mlsanityData to 7 Oct 2026

Monotonic Differentiable Sorting Networks

arXiv 2203.09630 ↗First posted 17 Mar 2022cs.LG cs.AI cs.IRcited by 25

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Abstract (arXiv)

Differentiable sorting algorithms allow training with sorting and ranking supervision, where only the ordering or ranking of samples is known. Various methods have been proposed to address this challenge, ranging from optimal transport-based differentiable Sinkhorn sorting algorithms to making classic sorting networks differentiable. One problem of current differentiable sorting methods is that they are non-monotonic. To address this issue, we propose a novel relaxation of conditional swap operations that guarantees monotonicity in differentiable sorting networks. We introduce a family of sigmoid functions and prove that they produce differentiable sorting networks that are monotonic. Monotonicity ensures that the gradients always have the correct sign, which is an advantage in gradient-based optimization. We demonstrate that monotonic differentiable sorting networks improve upon previous differentiable sorting methods.

Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). Builds on 12 of its 22 references that are in the map. First posted on arXiv 17 Mar 2022.

Builds on

12 of 22 references.

References · 12

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2022Generative Adversarial Networkscited by 5,603
  3. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
  4. 2020Fast Differentiable Sorting and Rankingcited by 196
  5. 2018Learning Latent Permutations with Gumbel-Sinkhorn Networkscited by 172
  6. 2019Differentiable Ranks and Sorting using Optimal Transportcited by 113
  7. 2019Stochastic Optimization of Sorting Networks via Continuous Relaxationscited by 111
  8. 2013Multi-digit Number Recognition from Street View Imagery using Deep Convolutional Neural Networkscited by 84
  9. 2021Differentiable Patch Selection for Image Recognitioncited by 68
  10. 2021Differentiable Sorting Networks for Scalable Sorting and Ranking Supervisioncited by 31
  11. 2021Learning with Algorithmic Supervision via Continuous Relaxationscited by 21
  12. 2017A Continuous Relaxation of Beam Search for End-to-end Training of Neural Sequence Modelscited by 10

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 3; 2023: 6; 2024: 7; 2025: 6; 2026: 3.

25 papers.

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  1. 2022Git Re-Basin: Merging Models modulo Permutation Symmetriescited by 460
  2. 2025LeJEPA: Provable and Scalable Self-Supervised Learning Without the Heuristicscited by 227
  3. 2022Deep Differentiable Logic Gate Networkscited by 67
  4. 2022Differentiable Top-k Classification Learningcited by 21
  5. 2024An Information Theoretic Perspective on Conformal Predictioncited by 21
  6. 2023Learning by Sorting: Self-supervised Learning with Group Ordering Constraintscited by 13
  7. 2025LapSum -- One Method to Differentiate Them All: Ranking, Sorting and Top-k Selectioncited by 12
  8. 2024Uncertainty Quantification via Stable Distribution Propagationcited by 10
  9. 2023Beam Tree Recursive Cellscited by 6
  10. 2023Adaptive Neural Ranking Framework: Toward Maximized Business Goal for Cascade Ranking Systemscited by 6
  11. 2024Made to Order: Discovering monotonic temporal changes via self-supervised video orderingcited by 5
  12. 2024SymmetricDiffusers: Learning Discrete Diffusion on Finite Symmetric Groupscited by 5
13 more
  1. 2023Generalized Neural Sorting Networks with Error-Free Differentiable Swap Functionscited by 4
  2. 2024Generalizing Stochastic Smoothing for Differentiation and Gradient Estimationcited by 4
  3. 2023Differentiable Random Partition Modelscited by 3
  4. 2023Hacking Generative Models with Differentiable Network Bendingcited by 3
  5. 2024Holistic Utility Preference Learning for Listwise Alignmentcited by 2
  6. 2024Newton Losses: Using Curvature Information for Learning with Differentiable Algorithmscited by 2
  7. 2025Learning Cascade Ranking as One Networkcited by 2
  8. 2025Permutation Learning with Only N Parameters: From SoftSort to Self-Organizing Gaussianscited by 0
  9. 2025Learning Distributions over Permutations and Rankings with Factorized Representationscited by 0
  10. 2025Structural Incompatibility of Differentiable Sorting and Within-Vector Rank Normalizationcited by 0
  11. 2026Reward Learning through Ranking Mean Squared Errorcited by 0
  12. 2026Class Adaptive Conformal Trainingcited by 0
  13. 2026Learning Permutation Distributions via Reflected Diffusion on Rankscited by 0