提出新方法让模型同时学习多个正确排列，突破传统方法只能输出单一结果的局限。
Learning Unbiased Permutations via Flow Matching
- 基于流匹配，在保持行列和为1的约束下直接建模排列空间
- 在模糊输入下可同时恢复两个正确排列，准确率显著优于基线
- 适合需要多解推理的排序、匹配任务，如模糊图像排序
学习排列是排序、排名和匹配的基础，但现有的基于熵正则化Sinkhorn的可微方法仅产生单一软化解，在模糊情况下会坍缩。我们提出PermFlow，一种在具有单位行和列和的矩阵仿射子空间上运行的条件流匹配框架。通过闭式切空间投影器，精确保持每条轨迹上的约束，而非依赖迭代修正；最近目标耦合机制将不同噪声初始化引导至不同有效排列。结果是模型能捕捉多模态排列分布，而非将其坍缩为单一模式。在包含混合数字模糊性的视觉排序任务和对称线性分配问题上，PermFlow在无歧义输入上实现高准确率，并在模糊情况下恢复两个有效排列，而基于Sinkhorn的基线方法结构上失效。
原文摘要 · Abstract (English)
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.
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