliced-gaussian-large-scale sub-skill, with only cross-link notes here.

Stay in scope

This sub-skill covers barycenter setup, shape validation, convergence recovery, and tiny self-checks. It does not teach core EMD/Sinkhorn theory, Gromov-Wasserstein barycenter internals, or Gaussian/GMM distribution-family modeling beyond routing hints.