Paper Citation Record · LEDGER

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem

As of 16 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 0 inbound Pith citation observations for arXiv:2411.15972.

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pith.paper-citation-record.v1
2411.15972 v1

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measured 43 of 43 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-12T13:50:05.932135Z

measured 43 of 43 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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Source: cited_works

Reference resolution

43 of 43 outbound references displayed

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verified fuzzy36
unresolved6
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External citation measurements

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Outbound references

Observation 56cfd67d-8893-43af-97da-bae52725b933 · outbound

This paper cites Phase retrieval via Wirtinger flow: Theory and algorithms,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Phase retrieval via Wirtinger flow: Theory and algorithms,

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.786230Z

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Observation f6b236d7-a2cf-4d5d-b152-b0b48a90f5c0 · outbound

This paper cites Solving random quadratic systems of equations is nearly as easy as solving linear systems,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Solving random quadratic systems of equations is nearly as easy as solving linear systems,

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.768217Z

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Observation c19d3f7b-ddf8-4be4-ae28-76ef51ad5445 · outbound

This paper cites Implicit regularization in nonconvex statistical estimation: Gradient descent converges linearly for phase retrieval and matrix completion,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Implicit regularization in nonconvex statistical estimation: Gradient descent converges linearly for phase retrieval and matrix completion,

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.750593Z

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Observation 1c8a0101-d333-4bf4-8000-7a6e62ed62dd · outbound

This paper cites Low-rank solutions of linear matrix equations via Procrustes Flow,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Low-rank solutions of linear matrix equations via Procrustes Flow,

Reference 4

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Observation f2455980-3af7-45b1-ad39-0d16e944aa53 · outbound

This paper cites Rapid, robust, and reliable blind deconvolution via nonconvex optimization,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Rapid, robust, and reliable blind deconvolution via nonconvex optimization,

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.714254Z

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Observation 9f6edf41-f0ee-4409-b245-236726749b27 · outbound

This paper cites Regularized gradient descent: A non-convex recipe for fast joint blind deconvolution and demixing,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Regularized gradient descent: A non-convex recipe for fast joint blind deconvolution and demixing,

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.695001Z

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Observation fe34e487-ac74-405a-a57a-d5dde70b2be0 · outbound

This paper cites Phase retrieval using alternating minimization,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Phase retrieval using alternating minimization,

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.672833Z

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Observation b9dfdecc-397e-471f-9ba7-05aebf3c6b12 · outbound

This paper cites Phase retrieval with random Gaussian sensing vectors by alternating projections,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Phase retrieval with random Gaussian sensing vectors by alternating projections,

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.653551Z

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Observation 06c681fc-c100-442d-b53b-5faccf11b055 · outbound

This paper cites Non-convex matrix sensing: Breaking the quadratic rank barrier in the sample complexity.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Non-convex matrix sensing: Breaking the quadratic rank barrier in the sample complexity

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-08-12T13:50:06.002085Z

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Observation 02b1b161-ad07-497e-8790-25d351314735 · outbound

This paper cites When Are Nonconvex Problems Not Scary?.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem When Are Nonconvex Problems Not Scary?

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-12T13:50:05.758398Z

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Observation dd94caf2-e77b-40a2-ad10-0834b02873c7 · outbound

This paper cites Cubic regularization of Newton method and its global performance,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Cubic regularization of Newton method and its global performance,

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.635295Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 26be160d-df8e-4c17-895f-f51708ce4c19 · outbound

This paper cites Trust-region methods,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Trust-region methods,

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.617089Z

Source-reported events for the cited work

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Observation 901d6c3d-8dff-4c6e-bda4-11e085048b8f · outbound

This paper cites How to escape saddle points efficiently,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem How to escape saddle points efficiently,

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.596932Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 81644cef-f6ec-4b6a-9935-2b5870686a36 · outbound

This paper cites Escaping from saddle points—online stochastic gradient for tensor decomposition,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Escaping from saddle points—online stochastic gradient for tensor decomposition,

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.575687Z

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Observation c0a012a3-00ec-4cf7-b7b8-42d038617782 · outbound

This paper cites Non-convex learning via stochastic gradient Langevin dynamics: A nonasymptotic analysis,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Non-convex learning via stochastic gradient Langevin dynamics: A nonasymptotic analysis,

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.553373Z

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Observation f4d4ec64-1632-4bff-9a56-6b7d2b650de5 · outbound

This paper cites A hitting time analysis of stochastic gradient Langevin dynamics,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem A hitting time analysis of stochastic gradient Langevin dynamics,

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.534050Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 96a0110b-869b-4b6e-9f50-ad4a7f28fc87 · outbound

This paper cites Implicit regularization in deep matrix factorization,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Implicit regularization in deep matrix factorization,

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.517205Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 5aae268f-33d1-463d-b73a-05ebb96e39fc · outbound

This paper cites Gradient descent with random initialization: Fast global convergence for nonconvex phase retrieval,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Gradient descent with random initialization: Fast global convergence for nonconvex phase retrieval,

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.501493Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 69c4b9dd-fc11-4a77-95cb-9980cf925e1d · outbound

This paper cites Small random initialization is akin to spectral learning: Optimization and generalization guarantees for overparameterized low-rank matrix reconstruction,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Small random initialization is akin to spectral learning: Optimization and generalization guarantees for overparameterized low-rank matrix reconstruction,

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.485091Z

Source-reported events for the cited work

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Observation 4f498a5a-abb8-4d7d-8e2d-7764530772e4 · outbound

This paper cites Implicit balancing and regular- ization: Generalization and convergence guarantees for overparameterized asymmetric matrix sensing,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Implicit balancing and regular- ization: Generalization and convergence guarantees for overparameterized asymmetric matrix sensing,

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.468163Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation eb245c2a-33b3-4195-a800-394bef84e2be · outbound

This paper cites Global convergence of gradient descent for asymmetric low-rank matrix factorization,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Global convergence of gradient descent for asymmetric low-rank matrix factorization,

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.451892Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c06816a2-0b34-4611-81c8-dd04bc7fcc0d · outbound

This paper cites On the stability of gradient flow dynamics for a rank-one matrix approximation problem,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem On the stability of gradient flow dynamics for a rank-one matrix approximation problem,

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.433767Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 2198b8c1-77d2-4c4f-9c69-7f8caf7bd69f · outbound

This paper cites Matrix completion has no spurious local minimum,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Matrix completion has no spurious local minimum,

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.412558Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation eae2c588-45ee-44f2-80a3-69688dbf1877 · outbound

This paper cites Deep learning without poor local minima,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Deep learning without poor local minima,

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.391149Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation fb6230b0-73de-46e2-a128-30f5826e08cc · outbound

This paper cites Fine-grained analysis of optimization and generalization for overparameterized two-layer neural networks,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Fine-grained analysis of optimization and generalization for overparameterized two-layer neural networks,

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.367397Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 413c03f4-4fe3-4165-b50c-80ae759275b3 · outbound

This paper cites Simplified neuron model as a principal component analyzer,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Simplified neuron model as a principal component analyzer,

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.336713Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 8e2e10f0-1765-4918-bc3a-6913c45b558f · outbound

This paper cites Neural networks, principal components, and subspaces,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Neural networks, principal components, and subspaces,

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.314903Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 0c9a48a4-1aa1-4b68-901c-d36446022515 · outbound

This paper cites Helmke and J.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Helmke and J

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.290339Z

Source-reported events for the cited work

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Observation 5e114b14-c88e-4b4d-b657-9ad89f870926 · outbound

This paper cites Weighted low-rank approximations,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Weighted low-rank approximations,

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.266772Z

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Observation 1f676429-edc8-488f-92ef-1a05a7069014 · outbound

This paper cites Understanding the dynamics of gradient flow in overparameterized linear models,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Understanding the dynamics of gradient flow in overparameterized linear models,

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.249145Z

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Observation c5c96ddc-53d2-492c-8850-96ec02393c29 · outbound

This paper cites Constrained nlp via gradient flow penalty continuation: Towards self-tuning robust penalty schemes,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Constrained nlp via gradient flow penalty continuation: Towards self-tuning robust penalty schemes,

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.232323Z

Source-reported events for the cited work

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Observation 78f9ac91-6533-4bf2-b96e-74913e8417a0 · outbound

This paper cites On the solution of differential-algebraic equations through gradient flow embedding,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem On the solution of differential-algebraic equations through gradient flow embedding,

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.215041Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 21482d12-f9ec-45d1-b169-8762a95cbb01 · outbound

This paper cites an unresolved cited work.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:50:06.198276Z

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Observation 07047b25-be19-4c1b-b9c9-6ef0d27747ec · outbound

This paper cites an unresolved cited work.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:50:06.180437Z

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Observation 97286546-bee0-4ccd-92da-811193e64cb6 · outbound

This paper cites An identity for the Schur complement of a matrix,.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem An identity for the Schur complement of a matrix,

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.163322Z

Source-reported events for the cited work

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Observation d700be97-ec17-47ba-8d75-9c80a1b2fc73 · outbound

This paper cites We observe that ¯P1Λ1 = ¯P1( ¯P1 + Λ 1 − ¯P1) = ¯P 2 1 + ¯P1(Λ1 − ¯P1) = ¯P 2 1 + ¯P1VoDoV T o (a) = ¯P 2 1 where (a) follow from the fact that Vi and Vo are orthogonal.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem We observe that ¯P1Λ1 = ¯P1( ¯P1 + Λ 1 − ¯P1) = ¯P 2 1 + ¯P1(Λ1 − ¯P1) = ¯P 2 1 + ¯P1VoDoV T o (a) = ¯P 2 1 where (a) follow from the fact that Vi and Vo are orthogonal

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.146040Z

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Observation 08c9c434-9bec-43f9-8bf5-f52f3f1f1e2d · outbound

This paper cites an unresolved cited work.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:50:06.128755Z

Source-reported events for the cited work

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Observation 651be3af-4c43-4996-9aa7-13f229c6cd30 · outbound

This paper cites an unresolved cited work.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:50:06.112233Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 79c3c0d6-08a0-4bc1-905b-e551fd4b8d6d · outbound

This paper cites an unresolved cited work.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Unresolved cited work

Reference 39

Resolution: unresolved; raw_fallback, observed 2026-08-12T13:50:06.091971Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation d9773957-7f4b-4e57-abd9-62a1ff55e90f · outbound

This paper cites The next lemma establishes the exponential decay of H0.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem The next lemma establishes the exponential decay of H0

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.074066Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation b9517d0f-3338-41c8-a13e-fd0dc741d227 · outbound

This paper cites Lemma 5: Let the matrices A ≻ 0 and B be such that ∥A − B∥2 < σ := σmin(A).

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Lemma 5: Let the matrices A ≻ 0 and B be such that ∥A − B∥2 < σ := σmin(A)

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.057268Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 64349538-044e-4ed0-80ab-aa96a0efe592 · outbound

This paper cites Thus, the convergence results in Theorem 1 hold.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Thus, the convergence results in Theorem 1 hold

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.039283Z

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Observation e6e827f8-9e1d-4867-a19e-1767ea61749b · outbound

This paper cites Equa- tion (36) for i = 1 follows from (31) and the fact that ˆP1 = ˆP1,1.

Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem Equa- tion (36) for i = 1 follows from (31) and the fact that ˆP1 = ˆP1,1

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:50:06.021062Z

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