Structural Incompatibility of Differentiable Sorting and Within-Vector Rank Normalization
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915859937624064 |
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| author | Kim, Taeyun |
| author_facet | Kim, Taeyun |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22587 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Structural Incompatibility of Differentiable Sorting and Within-Vector Rank Normalization Kim, Taeyun Machine Learning 62G30 (Primary), 68T07 (Secondary) 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. |
| title | Structural Incompatibility of Differentiable Sorting and Within-Vector Rank Normalization |
| topic | Machine Learning 62G30 (Primary), 68T07 (Secondary) |
| url | https://arxiv.org/abs/2512.22587 |