Paper Citation Record · LEDGER

How Deep Are Deep GPs, Really? A Sharp Threshold and a Non-Gaussian Limit for Compositional GPs

As of 9 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 0 inbound Pith citation observations for arXiv:2606.08218.

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

pith.paper-citation-record.v1
2606.08218 v1

Coverage vector

measured 12 of 12 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-27T20:11:41.317769Z

measured 12 of 12 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+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

12 of 12 outbound references displayed

verified exact3
verified fuzzy0
unresolved8
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation df6c4c21-7894-4bdc-ac0b-8cac76795be3 · outbound

This paper cites On the infinite-depth limit of finite-width neural networks.

How Deep Are Deep GPs, Really? A Sharp Threshold and a Non-Gaussian Limit for Compositional GPs On the infinite-depth limit of finite-width neural networks

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-07-02T20:47:22.771477Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e42733e0-ccaa-4f4a-8340-9c89a42e05ef · outbound

This paper cites Interpretable deep Gaussian processes with moments.

How Deep Are Deep GPs, Really? A Sharp Threshold and a Non-Gaussian Limit for Compositional GPs Interpretable deep Gaussian processes with moments

Reference 2

Resolution: verified exact; arxiv_id, observed 2026-07-02T20:47:22.774162Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 27e907ed-961d-4bcc-a5b3-b46ea4c08225 · outbound

This paper cites Scaling Limits of Wide Neural Networks with Weight Sharing: Gaussian Process Behavior, Gradient Independence, and Neural Tangent Kernel Derivation.

How Deep Are Deep GPs, Really? A Sharp Threshold and a Non-Gaussian Limit for Compositional GPs Scaling Limits of Wide Neural Networks with Weight Sharing: Gaussian Process Behavior, Gradient Independence, and Neural Tangent Kernel Derivation

Reference 3

Resolution: verified exact; arxiv_id, observed 2026-07-02T20:47:22.768393Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 23206917-5a5c-4033-a888-2fe04c0f7861 · outbound

This paper cites Then (11) reads ui+1 =F(u i)g 2 i .(12) Ifu 1 = 0thenu i ≡0; otherwiseu i >0a.s.

How Deep Are Deep GPs, Really? A Sharp Threshold and a Non-Gaussian Limit for Compositional GPs Then (11) reads ui+1 =F(u i)g 2 i .(12) Ifu 1 = 0thenu i ≡0; otherwiseu i >0a.s

Reference 4

Resolution: unresolved; no resolver link, observed 2026-06-27T20:11:41.317769Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 445811f9-fb9e-4964-8e63-84d49771962f · outbound

This paper cites By the strong Markov property applied atτk + 1 (from which point the chain restarts from the positive stateuτk+1), the same argument givesτk+1 <∞ a.s.

How Deep Are Deep GPs, Really? A Sharp Threshold and a Non-Gaussian Limit for Compositional GPs By the strong Markov property applied atτk + 1 (from which point the chain restarts from the positive stateuτk+1), the same argument givesτk+1 <∞ a.s

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-27T20:11:41.317769Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f3e64a5b-67fa-48ba-85e0-20953dacbec0 · outbound

This paper cites distance.

How Deep Are Deep GPs, Really? A Sharp Threshold and a Non-Gaussian Limit for Compositional GPs distance

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-27T20:11:41.317769Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cd9ba6e6-76ab-45ad-97ec-46bcae21f637 · outbound

This paper cites Now we use thisκ to delimit the small set.

How Deep Are Deep GPs, Really? A Sharp Threshold and a Non-Gaussian Limit for Compositional GPs Now we use thisκ to delimit the small set

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-27T20:11:41.317769Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f043e64e-2d71-44e3-930a-9fd7b4a6f403 · outbound

This paper cites The SLLN argument of part (i) goes through verbatim with logg 2 j replaced bylogX j and Elogg 2 replaced byElogX , givinglim supi Li/i≤ρ d a.s.

How Deep Are Deep GPs, Really? A Sharp Threshold and a Non-Gaussian Limit for Compositional GPs The SLLN argument of part (i) goes through verbatim with logg 2 j replaced bylogX j and Elogg 2 replaced byElogX , givinglim supi Li/i≤ρ d a.s

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-27T20:11:41.317769Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation de28140b-a1d8-4cca-9039-9613a5f12eaa · outbound

This paper cites an unresolved cited work.

How Deep Are Deep GPs, Really? A Sharp Threshold and a Non-Gaussian Limit for Compositional GPs Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-27T20:11:41.317769Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 068124c9-2864-4e67-827b-d43317c959b7 · outbound

This paper cites an unresolved cited work.

How Deep Are Deep GPs, Really? A Sharp Threshold and a Non-Gaussian Limit for Compositional GPs Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-27T20:11:41.317769Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e92148ab-f266-4862-bf74-919686b37387 · outbound

This paper cites an unresolved cited work.

How Deep Are Deep GPs, Really? A Sharp Threshold and a Non-Gaussian Limit for Compositional GPs Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-27T20:11:41.317769Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 69970813-c359-44ce-aab8-4a7aaa78f43f · outbound

This paper cites trajectories starting at v1 = 1; the grey dashed reference line has slope −2 logλ predicted by Theorem 4.1 (i), and is hidden behind the simulated curve in every case.

How Deep Are Deep GPs, Really? A Sharp Threshold and a Non-Gaussian Limit for Compositional GPs trajectories starting at v1 = 1; the grey dashed reference line has slope −2 logλ predicted by Theorem 4.1 (i), and is hidden behind the simulated curve in every case

Reference 12

Resolution: malformed identifier; no resolver link, observed 2026-06-27T20:11:41.317769Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.