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Paper Citation Record · LEDGER

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp

As of 21 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 0 inbound Pith citation observations for arXiv:2608.11760.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2608.11760 v2

Coverage vector

measured 43 of 43 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T00:38:41.703379Z

measured 43 of 43 standing notices

One-hop event checks from named stored sources.

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measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

43 of 43 outbound references displayed

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External citation measurements

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Outbound references

Observation 66ea058e-80eb-4feb-bc3c-f54a70e5f28a · outbound

This paper cites Katyusha: The first direct acceleration of stochastic gradient methods.Journal of Machine Learning Research, 18(221):1–51, 2018.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp Katyusha: The first direct acceleration of stochastic gradient methods.Journal of Machine Learning Research, 18(221):1–51, 2018

Reference 1

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Source-reported events for the cited work

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Observation dbcdaf16-3fbb-46b2-b351-166d62dc7f25 · outbound

This paper cites Much faster algorithms for matrix scaling.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp Much faster algorithms for matrix scaling

Reference 2

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

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Observation d8872248-af62-41aa-bdca-ffc5b8472825 · outbound

This paper cites Near-linear time approximation algorithms for optimal transport via sinkhorn iteration.Advances in Neural Information Processing Systems, 30, 2017.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp Near-linear time approximation algorithms for optimal transport via sinkhorn iteration.Advances in Neural Information Processing Systems, 30, 2017

Reference 3

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Source-reported events for the cited work

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Observation 09de9c69-dea7-4335-a418-195d3f465d08 · outbound

This paper cites Estimating nonnegative matrices from marginal data.International Economic Review, 6(3):294–310, 1965.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp Estimating nonnegative matrices from marginal data.International Economic Review, 6(3):294–310, 1965

Reference 4

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verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

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Observation c7332636-11b4-44fb-8b76-91e831872686 · outbound

This paper cites Towards Optimal Running Times for Optimal Transport.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp Towards Optimal Running Times for Optimal Transport

Reference 5

Resolution
verified exact
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

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Observation b22a4781-c73f-498d-b577-9398bd3f514c · outbound

This paper cites Better and simpler error analysis of the sinkhorn–knopp algorithm for matrix scaling.Mathematical Programming, 188(1):395–407, 2021.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp Better and simpler error analysis of the sinkhorn–knopp algorithm for matrix scaling.Mathematical Programming, 188(1):395–407, 2021

Reference 6

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

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Observation 5571bdc8-5329-44d0-802d-cf71484c28c3 · outbound

This paper cites Matrix scaling and balancing via box constrained newton’s method and interior point methods.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp Matrix scaling and balancing via box constrained newton’s method and interior point methods

Reference 7

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

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Observation e932197a-22fd-44d5-9949-2cfddd3b6d93 · outbound

This paper cites Semidual regularized optimal transport.SIAM Review, 60(4):941–965,.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp Semidual regularized optimal transport.SIAM Review, 60(4):941–965,

Reference 8

Resolution
verified fuzzy
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Source-reported events for the cited work

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Observation f4b15f4f-d96d-42ff-b374-c135ad55d275 · outbound

This paper cites Acceleration methods.Foundations and Trends®in Optimization, 5(1-2):1–245, 2021.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp Acceleration methods.Foundations and Trends®in Optimization, 5(1-2):1–245, 2021

Reference 9

Resolution
verified fuzzy
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Source-reported events for the cited work

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source=pdf_text observed=2026-08-16T00:38:41.064681Z digest=sha256:b66979aceee16fc5ee22b88a3e62e041e602ae026c17ce0bb3d62a9ad288c02c

Observation 8c5835a1-44fb-45b5-b7c9-c8fd4930f517 · outbound

This paper cites Stochastic matrix-free equilibration.Journal of Optimization Theory and Applications, 172(2):436–454, 2017.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp Stochastic matrix-free equilibration.Journal of Optimization Theory and Applications, 172(2):436–454, 2017

Reference 10

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Source-reported events for the cited work

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Observation ec3eb59c-c16b-4020-ad63-29065bba53b8 · outbound

This paper cites Computational optimal transport: Com- plexity by accelerated gradient descent is better than by sinkhorn’s algorithm.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp Computational optimal transport: Com- plexity by accelerated gradient descent is better than by sinkhorn’s algorithm

Reference 11

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Source-reported events for the cited work

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Observation 9efd1ffe-c72d-481e-9f52-5ff5bcbb366e · outbound

This paper cites Parameterselectionandpreconditioningforagraphformsolver.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp Parameterselectionandpreconditioningforagraphformsolver

Reference 12

Resolution
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Source-reported events for the cited work

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Observation 38b0a61b-30fa-44ce-93a7-41d17084ad54 · outbound

This paper cites On the scaling of multidimensional matrices.Linear Algebra and its applications, 114:717–735, 1989.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp On the scaling of multidimensional matrices.Linear Algebra and its applications, 114:717–735, 1989

Reference 13

Resolution
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Source-reported events for the cited work

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Observation f108af17-7b38-456c-8324-b01b8ec2be91 · outbound

This paper cites Non-asymptotic local convergence analysis of alternating minimization, April 2026.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp Non-asymptotic local convergence analysis of alternating minimization, April 2026

Reference 14

Resolution
verified fuzzy
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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

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Observation a17a2056-3d84-44f7-a89b-1f954def582f · outbound

This paper cites Gradient Methods with Online Scaling Part I. Theoretical Foundations.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp Gradient Methods with Online Scaling Part I. Theoretical Foundations

Reference 15

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-16T00:38:41.132738Z digest=sha256:aa6cdd6ba852f8ac5e8f68c83e2e15f5f68e154e9744801df94d6fb7fcd61811

Observation 1f8f6d97-54a5-4a88-a324-429dc6560b0f · outbound

This paper cites Fast and large-scale unbalanced optimal transport via its semi-dual and adaptive gradient methods.arXiv preprint arXiv:2602.10697, 2026.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp Fast and large-scale unbalanced optimal transport via its semi-dual and adaptive gradient methods.arXiv preprint arXiv:2602.10697, 2026

Reference 16

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Source-reported events for the cited work

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Observation 94fafc9e-c59c-4052-ac60-8090999f9e22 · outbound

This paper cites On the Efficiency of Sinkhorn-Knopp for Entropically Regularized Optimal Transport.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp On the Efficiency of Sinkhorn-Knopp for Entropically Regularized Optimal Transport

Reference 17

Resolution
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Source-reported events for the cited work

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Observation fbede85d-f04d-4bfd-81df-365636e7cd9b · outbound

This paper cites Phase transition of the sinkhorn-knopp algorithm.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp Phase transition of the sinkhorn-knopp algorithm

Reference 18

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Source-reported events for the cited work

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Observation c8b40211-814d-453b-880b-500151ae4ca3 · outbound

This paper cites A review of matrix scaling and Sinkhorn's normal form for matrices and positive maps.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp A review of matrix scaling and Sinkhorn's normal form for matrices and positive maps

Reference 19

Resolution
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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-16T00:38:41.253824Z digest=sha256:535eac739e9ad09f3c28d00904c46a8f00ed3f81309ca1afec192030a037d0eb

Observation 77119a49-6cca-4cb1-946a-497a31d7e4c3 · outbound

This paper cites A direct tilde{O}(1/epsilon) iteration parallel al- gorithm for optimal transport.Advances in Neural Information Processing Systems, 32, 2019.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp A direct tilde{O}(1/epsilon) iteration parallel al- gorithm for optimal transport.Advances in Neural Information Processing Systems, 32, 2019

Reference 20

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Source-reported events for the cited work

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source=pdf_text observed=2026-08-16T00:38:41.258571Z digest=sha256:82f265938f92ad4b675057708c82c0d57251fdd74c62f8e684d837fd604e968b

Observation 80931f80-6399-40b9-a9ae-697a4c94d356 · outbound

This paper cites A theorem of the alternative for multihomogeneous functions and its relationship to diagonal scaling of matrices.Linear Algebra and its Applications, 236:1–24, 1996.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp A theorem of the alternative for multihomogeneous functions and its relationship to diagonal scaling of matrices.Linear Algebra and its Applications, 236:1–24, 1996

Reference 21

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

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Observation 5cf9d86e-da41-436b-80c9-ba9f61cf6f2d · outbound

This paper cites On the rate of convergence of deterministic and randomized ras matrix scaling algorithms.Operations research letters, 14(5):237–244, 1993.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp On the rate of convergence of deterministic and randomized ras matrix scaling algorithms.Operations research letters, 14(5):237–244, 1993

Reference 22

Resolution
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Source-reported events for the cited work

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Observation 1328d555-6629-4c90-979f-a850f604c555 · outbound

This paper cites Onthecomplexityofnonnegative-matrixscaling.Linear Algebra and its applications, 240:87–103, 1996.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp Onthecomplexityofnonnegative-matrixscaling.Linear Algebra and its applications, 240:87–103, 1996

Reference 23

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verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

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Observation 3b95a39d-910c-44fd-acc6-7ae6df9d4596 · outbound

This paper cites On the complexity of general matrix scaling and entropy minimization via the ras algorithm.Mathematical Programming, 112(2):371–401, 2008.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp On the complexity of general matrix scaling and entropy minimization via the ras algorithm.Mathematical Programming, 112(2):371–401, 2008

Reference 24

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-16T00:38:41.277855Z digest=sha256:c35667c5a5edb1f027edbe4ce5e0a34b170fd6dab832cb83a49f48e06a7e897c

Observation 20785235-1683-4985-9e38-7cb9f73df252 · outbound

This paper cites The sinkhorn–knopp algorithm: convergence and applications.SIAM Journal on Matrix Analysis and Applications, 30(1):261–275, 2008.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp The sinkhorn–knopp algorithm: convergence and applications.SIAM Journal on Matrix Analysis and Applications, 30(1):261–275, 2008

Reference 25

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-16T00:38:41.340444Z digest=sha256:f5b75cd73e4bf300fd108a2ba839f5bc908c2a5d1fdef34e9858192945d8a6f3

Observation c2270a30-7f7f-47dc-8309-466182a485b1 · outbound

This paper cites A geometric structure of acceleration and its role in making gradients small fast.Advances in Neural Information Processing Systems, 34:11999–12012, 2021.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp A geometric structure of acceleration and its role in making gradients small fast.Advances in Neural Information Processing Systems, 34:11999–12012, 2021

Reference 26

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

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Observation b72ca6ab-9436-47b7-9dab-dddde3c7d924 · outbound

This paper cites A note on overrelax- ation in the sinkhorn algorithm.Optimization Letters, 16(8):2209–2220, 2022.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp A note on overrelax- ation in the sinkhorn algorithm.Optimization Letters, 16(8):2209–2220, 2022

Reference 27

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verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

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Observation c1e92cd9-fa80-42b5-8ea4-1badc9ccd2a8 · outbound

This paper cites On efficient optimal transport: An analysis of greedy and accelerated mirror descent algorithms.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp On efficient optimal transport: An analysis of greedy and accelerated mirror descent algorithms

Reference 28

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

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Observation 1cf8e6a1-b002-4b3e-9239-f18a73b605cb · outbound

This paper cites A deterministic strongly polynomial algorithm for matrix scaling and approximate permanents.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp A deterministic strongly polynomial algorithm for matrix scaling and approximate permanents

Reference 29

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-16T00:38:41.451993Z digest=sha256:bcdd61fed05522a027b360a7d0b0e652442639ce8b3447f9b285e64f03ca9858

Observation 3c60781c-5687-4db9-9e4d-bfb43a17098c · outbound

This paper cites Softmax is $1/2$-lipschitz: A tight bound across all $\ell_p$ norms.Transactions on Machine Learning Research, 2026.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp Softmax is $1/2$-lipschitz: A tight bound across all $\ell_p$ norms.Transactions on Machine Learning Research, 2026

Reference 30

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-16T00:38:41.458851Z digest=sha256:6cf26bccdc163448b914a62757abbe77e5360075bb38b7151a2ba476e351c756

Observation 54ec403b-9bf0-4bda-a22b-0cec84fa88ac · outbound

This paper cites On complexity of matrix scaling.Linear Algebra and its Applica- tions, 302:435–460, 1999.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp On complexity of matrix scaling.Linear Algebra and its Applica- tions, 302:435–460, 1999

Reference 31

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-16T00:38:41.463705Z digest=sha256:9d7eb0348abc2b51e7b82bf69d6c2283804da6875aba4f590937f1da07a87af6

Observation 772f51ba-28e9-4807-a5c0-09ce3f1ce797 · outbound

This paper cites Springer Science & Business Media, 2013.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp Springer Science & Business Media, 2013

Reference 32

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raw_fallback, observed 2026-08-16T00:38:42.677404Z

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Observation 820a360e-f1b8-4a4d-a0c3-8f8ccf68249d · outbound

This paper cites Quantum entropic regular- ization of matrix-valued optimal transport.European Journal of Applied Mathematics, 30(6):1079–1102,.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp Quantum entropic regular- ization of matrix-valued optimal transport.European Journal of Applied Mathematics, 30(6):1079–1102,

Reference 33

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raw_fallback, observed 2026-08-16T00:38:42.577941Z

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Observation d9c6123c-5560-42b6-9694-97142f13fd03 · outbound

This paper cites Now Foundations and Trends, 2019.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp Now Foundations and Trends, 2019

Reference 34

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Observation 02efcd5e-a7a4-4480-91ae-264877a32bc0 · outbound

This paper cites On sinkhorn’s algorithm and choice modeling.Operations Research, 2025.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp On sinkhorn’s algorithm and choice modeling.Operations Research, 2025

Reference 35

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raw_fallback, observed 2026-08-16T00:38:42.545427Z

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Observation 36ec1e96-8d53-440a-9a7d-081f1bd43283 · outbound

This paper cites Concerning nonnegative matrices and doubly stochastic matrices.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp Concerning nonnegative matrices and doubly stochastic matrices

Reference 36

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Observation e5a3fb97-d704-4bd5-a2df-ffd1fb6e70fe · outbound

This paper cites Exact worst-case convergence rates of the proximal gradient method for composite convex minimization.Journal of Optimization Theory and Appli- cations, 178(2):455–476, 2018.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp Exact worst-case convergence rates of the proximal gradient method for composite convex minimization.Journal of Optimization Theory and Appli- cations, 178(2):455–476, 2018

Reference 37

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raw_fallback, observed 2026-08-16T00:38:42.435255Z

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source=pdf_text observed=2026-08-16T00:38:41.648174Z digest=sha256:08f01bd7123807ef3add9b7358af0ba88ec7a503a2b1089406b9fdb829573e46

Observation 5305317b-277c-43d3-8c9d-72078ffcf8d5 · outbound

This paper cites Overrelaxed sinkhorn–knopp algorithm for regularized optimal transport.Algorithms, 14(5):143, 2021.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp Overrelaxed sinkhorn–knopp algorithm for regularized optimal transport.Algorithms, 14(5):143, 2021

Reference 38

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verified fuzzy
raw_fallback, observed 2026-08-16T00:38:42.339642Z

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source=pdf_text observed=2026-08-16T00:38:41.655828Z digest=sha256:3d5255a3ac4ffd9dcb7d8790e9a73376d9fb775702b7feb9666fd544774f5869

Observation abec382e-cbe5-49da-9ca8-7a1bdb1d00bb · outbound

This paper cites mHC: Manifold-Constrained Hyper-Connections.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp mHC: Manifold-Constrained Hyper-Connections

Reference 39

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source=pdf_text observed=2026-08-16T00:38:41.660700Z digest=sha256:911614bc67bb1339729251a50f8c02aa5b7becb8d001f2fb99c896cac1b0360a

Observation 84becbd0-36d5-4b7d-bdb3-03b73b906139 · outbound

This paper cites Accelerating Sinkhorn for Entropy-Regularized Optimal Transport.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp Accelerating Sinkhorn for Entropy-Regularized Optimal Transport

Reference 40

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local_arxiv, observed 2026-08-16T00:38:41.819465Z

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Observation 89500fc2-f7bf-4853-92d5-0bc14335f66d · outbound

This paper cites For∆ 2, sinceℓ(u)is a quadratic function minimized atu−P −1∇ℓ(u), we have ∆2 =ℓ(u−P −1∇α(u))−ℓ(u−P −1∇ℓ(u)) = 1 2∥∇α(u)−∇ℓ(u)∥ 2 P−1 ≤ 1 2∥∇φ(u,v)−∇λ(u,v)∥ 2 S−1≤ 2 sε2.

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp For∆ 2, sinceℓ(u)is a quadratic function minimized atu−P −1∇ℓ(u), we have ∆2 =ℓ(u−P −1∇α(u))−ℓ(u−P −1∇ℓ(u)) = 1 2∥∇α(u)−∇ℓ(u)∥ 2 P−1 ≤ 1 2∥∇φ(u,v)−∇λ(u,v)∥ 2 S−1≤ 2 sε2

Reference 43

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raw_fallback, observed 2026-08-16T00:38:42.293751Z

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source=pdf_text observed=2026-08-16T00:38:41.703379Z digest=sha256:28e9ea52fbcef079ad1e58077986e19ceff31a82bd04563f63c4328aceab39d4

Observation 50c3e2de-500b-4e63-af93-5435e438cd04 · outbound

This paper cites (cited on 2, 4, 7).

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp (cited on 2, 4, 7)

Reference 901

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raw_fallback, observed 2026-08-16T00:38:43.705558Z

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source=pdf_text observed=2026-08-16T00:38:40.829298Z digest=sha256:874aba3fe8ed8e35eb0617d92ef4430654fd336060d0af3fbad1b90421cceca1

Observation 783412e0-269e-45de-9b9b-ac1f9ad84495 · outbound

This paper cites (cited on 4, 7, 16).

Tight Nonasymptotic Local Convergence of Sinkhorn-Knopp (cited on 4, 7, 16)

Reference 3991

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