Learning Unbiased Permutations via Flow Matching
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Computer Science > Machine Learning
Title:Learning Unbiased Permutations via Flow Matching
Abstract:Learning permutations is fundamental to sorting, ranking, and matching, but existing differentiable methods based on entropy-regularized Sinkhorn produce a single softened solution and collapse under ambiguity. We present PermFlow, a conditional flow matching framework that operates directly on the affine subspace of matrices with unit row and column sums. A closed-form tangent-space projector preserves these constraints exactly along every trajectory, by construction rather than through iterative correction, and a nearest-target coupling routes distinct noisy initializations toward distinct valid permutations. The result is a model that captures multimodal permutation distributions rather than collapsing them to a single mode. On a visual sorting task with blended-digit ambiguity and a symmetric linear assignment problem, PermFlow achieves high accuracy on unambiguous inputs and recovers both valid permutations under ambiguity, where Sinkhorn-based baselines structurally fail.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2605.16755 [cs.LG] |
| (or arXiv:2605.16755v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.16755
arXiv-issued DOI via DataCite (pending registration)
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