CorrFlow: Exact and Permutation-Equivariant Flow Matching on the Correlation Elliptope

Key points

• We introduce CorrFlow, which separates them.1
• A graph flow-matching network learns the empirical distribution in those coordinates and is permutation equivariant: reordering the variables only reorders the output.1
• We compare a conditional CorrGAN reimplementation, image diffusion, and CorrFlow on $80\times80$ Taiwan equity matrices using five seeds per neural method.1
• CorrFlow produces 100% valid draws without repair and obtains feature sliced-Wasserstein distance $.712\pm.141$, versus $4.339\pm.252$ for CorrGAN and $4.610\pm.191$ for image diffusion after their invalid outputs are projected back to the correlation space.1

Sources (1)

• [1]CorrFlow: Exact and Permutation-Equivariant Flow Matching on the Correlation Elliptope
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 9, 01:53 PM

  Correlation matrices combine nonlinear positive-definiteness constraints with a simultaneous row-column permutation symmetry.

  We introduce CorrFlow, which separates them.

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