mlsanityData to 14 Oct 2026

Structural Incompatibility of Differentiable Sorting and Within-Vector Rank Normalization

arXiv 2512.22587 ↗First posted 27 Dec 2025cs.LG stat.MLcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 11 of its 17 references that are in the map. First posted on arXiv 27 Dec 2025.

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References · 11

  1. 2018Lipschitz regularity of deep neural networks: analysis and efficient estimationcited by 415
  2. 2018Regularisation of Neural Networks by Enforcing Lipschitz Continuitycited by 314
  3. 2019Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networkscited by 293
  4. 2020Fast Differentiable Sorting and Rankingcited by 197
  5. 2019Differentiable Ranks and Sorting using Optimal Transportcited by 113
  6. 2019Stochastic Optimization of Sorting Networks via Continuous Relaxationscited by 111
  7. 2020SoftSort: A Continuous Relaxation for the argsort Operatorcited by 66
  8. 2021Differentiable Sorting Networks for Scalable Sorting and Ranking Supervisioncited by 31
  9. 2022Monotonic Differentiable Sorting Networkscited by 25
  10. 2025LapSum -- One Method to Differentiate Them All: Ranking, Sorting and Top-k Selectioncited by 13
  11. 2023Generalized Neural Sorting Networks with Error-Free Differentiable Swap Functionscited by 4

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