Paper Citation Record · LEDGER

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking

As of 18 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 0 inbound Pith citation observations for arXiv:2506.07351.

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

pith.paper-citation-record.v1
2506.07351 v1

Coverage vector

measured 43 of 43 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:44:09.465818Z

measured 43 of 43 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

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

verified exact2
verified fuzzy24
unresolved17
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation eeb2339c-fe80-4a0e-9b19-316c3896c0e9 · outbound

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

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Distributed subgradient methods for multi- agent optimization,

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:03.419390Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dbe30f42-1ff5-4419-8b46-3549541f5341 · outbound

This paper cites On the convergence of decentralized gradient descent,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking On the convergence of decentralized gradient descent,

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:03.531633Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 67883231-44af-4297-8e71-44cb6f34d61d · outbound

This paper cites Harnessing smoothness to accelerate distributed optimization,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Harnessing smoothness to accelerate distributed optimization,

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:03.664508Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 08943675-703f-4a93-adbf-2cf657cc0742 · outbound

This paper cites Exact diffusion for distributed optimization and learning—part i: Algorithm development,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Exact diffusion for distributed optimization and learning—part i: Algorithm development,

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:44:17.069172Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e1af21bc-ef2c-4808-b8c2-888b3baad909 · outbound

This paper cites Decentralized proximal gradient algorithms with linear convergence rates,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Decentralized proximal gradient algorithms with linear convergence rates,

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:44:16.797963Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 1a32cb79-584e-466f-a538-254347e2cd37 · outbound

This paper cites On the linear convergence of the admm in decentralized consensus optimization,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking On the linear convergence of the admm in decentralized consensus optimization,

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:44:16.553716Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 2acbaff2-ffd6-4f39-88bf-d1b10d45b921 · outbound

This paper cites Distributed linearized alter- nating direction method of multipliers for composite convex consensus optimization,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Distributed linearized alter- nating direction method of multipliers for composite convex consensus optimization,

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:04.240469Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d90b1be0-a070-4b33-85ae-27eb28a6f86d · outbound

This paper cites Decentralized riemannian gradient descent on the stiefel manifold,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Decentralized riemannian gradient descent on the stiefel manifold,

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:04.396184Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 19d3632d-3cae-47af-99df-5bafacc789d3 · outbound

This paper cites Decentralized projected Riemannian gradient method for smooth optimization on compact submanifolds.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Decentralized projected Riemannian gradient method for smooth optimization on compact submanifolds

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:04.530396Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ed722086-1467-43bd-b2a8-381a10e722a6 · outbound

This paper cites Decentralized riemannian conjugate gradient method on the stiefel manifold,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Decentralized riemannian conjugate gradient method on the stiefel manifold,

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:44:16.255039Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 69517a00-7ddb-440e-8ef9-77f5beaf8e71 · outbound

This paper cites Decentralized Riemannian natural gradient methods with Kronecker-product approximations.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Decentralized Riemannian natural gradient methods with Kronecker-product approximations

Reference 11

Resolution: verified exact; local_arxiv, observed 2026-08-07T05:44:10.032647Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 9df5943a-a51f-4e00-bd19-b11c5eb087d6 · outbound

This paper cites Distributed Riemannian Stochastic Gradient Tracking Algorithm on the Stiefel Manifold.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Distributed Riemannian Stochastic Gradient Tracking Algorithm on the Stiefel Manifold

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-08-07T05:44:09.801191Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation b869794f-0af7-49d0-b382-e324983fa217 · outbound

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

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Improving the communication in decentralized manifold optimization through single-step consensus and compression

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:05.121164Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f8a9d7c1-40a8-4c5f-8346-42390f597d94 · outbound

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

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Retraction-Free Decentralized Non-convex Optimization with Orthogonal Constraints

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:05.242497Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bac8c661-0d59-405b-914a-1ad37ffaa84a · outbound

This paper cites Deepca: Decentralized exact pca with linear convergence rate,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Deepca: Decentralized exact pca with linear convergence rate,

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:44:15.985432Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 153ba13c-75b2-4dbb-899b-adf9b28d72c6 · outbound

This paper cites Cloud k-svd: A collaborative dictionary learning algorithm for big, distributed data,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Cloud k-svd: A collaborative dictionary learning algorithm for big, distributed data,

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:44:15.624497Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6c61254a-59fe-4d3e-a1a3-dbd313fbc436 · outbound

This paper cites On orthogonality and learning recurrent networks with long term dependencies,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking On orthogonality and learning recurrent networks with long term dependencies,

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:44:15.366249Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c475b345-58f9-4e69-bfd5-4ec49ab32afe · outbound

This paper cites Orthogonal weight normalization: Solution to optimization over multiple dependent stiefel manifolds in deep neural networks,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Orthogonal weight normalization: Solution to optimization over multiple dependent stiefel manifolds in deep neural networks,

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:44:15.056426Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ea21bf9f-b7eb-401d-b1c0-b93d05d4e80f · outbound

This paper cites Understanding how orthogonality of pa- rameters improves quantization of neural networks,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Understanding how orthogonality of pa- rameters improves quantization of neural networks,

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:44:14.750977Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5d450411-cd10-4cdd-8b97-27d945fed815 · outbound

This paper cites Distributed asynchronous deterministic and stochastic gradient optimization algorithms,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Distributed asynchronous deterministic and stochastic gradient optimization algorithms,

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:06.028741Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2a3f1236-b89d-4a80-b19a-44fbdd2d2da7 · outbound

This paper cites On distributed nonconvex optimization: Projected subgradient method for weakly convex problems in networks,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking On distributed nonconvex optimization: Projected subgradient method for weakly convex problems in networks,

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:06.217130Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 23d940d6-b880-4de3-804e-75e7b613995f · outbound

This paper cites Extra: An exact first-order algorithm for decentralized consensus optimization,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Extra: An exact first-order algorithm for decentralized consensus optimization,

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:06.317763Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation abe8655e-f7d6-45bb-99b0-6f7fee8e5766 · outbound

This paper cites Next: In-network nonconvex optimiza- tion,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Next: In-network nonconvex optimiza- tion,

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:06.522608Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3480f5db-0a13-48cc-aca9-2ffdbdd4b10d · outbound

This paper cites On centralized and distributed mirror descent: Convergence analysis using quadratic constraints,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking On centralized and distributed mirror descent: Convergence analysis using quadratic constraints,

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:44:14.472502Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 089090d0-5d0d-464f-92d3-686e6a335c33 · outbound

This paper cites On the local linear rate of consensus on the stiefel manifold,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking On the local linear rate of consensus on the stiefel manifold,

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:44:14.121020Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 2a9bd1d4-ec9f-47d1-905d-aae16a32751a · outbound

This paper cites Decentralized optimization over the stiefel manifold by an approximate augmented lagrangian function,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Decentralized optimization over the stiefel manifold by an approximate augmented lagrangian function,

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:44:13.803065Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 1ed0d194-c16e-46e0-a272-c0bb094de006 · outbound

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

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Fast and accurate optimization on the orthogonal manifold without retraction,

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:44:13.555923Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 203a89c1-42ce-42fc-8359-51a7def3b866 · outbound

This paper cites Design and analysis of distributed averaging with quantized communication,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Design and analysis of distributed averaging with quantized communication,

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:44:13.256915Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 30196b99-69a7-4f2d-a9a5-94d5f6b1d9cd · outbound

This paper cites An exact quantized decentralized gradient descent algorithm,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking An exact quantized decentralized gradient descent algorithm,

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:44:12.935483Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ff6ef3e8-0211-489f-ac09-a72169409cd9 · outbound

This paper cites Quantized decentralized stochastic learning over directed graphs,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Quantized decentralized stochastic learning over directed graphs,

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:07.618658Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation becfa2d0-25f0-41da-be0a-80516f15e383 · outbound

This paper cites A linearly convergent algorithm for decentralized optimization: Sending less bits for free!.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking A linearly convergent algorithm for decentralized optimization: Sending less bits for free!

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:44:12.665172Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6459e111-56bd-4c60-918e-5668d20acae8 · outbound

This paper cites Linear convergent decentralized optimization with compression,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Linear convergent decentralized optimization with compression,

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:44:12.386424Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 05848a6a-0d14-4a49-9d65-747bdcbf216c · outbound

This paper cites Quantized distributed gradient tracking algorithm with linear convergence in directed networks,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Quantized distributed gradient tracking algorithm with linear convergence in directed networks,

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:44:12.083741Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4ad216f5-dc99-4633-a5b3-a4bdf8bedda5 · outbound

This paper cites Absil, R.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Absil, R

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:08.166493Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 68265437-e4b4-49e7-b3b9-12f838758edc · outbound

This paper cites The geometry of algorithms with orthogonality constraints,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking The geometry of algorithms with orthogonality constraints,

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:08.330623Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 115bbe4d-b8a1-47d1-8b71-6d5f278423e4 · outbound

This paper cites A riemannian conjugate gradient method for optimization on the stiefel manifold,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking A riemannian conjugate gradient method for optimization on the stiefel manifold,

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:44:11.772379Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 14479401-9643-4c89-b7fd-4766d776c581 · outbound

This paper cites Riemannian conjugate gradient methods: General framework and specific algorithms with convergence analyses,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Riemannian conjugate gradient methods: General framework and specific algorithms with convergence analyses,

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:44:11.498495Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 72fd9036-5e2d-4c18-8f4e-acc046d8ecfe · outbound

This paper cites Proximal smoothness and the lower-c2 property,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Proximal smoothness and the lower-c2 property,

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:44:11.207847Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation dc8bad1f-cfc0-4203-8023-62e347e85923 · outbound

This paper cites The gradient projection method with armijo’s step size on manifolds,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking The gradient projection method with armijo’s step size on manifolds,

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:44:10.933027Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a6eb8782-cfb2-44b5-983f-b75af2e82ab8 · outbound

This paper cites First-order methods for geodesically convex optimization,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking First-order methods for geodesically convex optimization,

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:09.068397Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4a1950dc-92d6-4489-b496-3991a1705fbc · outbound

This paper cites Equivariant adaptive source separa- tion,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Equivariant adaptive source separa- tion,

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:44:10.681322Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 41e42e96-0fc9-4e18-9ba3-6a811bc44359 · outbound

This paper cites Infeasible deterministic, stochastic, and variance-reduction algorithms for optimization under or- thogonality constraints,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking Infeasible deterministic, stochastic, and variance-reduction algorithms for optimization under or- thogonality constraints,

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:44:10.399520Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 22221eb2-25bb-4e03-bea0-3bd7d07d910d · outbound

This paper cites The mnist database of handwritten digits,.

Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking The mnist database of handwritten digits,

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:09.465818Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.