Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-12T21:23:11.925428Z
Paper Citation Record · LEDGER
The geometry of the deep linear network
As of 20 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 6 inbound Pith citation observations for arXiv:2411.09004.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-15T18:47:32.294872Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-07-04T02:59:25.650690Z
Reference resolution
40 of 40 outbound references displayed
- verified exact1
- verified fuzzy20
- unresolved19
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation f523662d-1481-412c-a5ab-bd35c3d1aa48 · outbound
This paper cites Arora, S.
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T21:23:12.402615Z
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.
Observation 4638cb9f-edc3-4f2a-92da-ff5ffe43e441 · outbound
This paper cites Arora, N.
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T21:23:12.391211Z
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.
Observation be9822b8-763b-4940-bfc1-2b166bad4e93 · outbound
This paper cites Arora, N.
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T21:23:12.379454Z
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.
Observation f7ef6788-333c-4e91-b417-73ab635c065e · outbound
This paper cites Arora, N.
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T21:23:12.367932Z
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.
Observation 159340cd-8221-4606-862c-ac3568430e66 · outbound
This paper cites an unresolved cited work.
The geometry of the deep linear network Unresolved cited work
Reference 5
- Resolution
- unresolved
- no resolver link, observed 2026-08-12T21:23:11.792996Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3261997a-59dc-49a1-bbc6-067050433b98 · outbound
This paper cites an unresolved cited work.
The geometry of the deep linear network Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T21:23:12.348622Z
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.
Observation b5bc2f7d-3ce9-4b68-b17f-a1267c54ea0f · outbound
This paper cites Baldi and K.
The geometry of the deep linear network Baldi and K
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T21:23:12.337198Z
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.
Observation 79d2f6a4-3b9a-4e8a-ab28-16082c00ad33 · outbound
This paper cites an unresolved cited work.
The geometry of the deep linear network Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T21:23:12.324832Z
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.
Observation 47bb9376-068e-485e-9f26-702738c7abf7 · outbound
This paper cites an unresolved cited work.
The geometry of the deep linear network Unresolved cited work
Reference 9
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T21:23:12.313257Z
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.
Observation 10054df0-57da-41bf-b6a6-efbb70ec3a6d · outbound
This paper cites Bhatia, T.
The geometry of the deep linear network Bhatia, T
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T21:23:12.300768Z
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.
Observation 366761ad-8a00-46c4-ae7c-dd0e0d1b12a8 · outbound
This paper cites an unresolved cited work.
The geometry of the deep linear network Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T21:23:12.288805Z
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.
Observation 1448050a-3805-44b4-b217-8f47e010448b · outbound
This paper cites Br ´echet, K.
The geometry of the deep linear network Br ´echet, K
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T21:23:12.275823Z
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.
Observation 830ed555-f251-42c5-bb0f-d232ba4f5b40 · outbound
This paper cites Implicit Regularization via Spectral Neural Networks and Non-linear Matrix Sensing.
The geometry of the deep linear network Implicit Regularization via Spectral Neural Networks and Non-linear Matrix Sensing
Reference 13
- Resolution
- unresolved
- no resolver link, observed 2026-08-12T21:23:11.824250Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a3a4af35-50e2-4a5b-99a2-609901647ef1 · outbound
This paper cites Cohen, G.
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T21:23:12.263898Z
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.
Observation 19efc106-0e05-4c47-9506-34c406e51a58 · outbound
This paper cites DeVore, B.
The geometry of the deep linear network DeVore, B
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T21:23:12.252100Z
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.
Observation a43ef40d-2df3-4abc-8a9d-54416d4452bc · outbound
This paper cites From Lazy to Rich: Exact Learning Dynamics in Deep Linear Networks.
The geometry of the deep linear network From Lazy to Rich: Exact Learning Dynamics in Deep Linear Networks
Reference 16
- Resolution
- unresolved
- no resolver link, observed 2026-08-12T21:23:11.835540Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation bb6a9488-0534-4936-a5f9-e7ea03a6b93c · outbound
This paper cites an unresolved cited work.
The geometry of the deep linear network Unresolved cited work
Reference 17
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T21:23:12.240583Z
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.
Observation 8b038428-69a7-47ee-a9d8-86299efdd3fd · outbound
This paper cites an unresolved cited work.
The geometry of the deep linear network Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T21:23:12.227458Z
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.
Observation 8cdc45f5-71c4-4387-9965-a7f93d4ca14f · outbound
This paper cites Gunasekar, J.
The geometry of the deep linear network Gunasekar, J
Reference 19
- Resolution
- unresolved
- no resolver link, observed 2026-08-12T21:23:11.847243Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 96d1d2e8-a260-47b8-9969-acce2c68d466 · outbound
This paper cites Gunasekar, B.
The geometry of the deep linear network Gunasekar, B
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T21:23:12.207711Z
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.
Observation 9a0633d7-018c-4cd0-9ce9-4448ab7ca400 · outbound
This paper cites an unresolved cited work.
The geometry of the deep linear network Unresolved cited work
Reference 21
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T21:23:12.196312Z
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.
Observation 6fa7034c-3810-4150-9e10-a209811457bd · outbound
This paper cites Huang, D.
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T21:23:12.185583Z
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.
Observation 61562d91-1f3a-48cd-ae8e-a2d659ea5117 · outbound
This paper cites Ikeda and S.
The geometry of the deep linear network Ikeda and S
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T21:23:12.174886Z
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.
Observation 76903779-7a2d-42df-bfd9-13003bf653e8 · outbound
This paper cites Stochastic Nash evolution.
The geometry of the deep linear network Stochastic Nash evolution
Reference 24
- Resolution
- verified exact
- local_arxiv, observed 2026-08-12T21:23:11.980186Z
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.
Observation da6bd49f-7e86-4ad7-a836-bea36cb7a263 · outbound
This paper cites an unresolved cited work.
The geometry of the deep linear network Unresolved cited work
Reference 25
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T21:23:12.163200Z
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.
Observation 975c3f36-c743-4f96-9b2c-e04a1c03b210 · outbound
This paper cites an unresolved cited work.
The geometry of the deep linear network Unresolved cited work
Reference 26
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T21:23:12.150920Z
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.
Observation ad409f31-0319-49f4-b0e7-44a380d9669f · outbound
This paper cites L ojasiewicz, Sur les trajectoires du gradient d’une fonction analytique , in Geometry seminars, 1982–1983 (Bologna, 1982/1983), Univ.
The geometry of the deep linear network L ojasiewicz, Sur les trajectoires du gradient d’une fonction analytique , in Geometry seminars, 1982–1983 (Bologna, 1982/1983), Univ
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T21:23:12.138945Z
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.
Observation 260dfa53-9000-4258-aca4-4be524a4fcec · outbound
This paper cites Lapedes and R.
The geometry of the deep linear network Lapedes and R
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T21:23:12.128837Z
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.
Observation 3cbaa838-0cb2-421f-ac3c-a45eb9ca817d · outbound
This paper cites an unresolved cited work.
The geometry of the deep linear network Unresolved cited work
Reference 29
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T21:23:12.117630Z
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.
Observation 0f62a89c-eac0-40f9-9cf5-39f58d92e439 · outbound
This paper cites an unresolved cited work.
The geometry of the deep linear network Unresolved cited work
Reference 30
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T21:23:12.107272Z
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.
Observation 33eae493-e6fa-42eb-8cc4-e93bbdf92287 · outbound
This paper cites Marcotte, R.
The geometry of the deep linear network Marcotte, R
Reference 31
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T21:23:12.096414Z
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.
Observation e1ddc484-5f53-4e55-b6d6-96b4d25262a0 · outbound
This paper cites Keep the Momentum: Conservation Laws beyond Euclidean Gradient Flows.
The geometry of the deep linear network Keep the Momentum: Conservation Laws beyond Euclidean Gradient Flows
Reference 32
- Resolution
- unresolved
- no resolver link, observed 2026-08-12T21:23:11.896252Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation bd9b493e-2a42-4a29-a3f2-36b62b80924c · outbound
This paper cites Menon, Pattern theory: old and new , Lecture notes, Brown University, June 2023.
The geometry of the deep linear network Menon, Pattern theory: old and new , Lecture notes, Brown University, June 2023
Reference 33
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T21:23:12.084640Z
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.
Observation 51ff6bb1-7d1d-4dba-adef-16aded457fa1 · outbound
This paper cites Menon and T.
The geometry of the deep linear network Menon and T
Reference 34
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T21:23:12.073771Z
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.
Observation ec33df9a-701a-4c92-8b24-6a4b499863fd · outbound
This paper cites Milnor, Morse theory, vol.
The geometry of the deep linear network Milnor, Morse theory, vol
Reference 35
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T21:23:12.061267Z
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.
Observation 2c6b3fee-c646-4ad3-8cc5-cb17dc49777a · outbound
This paper cites an unresolved cited work.
The geometry of the deep linear network Unresolved cited work
Reference 36
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T21:23:12.049726Z
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.
Observation 01bca9ec-992f-4abc-b497-3216dc574c10 · outbound
This paper cites an unresolved cited work.
The geometry of the deep linear network Unresolved cited work
Reference 37
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T21:23:12.037788Z
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.
Observation fe589532-e7d2-455a-963c-528c1ca4adbf · outbound
This paper cites Exact solutions to the nonlinear dynamics of learning in deep linear neural networks.
The geometry of the deep linear network Exact solutions to the nonlinear dynamics of learning in deep linear neural networks
Reference 38
- Resolution
- unresolved
- no resolver link, observed 2026-08-12T21:23:11.918199Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b45f3de3-a362-4b16-8c39-f07affc00826 · outbound
This paper cites 11537–11546.
The geometry of the deep linear network 11537–11546
Reference 39
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T21:23:12.026337Z
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.
Observation a9e4ab0d-d9f1-468f-a9bc-7f8e19bfc61b · outbound
This paper cites Simon , Theorems on regularity and singularity of energy minimizing maps , Lectures in Mathematics ETH Z¨ urich, Birkh¨ auser Verlag, Basel, 1996.
The geometry of the deep linear network Simon , Theorems on regularity and singularity of energy minimizing maps , Lectures in Mathematics ETH Z¨ urich, Birkh¨ auser Verlag, Basel, 1996
Reference 40
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T21:23:12.015163Z
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.
Pith citing papers
Observation 5f70a085-1791-44d0-8cfb-dc5bedd56a72 · inbound
The Effect of Depth on the Expressivity of Deep Linear State-Space Models cites this paper.
The Effect of Depth on the Expressivity of Deep Linear State-Space Models The geometry of the deep linear network
Reference 13
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T18:47:32.294872Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1be24f28-cc07-44ef-9233-81e7d86096d6 · inbound
Geodesics in the Deep Linear Network cites this paper.
Geodesics in the Deep Linear Network The geometry of the deep linear network
Reference 9
- Resolution
- verified exact
- arxiv_id, observed 2026-05-18T16:51:38.210340Z
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.
Observation 17b97996-dfb4-4be2-8102-77773c5cc95d · inbound
Rapid mixing for Gibbs measures in Riemannian manifolds cites this paper.
Rapid mixing for Gibbs measures in Riemannian manifolds The geometry of the deep linear network
Reference 25
- Resolution
- verified exact
- arxiv_id, observed 2026-06-27T05:30:35.618273Z
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.
Observation 33f1cbcc-b585-428e-912c-23bd2782dac1 · inbound
Patnaik-Pearson intrinsic dimension for internal representations of neural networks cites this paper.
Patnaik-Pearson intrinsic dimension for internal representations of neural networks The geometry of the deep linear network
Reference 24
- Resolution
- verified exact
- arxiv_id, observed 2026-07-04T02:59:25.652375Z
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.
Observation 734be857-7834-494c-ac32-aed178e2f72f · inbound
Patnaik-Pearson intrinsic dimension for internal representations of neural networks cites this paper.
Patnaik-Pearson intrinsic dimension for internal representations of neural networks The geometry of the deep linear network
Reference 25
- Resolution
- verified exact
- arxiv_id, observed 2026-07-03T23:49:02.132689Z
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.
Observation 0d6c4c9e-eb7b-4c49-8349-af94b7664b05 · inbound
Implicit Bias of SGD in Multivariate ReLU Networks: Effective Width Collapse cites this paper.
Implicit Bias of SGD in Multivariate ReLU Networks: Effective Width Collapse The geometry of the deep linear network
Reference 222
- Resolution
- unresolved
- no resolver link, observed 2026-07-12T01:11:50.444218Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.