A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold | Paper Citation Record

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This paper cites Distributed asynchronous deterministic and stochastic gradient optimization algorithms.IEEE transactions on automatic control, 31(9):803–812.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Distributed asynchronous deterministic and stochastic gradient optimization algorithms.IEEE transactions on automatic control, 31(9):803–812

Reference 1

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This paper cites Distributed subgradient methods for multi-agent optimization.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Distributed subgradient methods for multi-agent optimization

Reference 2

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This paper cites On the convergence of decentralized gradient descent.SIAM Journal on Optimization, 26(3):1835–1854.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold On the convergence of decentralized gradient descent.SIAM Journal on Optimization, 26(3):1835–1854

Reference 3

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This paper cites Alghunaim and Kun Yuan.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Alghunaim and Kun Yuan

Reference 4

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A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Unresolved cited work

Reference 5

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This paper cites EXTRA: An exact first-order algorithm for decentralized consensus optimization.SIAM Journal on Optimization, 25(2):944–966.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold EXTRA: An exact first-order algorithm for decentralized consensus optimization.SIAM Journal on Optimization, 25(2):944–966

Reference 6

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Observation 5208fdac-0f72-4755-bffe-eafc4ddb3c88 · outbound

This paper cites Distributed constrained optimal consensus of multi- agent systems.Automatica, 68:209–215.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Distributed constrained optimal consensus of multi- agent systems.Automatica, 68:209–215

Reference 7

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Observation f60ecbe4-a80d-4903-88f5-b046af73b1b9 · outbound

This paper cites Dual averaging for distributed optimization: Convergence analysis and network scaling.IEEE Transactions on Automatic Control.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Dual averaging for distributed optimization: Convergence analysis and network scaling.IEEE Transactions on Automatic Control

Reference 8

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Observation 5df35d42-1792-4982-b8f7-888f0fedf727 · outbound

This paper cites Orthogonal weight nor- malization: Solution to optimization over multiple dependent Stiefel manifolds in deep neural networks.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Orthogonal weight nor- malization: Solution to optimization over multiple dependent Stiefel manifolds in deep neural networks

Reference 9

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Observation f5346351-6cee-4ecb-806b-ae792cf971de · outbound

This paper cites Riemannian approach to batch normalization.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Riemannian approach to batch normalization

Reference 10

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Observation bc9a28ff-d8bd-4163-baa5-b731b91a1b27 · outbound

This paper cites Riemannian Preconditioned LoRA for Fine-Tuning Foundation Models.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Riemannian Preconditioned LoRA for Fine-Tuning Foundation Models

Reference 11

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Observation 328a8c32-8cae-48f5-a84d-d311c9c6ca15 · outbound

This paper cites Retraction-free optimization over the Stiefel manifold with application to the LoRA fine-tuning.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Retraction-free optimization over the Stiefel manifold with application to the LoRA fine-tuning

Reference 12

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Observation 6a5c2cef-9e41-4b67-bb7c-51411eca69c8 · outbound

This paper cites Susan Blackford, Antoine Petitet, Roldan Pozo, Karin Remington, R.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Susan Blackford, Antoine Petitet, Roldan Pozo, Karin Remington, R

Reference 13

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A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Unresolved cited work

Reference 14

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Observation a6bbb8c6-17bb-4cd0-a216-7ffd66f47f23 · outbound

This paper cites D2: Decentralized training over decen- tralized data.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold D2: Decentralized training over decen- tralized data

Reference 15

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Observation 77fb06d7-cd91-45d8-a35d-9dd4ea69dc9a · outbound

This paper cites Achieving geometric convergence for distributed optimiza- tion over time-varying graphs.SIAM Journal on Optimization, 27(4):2597–2633.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Achieving geometric convergence for distributed optimiza- tion over time-varying graphs.SIAM Journal on Optimization, 27(4):2597–2633

Reference 16

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This paper cites Harnessing smoothness to accelerate distributed optimization.IEEE Trans- actions on Control of Network Systems, 5(3):1245–1260.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Harnessing smoothness to accelerate distributed optimization.IEEE Trans- actions on Control of Network Systems, 5(3):1245–1260

Reference 17

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Observation 79bf63dd-7127-43c1-8c7b-38798120e08e · outbound

This paper cites S-diging: A stochastic gradient tracking algorithm for distributed optimization.IEEE Transactions on Emerging Topics in Computational Intelligence.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold S-diging: A stochastic gradient tracking algorithm for distributed optimization.IEEE Transactions on Emerging Topics in Computational Intelligence

Reference 18

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Observation 57195c55-05a3-4a94-84f9-1723ccf66b94 · outbound

This paper cites Distributed stochastic gradient tracking methods.Mathematical Program- ming.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Distributed stochastic gradient tracking methods.Mathematical Program- ming

Reference 19

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A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Unresolved cited work

Reference 20

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This paper cites A decentralized proximal-gradient method with network independent step-sizes and separated convergence rates.IEEE Transactions on Signal Processing, 67(17):4494–4506.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold A decentralized proximal-gradient method with network independent step-sizes and separated convergence rates.IEEE Transactions on Signal Processing, 67(17):4494–4506

Reference 21

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Observation 04865cbb-ee81-44f9-87d2-6ad7af4ce90c · outbound

This paper cites Prox-PDA:Theproximalprimal-dualalgorithm for fast distributed nonconvex optimization and learning over networks.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Prox-PDA:Theproximalprimal-dualalgorithm for fast distributed nonconvex optimization and learning over networks

Reference 22

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Observation 0740b898-b3af-4a50-b10a-1d34e8fefb98 · outbound

This paper cites Alghunaim, and Xinmeng Huang.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Alghunaim, and Xinmeng Huang

Reference 23

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Observation 8ef8dd71-e2a0-49e9-9152-cc57e97d30cf · outbound

This paper cites Next: In-network nonconvex optimization.IEEE Transactions on Signal and Information Processing over Networks.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Next: In-network nonconvex optimization.IEEE Transactions on Signal and Information Processing over Networks

Reference 24

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Observation b734de47-b67a-471d-a4d0-95c8fb9703e7 · outbound

This paper cites Stich, and Martin Jaggi.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Stich, and Martin Jaggi

Reference 25

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Observation 8d58b733-202e-424b-bf05-2960394580f5 · outbound

This paper cites Unbiased compression saves communication in distributed optimization: When and how much? InAdvances in Neural Information Processing Systems.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Unbiased compression saves communication in distributed optimization: When and how much? InAdvances in Neural Information Processing Systems

Reference 26

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Observation 1954de44-2592-461c-b2bf-e9c2414953f8 · outbound

This paper cites Greedy low-rank gradient com- pression for distributed learning with convergence guarantees.IEEE Transactions on Signal Processing.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Greedy low-rank gradient com- pression for distributed learning with convergence guarantees.IEEE Transactions on Signal Processing

Reference 27

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Observation cba5c5a2-6492-48d4-9010-f0243d927391 · outbound

This paper cites On biased compression for distributed learning.Journal of Machine Learning Research.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold On biased compression for distributed learning.Journal of Machine Learning Research

Reference 28

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Observation afdcd2d6-246a-47ca-bb62-91d582cbdedc · outbound

This paper cites Error compensated distributed SGD can be accelerated.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Error compensated distributed SGD can be accelerated

Reference 29

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Observation cfa2bbcb-d822-45a4-b4a2-f078607ca6a9 · outbound

This paper cites Understanding the influence of digraphs on decentralized optimization: Effective metrics, lower bound, and optimal algorithm.SIAM Journal on Optimization.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Understanding the influence of digraphs on decentralized optimization: Effective metrics, lower bound, and optimal algorithm.SIAM Journal on Optimization

Reference 30

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Observation a3028dfd-1dd3-41f4-8c9c-7cb53b90dde5 · outbound

This paper cites Alghunaim.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Alghunaim

Reference 31

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Observation c24d8f99-49e4-4deb-b70f-778fd4a0dc91 · outbound

This paper cites Exponential graph is provably efficient for decentralized deep training.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Exponential graph is provably efficient for decentralized deep training

Reference 32

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Observation 08687dc9-a4a6-453e-8704-43ab6251d936 · outbound

This paper cites Decentralized Riemannian gradient descent on the Stiefel manifold.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Decentralized Riemannian gradient descent on the Stiefel manifold

Reference 33

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Observation 570dab4e-81a9-4c9d-8ed8-963274fc6436 · outbound

This paper cites Decentralized projected Riemannian gradient method for smooth opti- mization on compact submanifolds embedded in the euclidean space.Numerische Mathematik.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Decentralized projected Riemannian gradient method for smooth opti- mization on compact submanifolds embedded in the euclidean space.Numerische Mathematik

Reference 34

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Observation 92f3fc39-727d-4490-b1d7-a5b20068d5a2 · outbound

This paper cites A decentralized proximal gradient tracking algorithm for composite optimization on Riemannian manifolds.Journal of Machine Learning Research.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold A decentralized proximal gradient tracking algorithm for composite optimization on Riemannian manifolds.Journal of Machine Learning Research

Reference 35

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Observation af495068-65af-44ff-bda7-4d110faac46d · outbound

This paper cites Riemannian EXTRA: Communication-efficient decentralized optimization over compact submanifolds with data heterogeneity.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Riemannian EXTRA: Communication-efficient decentralized optimization over compact submanifolds with data heterogeneity

Reference 36

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Observation 88a512e0-4ff6-4799-82e1-924959cf80fe · outbound

This paper cites Decentralized optimization on compact submanifolds by quantized Riemannian gradient tracking.IEEE Transactions on Signal Processing.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Decentralized optimization on compact submanifolds by quantized Riemannian gradient tracking.IEEE Transactions on Signal Processing

Reference 37

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Observation 7cd9ac85-356c-483c-93f9-a90767dd7ba2 · outbound

This paper cites Improving the communication in decentralized manifold optimization through single-step consensus and compression.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Improving the communication in decentralized manifold optimization through single-step consensus and compression

Reference 38

Resolution: verified exact; arxiv_id, observed 2026-05-11T21:21:11.387823Z

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Observation b9f862ab-995d-4bc4-a097-6a8837c50f85 · outbound

This paper cites Decentralized projected Riemannian stochastic recursive momentum method for nonconvex optimization.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Decentralized projected Riemannian stochastic recursive momentum method for nonconvex optimization

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T19:27:55.248448Z

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Observation f9604ccd-8b70-4d47-b764-43040b0de3f9 · outbound

This paper cites Decentralized Riemannian Conjugate Gradient Method on the Stiefel Manifold.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Decentralized Riemannian Conjugate Gradient Method on the Stiefel Manifold

Reference 40

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Observation 6c3b1755-7c31-46b0-b0ae-932581f21b44 · outbound

This paper cites Decentralized Riemannian natural gradient methods with Kronecker product approximations.Journal of the Operations Research Society of China.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Decentralized Riemannian natural gradient methods with Kronecker product approximations.Journal of the Operations Research Society of China

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T19:27:55.277333Z

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Observation 4bd3c79c-6191-4422-937c-77f7a4c144fb · outbound

This paper cites On the local linear rate of consensus on the Stiefel manifold.IEEE Transactions on Automatic Control.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold On the local linear rate of consensus on the Stiefel manifold.IEEE Transactions on Automatic Control

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T19:27:55.273550Z

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Observation 085414a1-0635-4581-b7cc-b7c2faed23ff · outbound

This paper cites Riemannian consensus for manifolds with bounded curva- ture.IEEE Transactions on Automatic Control.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Riemannian consensus for manifolds with bounded curva- ture.IEEE Transactions on Automatic Control

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T19:27:55.168937Z

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Observation 0523fec4-7613-435c-bec6-116af9b8d2d4 · outbound

This paper cites Consensus optimization on manifolds.SIAM Journal on Control and Optimization.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Consensus optimization on manifolds.SIAM Journal on Control and Optimization

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T19:27:55.172946Z

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Observation 29f85aa4-7d9c-493f-a96e-f3f9a26a05f4 · outbound

This paper cites Achieving local consensus over compact submanifolds.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Achieving local consensus over compact submanifolds

Reference 45

Resolution: verified exact; arxiv_id, observed 2026-05-08T23:34:24.479848Z

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Observation cb76a7f3-65a6-4eaa-8acc-cbfff6c52ab5 · outbound

This paper cites Retraction-Free Decentralized Non-convex Optimization with Orthogonal Constraints.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Retraction-Free Decentralized Non-convex Optimization with Orthogonal Constraints

Reference 46

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Observation 3e4c49f9-7067-4ece-b1a5-e719e83b8392 · outbound

This paper cites Decentralized optimization over the Stiefel manifold by an approximate aug- mented Lagrangian function.IEEE Transactions on Signal Processing.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Decentralized optimization over the Stiefel manifold by an approximate aug- mented Lagrangian function.IEEE Transactions on Signal Processing

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T19:27:55.160906Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 72de694b-1559-4d5e-a728-13e4d0ad93d1 · outbound

This paper cites Fast and accurate optimization on the orthogonal manifold without retraction.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Fast and accurate optimization on the orthogonal manifold without retraction

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T19:27:55.269940Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 33c4dd70-324d-41da-88b4-91a0ba313fb4 · outbound

This paper cites Parallelizable algorithms for optimization problems with orthog- onality constraints.SIAM Journal on Scientific Computing, 41(3):A1949–A1983.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Parallelizable algorithms for optimization problems with orthog- onality constraints.SIAM Journal on Scientific Computing, 41(3):A1949–A1983

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T19:27:55.156851Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 81397b81-f5be-4720-a1ea-ede16ff3ee31 · outbound

This paper cites Dissolving constraints for Riemannian optimization.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Dissolving constraints for Riemannian optimization

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T19:27:55.164818Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f37d851c-2c0a-4645-977d-8e8d7f068ea8 · outbound

This paper cites Horn and Charles R.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Horn and Charles R

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T19:27:55.176477Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 430114f9-8467-4051-b2ab-0cd6a6ce0cf5 · outbound

This paper cites Convergence analysis of EXTRA in non-convex distributed optimization.IEEE Control Systems Letters.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Convergence analysis of EXTRA in non-convex distributed optimization.IEEE Control Systems Letters

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T19:27:55.191929Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 0285e608-3895-44f5-9fd2-22fe6739d111 · outbound

This paper cites Reasflow: Assisting reasoning-centric scientific discovery in applied mathematics via a knowledge-based multi-agent system.

A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold Reasflow: Assisting reasoning-centric scientific discovery in applied mathematics via a knowledge-based multi-agent system

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-05-26T19:27:55.233634Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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