Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-16T00:25:15.258156Z
Paper Citation Record · LEDGER
As of 19 August 2026, this Paper Citation Record lists 71 of 71 outbound references and 0 inbound Pith citation observations for arXiv:2608.12183.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-16T00:25:15.258156Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
71 of 71 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 06c9f946-3942-4b0b-b3b4-860297e27f59 · outbound
Spectral phase transitions in Gaussian multi-index models SGD learning on neural networks: leap complex- ity and saddle-to-saddle dynamics
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 40d439c2-ff46-42cc-a502-4ae8e6186c10 · outbound
Spectral phase transitions in Gaussian multi-index models Theory Related Fields173, 293–373 (2019)
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 576371dc-3d71-44c8-b47b-e34cdc34cb24 · outbound
Spectral phase transitions in Gaussian multi-index models Unresolved cited work
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 9ebf5826-7a5e-419d-b162-e102f23251f1 · outbound
Spectral phase transitions in Gaussian multi-index models Unresolved cited work
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 26b509c3-3c33-417f-a516-2d54dfd424c8 · outbound
Spectral phase transitions in Gaussian multi-index models Overparametrization bends the landscape: BBP transitions at initialization in simple neural networks
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 796e3e5b-daee-4283-aa7c-8f5770c145ae · outbound
Spectral phase transitions in Gaussian multi-index models Repetita Iuvant: Data Repetition Allows SGD to Learn High-Dimensional Multi-Index Functions
Reference 6
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 81374f7b-8589-4f4d-8305-adf312679dbd · outbound
Spectral phase transitions in Gaussian multi-index models Aubin, A
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation c4780c07-f4a0-48d4-8f2d-8d7b284ff112 · outbound
Spectral phase transitions in Gaussian multi-index models Bai and J
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 659bf8b1-ef51-4d55-9bea-dba1cce40974 · outbound
Spectral phase transitions in Gaussian multi-index models Unresolved cited work
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 83bbba85-3615-4109-aba8-c2e04e72aad3 · outbound
Spectral phase transitions in Gaussian multi-index models Bandeira, G
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation a0f04110-52ad-42b5-8daf-ecf36a63d8b9 · outbound
Spectral phase transitions in Gaussian multi-index models Ben Arous, R
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 68afabbf-f95a-43ad-936c-6b4d3865a210 · outbound
Spectral phase transitions in Gaussian multi-index models Ben Arous, R
Reference 12
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e8832653-f29f-4cc6-935e-74e21f5552e7 · outbound
Spectral phase transitions in Gaussian multi-index models Ben Arous, R
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation c704ea98-71c5-4811-b645-ba74615c0baa · outbound
Spectral phase transitions in Gaussian multi-index models Bietti, J
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 93de1ec2-7e1e-4168-b842-a67ecf566aff · outbound
Spectral phase transitions in Gaussian multi-index models Escape dynamics and implicit bias of one-pass SGD in overparameterized quadratic networks
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 0b62dfc1-6721-4bfe-bf2e-e7de95d1a3d4 · outbound
Spectral phase transitions in Gaussian multi-index models Bolthausen,An iterative construction of solutions of the TAP equations for the Sherrington- Kirkpatrick model, Comm
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation c598ed43-0132-418b-a8e8-84eb07d7dadc · outbound
Spectral phase transitions in Gaussian multi-index models Bonnaire, G
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 008347a5-aaa6-49a3-bf1a-b0e1342f0fcb · outbound
Spectral phase transitions in Gaussian multi-index models Bruna and D
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 81eb85da-79a8-45c8-be73-385f55c0da89 · outbound
Spectral phase transitions in Gaussian multi-index models Random Matrix Theory of Early-Stopped Gradient Flow: A Transient BBP Scenario
Reference 19
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8831fe6d-aec4-4349-a434-764da3bcfd19 · outbound
Spectral phase transitions in Gaussian multi-index models Collins-Woodfin, C
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation da007663-3523-46c4-8798-add51143fb81 · outbound
Spectral phase transitions in Gaussian multi-index models Unresolved cited work
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 0e737131-2703-4654-a76e-d5537d185f37 · outbound
Spectral phase transitions in Gaussian multi-index models The generative leap: tight sample complexity for efficiently learninggaussian multi-indexmodels
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation a5b1f322-bce0-4019-ac9f-c42c46c097eb · outbound
Spectral phase transitions in Gaussian multi-index models Neural networks can learn representations with gradient descent
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation f7d217e9-6972-484c-9a52-a1814e2b2e29 · outbound
Spectral phase transitions in Gaussian multi-index models The benefits of reusing batches for gradient descent in two-layer networks: breaking the curse of informa- tion and leap exponents
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation c4f50371-14cc-4241-833e-a6b8b581b800 · outbound
Spectral phase transitions in Gaussian multi-index models Deep learning as neural low-degree filtering: a theory of hierarchical feature learning
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation ea5d9c23-f804-4468-a251-c83d855ee098 · outbound
Spectral phase transitions in Gaussian multi-index models Optimal spectral transitions in high-dimensional multi-index models
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation ee5a870e-2f7f-48b9-8049-2bbc780597c0 · outbound
Spectral phase transitions in Gaussian multi-index models Defilippis, F
Reference 27
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 08af7366-f650-4bcb-980a-338a0a590855 · outbound
Spectral phase transitions in Gaussian multi-index models Optimal Spectral Algorithms for Correlated Two-view Models in High Dimensions
Reference 28
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e9628978-2802-4d84-a923-64b1f5d1a9c2 · outbound
Spectral phase transitions in Gaussian multi-index models The matrix Dyson equation and its applications for random matrices
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation ceb34aa0-a7d9-438e-ad82-d128ce878f1c · outbound
Spectral phase transitions in Gaussian multi-index models Unresolved cited work
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation e36ad489-f378-4794-97b8-fca23dd73e5c · outbound
Spectral phase transitions in Gaussian multi-index models Unresolved cited work
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation b74a2263-3485-4ca6-9e9e-e4fbd47265f5 · outbound
Spectral phase transitions in Gaussian multi-index models Gerbelot and R
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 840514fb-5623-4297-a0c2-bf173537eb1a · outbound
Spectral phase transitions in Gaussian multi-index models Gesztesy and E
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 5c396a25-0b9c-4b5c-b0f8-f4f260eb9cfa · outbound
Spectral phase transitions in Gaussian multi-index models Unresolved cited work
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 8d4de211-f7c9-41cf-b611-fa30910acc3a · outbound
Spectral phase transitions in Gaussian multi-index models Unresolved cited work
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation c92aadb1-bb8e-4fd4-b89d-5a4838e566be · outbound
Spectral phase transitions in Gaussian multi-index models Javanmard and A
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 911033fe-001b-447c-96d4-02e059da0a9b · outbound
Spectral phase transitions in Gaussian multi-index models Spectral Estimators for Multi-Index Models: Precise Asymptotics and Optimal Weak Recovery
Reference 37
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 882b4c40-b02b-4fe1-9086-aa528d9651ad · outbound
Spectral phase transitions in Gaussian multi-index models Lehner,Computing norms of free operators with matrix coefficients, Amer
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation c96633fa-de3a-42ed-9aa1-502065e6e57c · outbound
Spectral phase transitions in Gaussian multi-index models Li,Sliced inverse regression for dimension reduction, J
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 45ac7a1d-78a1-4012-8d68-eef0ff3e4f88 · outbound
Spectral phase transitions in Gaussian multi-index models Unresolved cited work
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation ed7568be-9a85-4ba6-91c9-d4562a39afe4 · outbound
Spectral phase transitions in Gaussian multi-index models Unresolved cited work
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation ad7fcd6e-9104-450b-87ff-3f5fb390897a · outbound
Spectral phase transitions in Gaussian multi-index models Unresolved cited work
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 357f882a-f952-4617-b32b-1ab5dcf09424 · outbound
Spectral phase transitions in Gaussian multi-index models Construction of optimal spectral methods in phase retrieval
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 5a0326c0-2bed-471a-998a-6392fb61f52b · outbound
Spectral phase transitions in Gaussian multi-index models Spectral phase transition and optimal PCA in block- structured spiked models
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation aa2472b5-f811-45e0-94af-e49d1759588a · outbound
Spectral phase transitions in Gaussian multi-index models Unresolved cited work
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 3a3c4e5b-4267-4dcf-8786-a5bdfdf9ac68 · outbound
Spectral phase transitions in Gaussian multi-index models Mondelli and A
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 1585f20d-4c7f-415e-9155-4ccab10adf93 · outbound
Spectral phase transitions in Gaussian multi-index models Mondelli, C
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 68a0fbc9-d0b0-447f-8c5f-a313b416a749 · outbound
Spectral phase transitions in Gaussian multi-index models Mondelli and R
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 440d89ea-4f4c-40dc-a7e0-6ae4313b9e74 · outbound
Spectral phase transitions in Gaussian multi-index models Variational Formulas for the Spectrum of Block Wishart Matrices
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 790e6ab5-9341-4d85-900b-67b55b156089 · outbound
Spectral phase transitions in Gaussian multi-index models Montanari and Z
Reference 50
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3c2d117b-4e7a-47a2-afd2-3d00a21c2069 · outbound
Spectral phase transitions in Gaussian multi-index models Neural networks efficiently learn low-dimensional representations with SGD
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 70004b82-597d-4c50-b38f-25dcb641b3de · outbound
Spectral phase transitions in Gaussian multi-index models Nica and R
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation f9afd0f3-9930-4dba-bd7f-fc403611a18e · outbound
Spectral phase transitions in Gaussian multi-index models Parmaksiz and R
Reference 53
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 599a723e-a7f4-4e31-a424-9b508b5c5b84 · outbound
Spectral phase transitions in Gaussian multi-index models Spectral clustering of graphs with the bethe hessian
Reference 54
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 3db6f203-8dd8-4af6-b30d-aa06abe6718e · outbound
Spectral phase transitions in Gaussian multi-index models Complex dynamics in simple neural networks: understanding gradient flow in phase retrieval
Reference 55
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation aad638d3-a99a-40df-b9e6-83efcd0d280e · outbound
Spectral phase transitions in Gaussian multi-index models Who is afraid of big bad minima? analysis of gradient-flow in spiked matrix-tensor models
Reference 56
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation d4810396-2277-4870-b6d4-530bd8c600fb · outbound
Spectral phase transitions in Gaussian multi-index models Unresolved cited work
Reference 57
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation c7f39395-b4e6-4d3f-99e2-454ca4fd0e67 · outbound
Spectral phase transitions in Gaussian multi-index models Learning gaussian multi-index models with gradient flow: time complexity and directional convergence
Reference 58
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 3cbe9465-a0ba-40dc-8791-66aed07e5268 · outbound
Spectral phase transitions in Gaussian multi-index models Subag,TAP approach for multispecies spherical spin glasses II: the free energy of the pure models, Ann
Reference 59
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 5d06b28d-7e71-4a01-b19e-081653624d16 · outbound
Spectral phase transitions in Gaussian multi-index models Subag,TAP approach for multi-species spherical spin glasses I: General theory, Electron
Reference 60
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 5bd96de4-8d48-4815-9c87-614328e29812 · outbound
Spectral phase transitions in Gaussian multi-index models Tao,Topics in random matrix theory, Vol
Reference 61
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation f90feeea-0a21-4723-a95f-5e4f7cb3a15e · outbound
Spectral phase transitions in Gaussian multi-index models Unresolved cited work
Reference 62
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 5a009587-a7d3-410d-86fc-0f60baedae01 · outbound
Spectral phase transitions in Gaussian multi-index models Fundamental computational limits of weak learnability in high-dimensional multi-index models
Reference 63
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 33f4e918-ec85-4f2f-9c53-855562b59b08 · outbound
Spectral phase transitions in Gaussian multi-index models Vershynin,High-dimensional probability, Vol
Reference 64
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation d77c52f3-36b8-47ad-a9f9-41ee0cf4a7ff · outbound
Spectral phase transitions in Gaussian multi-index models Sharp Spectral Thresholds for Multi-View Spiked Wigner Models
Reference 65
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b13f0e57-94d1-41d4-b91a-414345b629b5 · outbound
Spectral phase transitions in Gaussian multi-index models Unresolved cited work
Reference 66
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation a703cd71-dadd-4ee9-ab86-84474076d889 · outbound
Spectral phase transitions in Gaussian multi-index models Zdeborová andF
Reference 67
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation e07be315-047b-4da7-998a-3d2305de5e55 · outbound
Spectral phase transitions in Gaussian multi-index models Zhang, Z
Reference 68
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9aac4896-1433-4c0b-a044-edb837c39f6d · outbound
Spectral phase transitions in Gaussian multi-index models Zhang, H
Reference 69
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation eaa3fc94-6d8b-4fff-b702-88677a9a922a · outbound
Spectral phase transitions in Gaussian multi-index models Zhang, H
Reference 70
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 90f4658a-ca80-4292-b4b5-f39ea894b595 · outbound
Spectral phase transitions in Gaussian multi-index models Zhang, M
Reference 71
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
No inbound Pith citation observations are available.