Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-12T00:17:57.968936Z
Paper Citation Record · LEDGER
As of 18 August 2026, this Paper Citation Record lists 67 of 67 outbound references and 0 inbound Pith citation observations for arXiv:2608.08350.
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 2026-08-12T00:17:57.968936Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+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
67 of 67 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation ad0b7081-e098-4c6d-9fca-392d549a3c6e · outbound
Correlation flow governs learning at criticality In particular, it shows that the asymptotic NTK is strongly governed by the correlation dynamics
Reference 1
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 837f09f2-f5eb-4854-bf9a-881e9b1bea56 · outbound
Reference 2
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 64c32991-a6e5-4519-9af2-ae19dff3a52a · outbound
Correlation flow governs learning at criticality Scaling Laws for Neural Language Models
Reference 3
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0c9b3deb-d71e-494c-b732-f77f1ef2d400 · outbound
Correlation flow governs learning at criticality Varoquaux, S
Reference 4
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 db810fa3-7c25-497c-a0d5-bbd89341ca32 · outbound
Correlation flow governs learning at criticality Unresolved cited work
Reference 5
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 87be659a-7b0b-4298-b92a-ac26690c5366 · outbound
Reference 6
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 abccb503-4797-4100-8ca6-156aed3cb2dc · outbound
Correlation flow governs learning at criticality Glorot and Y
Reference 7
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 80861a02-b448-4c1e-a0a1-9a617d5c6e05 · outbound
Correlation flow governs learning at criticality Unresolved cited work
Reference 8
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 fe9bbb00-3c64-41f8-8af0-92dca7606cfb · outbound
Correlation flow governs learning at criticality Unresolved cited work
Reference 9
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 dcb0a09e-9bb5-40e0-a294-f38c4e6faef0 · outbound
Correlation flow governs learning at criticality There Will Be a Scientific Theory of Deep Learning
Reference 10
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ee55dbde-d7f5-4fc3-ae2e-bf7c6b199d10 · outbound
Correlation flow governs learning at criticality Sompolinsky, Statistical mechanics of neural networks, Physics Today41, 70 (1988)
Reference 11
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 47d531a2-cf43-46e5-9986-4343166d8e9b · outbound
Reference 12
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 90b4a365-ec90-4b19-b6a6-89f8106ee938 · outbound
Reference 13
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 81f72837-dad6-4e25-bba5-7aea92404c16 · outbound
Correlation flow governs learning at criticality Unresolved cited work
Reference 14
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 bd42d376-3c26-458f-9955-3c118b1995a4 · outbound
Correlation flow governs learning at criticality Unresolved cited work
Reference 15
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 e8ddd103-f8ff-4437-9522-556a0dd363dc · outbound
Correlation flow governs learning at criticality Unresolved cited work
Reference 16
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 977fc84a-b9f1-439c-ba28-f15c457dab21 · outbound
Correlation flow governs learning at criticality Rotskoff and E
Reference 17
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 177cce20-0f8b-4dc3-849b-3234061fd375 · outbound
Reference 18
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 25712cef-11cf-4fe2-b87a-1597877dd8d5 · outbound
Reference 19
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 ea3d4079-39ae-4f10-a0f0-5bb263c97e98 · outbound
Correlation flow governs learning at criticality Unresolved cited work
Reference 20
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 e4b655c1-8a98-4231-a5d9-fca506e1fc39 · outbound
Reference 21
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 2dda09f3-33a8-4438-b474-7116a0e74d02 · outbound
Correlation flow governs learning at criticality Unresolved cited work
Reference 22
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 dc783da6-31d6-4268-9f7b-222bdb324cb5 · outbound
Reference 23
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 f9bab682-df22-49d1-9585-4691f88d2b5b · outbound
Correlation flow governs learning at criticality Pennington, S
Reference 24
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 2c98e4b4-efb2-4977-b31b-14d93584c59c · outbound
Correlation flow governs learning at criticality Collins and T
Reference 25
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 1aafd8c3-200f-4338-bc1f-81e317ecd103 · outbound
Reference 26
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 855da077-ce93-4b5b-9979-b7121bb3b7ce · outbound
Correlation flow governs learning at criticality Unresolved cited work
Reference 27
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 88b5d8f2-dfcd-4bbd-849f-a49bc6bee915 · outbound
Reference 28
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 56514ace-f576-4db3-afce-e8a3473d4840 · outbound
Reference 29
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 683eba87-a93a-432f-8479-d2f30761661b · outbound
Correlation flow governs learning at criticality Yaida, Non-gaussian processes and neural networks at finite widths, inMathematical and Scientific Machine Learning(PMLR, 2020) pp
Reference 30
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 077f42d4-9133-49d9-81ce-6b75810fe820 · outbound
Correlation flow governs learning at criticality Hanin, Random fully connected neural networks as perturbatively solvable hierarchies, Journal of Machine Learning Research25, 1 (2024)
Reference 31
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 b271d63a-4479-48fe-924a-ddc87372a8d4 · outbound
Correlation flow governs learning at criticality Hanin and M
Reference 32
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 3c39283f-4aa6-4a92-98ff-4a0920b0f1fb · outbound
Correlation flow governs learning at criticality Unresolved cited work
Reference 33
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 b60c682f-1bbe-4f4c-bcc6-0b718a55927a · outbound
Correlation flow governs learning at criticality Scaling Limits of Wide Neural Networks with Weight Sharing: Gaussian Process Behavior, Gradient Independence, and Neural Tangent Kernel Derivation
Reference 34
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ce6c75d8-c60c-4bf8-b8b6-35caaddbe526 · outbound
Reference 35
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 32a6b651-4988-4a92-9150-ffbad579329e · outbound
Correlation flow governs learning at criticality Unresolved cited work
Reference 36
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 9c684ccc-4c1e-4138-91a2-dafd2e224979 · outbound
Correlation flow governs learning at criticality Sitzmann, J
Reference 37
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 6671415a-753a-4878-84d1-50edf486d0b6 · outbound
Reference 38
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 20869c14-d332-4c5a-9c91-ac2a5c510e1c · outbound
Reference 39
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 8e1410c7-1dd8-4cba-a245-538dcd40e231 · outbound
Correlation flow governs learning at criticality Combette, A
Reference 40
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 02644171-eb97-418d-b75b-68cde920b112 · outbound
Reference 41
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 70ca4a6e-4241-4b44-9f8b-c8ba1823563f · outbound
Correlation flow governs learning at criticality Free probability and random matrices
Reference 42
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 d11937df-dab8-4e2c-8e4c-227e65f24fea · outbound
Correlation flow governs learning at criticality Tensor Programs III: Neural Matrix Laws
Reference 43
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7f41ae7f-da0f-499b-a63f-62dad5992a18 · outbound
Reference 44
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 547d0ccb-b3f9-473f-a2ca-b57303073eed · outbound
Reference 45
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 e718e65a-01a2-47a4-9a48-bf3a94083635 · outbound
Correlation flow governs learning at criticality Rahimi and B
Reference 46
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 72b0f599-24ee-46ee-a7e8-b47a5d2d4e49 · outbound
Correlation flow governs learning at criticality Unresolved cited work
Reference 47
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 15a722e0-0596-4320-92fc-9f173569bd58 · outbound
Reference 48
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 d39b2260-8671-4445-a748-4995ef1a0807 · outbound
Correlation flow governs learning at criticality Unresolved cited work
Reference 49
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 302250f4-5237-4ec0-a549-fe65a0827bfa · outbound
Correlation flow governs learning at criticality Price, A useful theorem for nonlinear devices having gaussian inputs, IEEE Transactions on Information Theory 1958-jun vol
Reference 50
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 729b2999-7e9e-47ba-9e77-a263a76409ae · outbound
Correlation flow governs learning at criticality Mingo and R
Reference 51
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 ac563fcf-c448-4a81-b87c-70569d0a1417 · outbound
Correlation flow governs learning at criticality We begin by rewriting the fixed point condition: K⋆ =F K(K⋆) :=σ 2 wE [ ϕ(z)2] +σ 2 b withz∼N(0,K ⋆).(B2) We consider two distinct cases depending on the value ofσ2 b
Reference 52
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 a470fdc3-f5fe-4bbd-a70a-ca9d489d2724 · outbound
Correlation flow governs learning at criticality Unresolved cited work
Reference 53
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 c6636421-a898-48b8-899b-04e8b28ab22d · outbound
Correlation flow governs learning at criticality Unresolved cited work
Reference 54
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 61971d93-aa6b-444d-b243-3beb61f92aba · outbound
Correlation flow governs learning at criticality In other words, we want to show that, for everyKαβ 0 in this interval, the sequence generated by the limiting map converges
Reference 55
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 53a289be-eed9-4b16-a798-32d635522f5f · outbound
Correlation flow governs learning at criticality Discussion of HypothesisH2We verify that hypothesis (H2), equivalently stated in (B7), is reasonable and holds for common activation functions
Reference 56
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 9b0f8655-53bc-4a28-80c6-d90f994a1ba0 · outbound
Correlation flow governs learning at criticality Unresolved cited work
Reference 57
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 f302d7a3-9689-4264-9255-68e9b8a97599 · outbound
Correlation flow governs learning at criticality Unresolved cited work
Reference 58
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 d7e433cf-4d09-4deb-910d-3e3c1aa76b86 · outbound
Correlation flow governs learning at criticality Unresolved cited work
Reference 59
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 76596af8-c050-4995-a56f-8d0ecfa55e08 · outbound
Correlation flow governs learning at criticality Unresolved cited work
Reference 60
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 7af884d3-dc09-4eef-b18c-3e373f6dd9d9 · outbound
Correlation flow governs learning at criticality Unresolved cited work
Reference 61
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 182c23fd-a08a-4d15-ac5f-d77c744bba76 · outbound
Correlation flow governs learning at criticality Unresolved cited work
Reference 62
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 80035966-efe5-4411-9ca8-06425e6c3dbd · outbound
Correlation flow governs learning at criticality This gives the scaling ( m(2) Dα ℓ Dβ ℓ /(m(1) Dα ℓ Dβ ℓ )2−1 ) =O(ℓ−2), giving us the convergence of the studied sum
Reference 63
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 32b0e3f1-a95a-448c-8c1c-74b931330a5a · outbound
Correlation flow governs learning at criticality Unresolved cited work
Reference 64
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 90debe0c-43a4-4be4-9257-620453d5b97e · outbound
Correlation flow governs learning at criticality Unresolved cited work
Reference 65
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 cf00afc8-9ef6-4715-80ae-5cc16235aed1 · outbound
Correlation flow governs learning at criticality Bound on ‖‖‖1 L ∑L ℓ=1 Pαβ L→ℓ−I ‖‖‖ 2 F In this section we will prove(91)
Reference 66
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 5b8d914a-fc66-475a-ae04-62847fdeae91 · outbound
Correlation flow governs learning at criticality Unresolved cited work
Reference 67
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.
No inbound Pith citation observations are available.