发现可微排序与向量内排名归一化存在根本冲突，影响模型稳定性。
Structural Incompatibility of Differentiable Sorting and Within-Vector Rank Normalization
- 通过单调不变性、批量独立性等三条件定义合理排序算子
- 软排序（SoftSort）和批处理排序（SinkhornSort）分别违反前两个条件
- 只有通过秩表示的李普希茨函数才可能满足全部约束
我们证明可微排序与排名算子在结构上与向量内秩归一化不相容。通过单调不变性（C1）、批量独立性（C2）和秩空间稳定性（C3）三个条件形式化合理性。温度敏感的松弛方法如 SoftSort 在量化上违反（C1），其程度取决于温度和输入尺度；批处理式松弛如 SinkhornSort 违反（C2）：同一样本在不同批量中可被映射至任意接近 0 或 1 的输出。条件（C3）在此秩表示下蕴含（C1），不应视为独立失效模式。我们进一步刻画了可接受算子类：任何合法算子必须通过秩表示并经由一个李普希茨函数实现。
原文摘要 · Abstract (English)
We show that differentiable sorting and ranking operators are structurally incompatible with within-vector rank normalization. We formalize admissibility through monotone invariance (C1), batch independence (C2), and a rank-space stability condition (C3). Gap-sensitive relaxations such as SoftSort violate (C1) by a quantitative margin that depends on the temperature and input scale. Batchwise rank relaxations such as SinkhornSort violate (C2): the same sample can be assigned outputs arbitrarily close to 0 or 1 depending solely on batch context. Condition (C3) implies (C1) under the rank representation used here and should not be read as a third independent failure mode. We also characterize the admissible class: any admissible operator must factor through the rank representation via a Lipschitz function.
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