Paper Citation Record · LEDGER

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks

As of 7 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 0 inbound Pith citation observations for arXiv:2607.25200.

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

pith.paper-citation-record.v1
2607.25200 v1

Coverage vector

measured 35 of 35 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-01T03:14:40.031214Z

measured 35 of 35 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+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

35 of 35 outbound references displayed

verified exact2
verified fuzzy0
unresolved33
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 2c8999f1-332a-4ab8-812f-62fb0759ebc4 · outbound

This paper cites A Spectral Condition for Feature Learning.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks A Spectral Condition for Feature Learning

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:39.925495Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2f05a4e0-72a1-4ace-a27d-f5ce17d3b243 · outbound

This paper cites , month = jul, year =.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks , month = jul, year =

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:39.929490Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 36718faa-49bd-46ca-982b-51f3f1e8b3d7 · outbound

This paper cites Proceedings of the IEEE International Conference on Computer Vision (ICCV) , month =.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks Proceedings of the IEEE International Conference on Computer Vision (ICCV) , month =

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:39.934048Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0bde6a8f-3dba-48fa-a79a-92bb68cbd797 · outbound

This paper cites 2026 , eprint=.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks 2026 , eprint=

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:39.937135Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 044cc3e0-2c00-4b3f-a88b-aa147a3e12b2 · outbound

This paper cites Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics , pages =.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics , pages =

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:39.940192Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation debd3ef2-ef8c-443d-868c-d01450cf784b · outbound

This paper cites Journal of the ACM (JACM) , author =.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks Journal of the ACM (JACM) , author =

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:39.943517Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 42853685-dbf3-48e2-a1cf-85c640374437 · outbound

This paper cites Failures of.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks Failures of

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:39.946656Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1b1e3e37-0966-4b0d-a65c-e758d6955df8 · outbound

This paper cites The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning

Reference 8

Resolution: verified exact; local_arxiv, observed 2026-08-01T03:19:17.644733Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 344be888-409d-417c-972c-6e0a6a185bf5 · outbound

This paper cites an unresolved cited work.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:39.952843Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f7fa04bf-0244-41ad-bca1-efbaf514f164 · outbound

This paper cites an unresolved cited work.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:39.955941Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d9ac52cf-1702-4ce6-aa51-6197955b5d30 · outbound

This paper cites and Favero, Alessandro and Wyart, Matthieu , month = jul, year =.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks and Favero, Alessandro and Wyart, Matthieu , month = jul, year =

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:39.959367Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6db83150-6de6-4c47-a8ee-ed2ade99d7e3 · outbound

This paper cites an unresolved cited work.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks Unresolved cited work

Reference 12

Resolution: verified exact; arxiv_id, observed 2026-08-01T03:19:17.575477Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 56336011-ffbb-4dd8-80d8-a004b88963cf · outbound

This paper cites What can.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks What can

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:39.965736Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7c7d107d-f67b-4dd8-87a2-d6ec63c9f3b3 · outbound

This paper cites Backward.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks Backward

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:39.968482Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2c28ab14-5f02-4905-bbc3-b3b56951d99c · outbound

This paper cites , month = oct, year =.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks , month = oct, year =

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:39.971256Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3f0dbac9-8fdb-491f-bb42-2a4074628006 · outbound

This paper cites International Conference on Representation Learning , author =.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks International Conference on Representation Learning , author =

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:39.974436Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4432163e-ba38-4c3f-8126-90e40333c1f3 · outbound

This paper cites The merged-staircase property: a necessary and nearly sufficient condition for.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks The merged-staircase property: a necessary and nearly sufficient condition for

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:39.977392Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8d6f5ba3-64f7-4899-9a8c-c6fa797c25cc · outbound

This paper cites The staircase property:.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks The staircase property:

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:39.980193Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 57bd9f5d-f352-4fdc-9b2a-a3b5f24c9a6c · outbound

This paper cites 2024 , eprint=.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks 2024 , eprint=

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:39.983152Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 71184ade-1965-4948-82bf-0c0ce22eb199 · outbound

This paper cites Proceedings of.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks Proceedings of

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:39.986185Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6500dea9-5215-446c-848d-677c5f977298 · outbound

This paper cites , editor =.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks , editor =

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:39.989334Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 844dfde8-5dd7-42c2-8f1a-b70d6a858889 · outbound

This paper cites an unresolved cited work.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks Unresolved cited work

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:39.992099Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7cee90bf-3dc3-4061-87b1-e733e9ea1104 · outbound

This paper cites Optimization-.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks Optimization-

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:39.994962Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c9e27c70-7663-4d52-befe-f492442282a5 · outbound

This paper cites Provable.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks Provable

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:39.997847Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 551ae528-be24-4892-84db-a923d8f14ec9 · outbound

This paper cites an unresolved cited work.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks Unresolved cited work

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:40.001111Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a3bf6034-6711-44cb-87cd-b19957a20be0 · outbound

This paper cites Journal of Machine Learning Research , author =.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks Journal of Machine Learning Research , author =

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:40.004344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9bfd6638-3f9b-4daa-9e16-0f91ee76e557 · outbound

This paper cites an unresolved cited work.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks Unresolved cited work

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:40.007385Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2b07e3af-6402-47b9-87a0-9f01ba1f855f · outbound

This paper cites an unresolved cited work.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks Unresolved cited work

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:40.010302Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 96d0d7b5-cfa3-49b1-8a29-842f65518265 · outbound

This paper cites an unresolved cited work.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks Unresolved cited work

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:40.013119Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1c271235-2791-4120-8cd7-649eaa3fed67 · outbound

This paper cites an unresolved cited work.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks Unresolved cited work

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:40.015977Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a7a496f2-6d6b-4d4d-ab91-4d03cb68ba5b · outbound

This paper cites benefits of depth in neural networks , volume =.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks benefits of depth in neural networks , volume =

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:40.019238Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3288a254-eae1-40df-a106-5853b7b05e26 · outbound

This paper cites , year =.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks , year =

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:40.022027Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ff8756fd-2eea-4e94-9e2b-69daf28b49f6 · outbound

This paper cites , year =.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks , year =

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:40.025011Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 20a91c80-9127-45ff-987d-6956c97674de · outbound

This paper cites Concentration inequalities: a nonasymptotic theory of independence , isbn =.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks Concentration inequalities: a nonasymptotic theory of independence , isbn =

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:40.028139Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 971f4860-6998-497a-89e4-78d998f24f8d · outbound

This paper cites Analysis of.

Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks Analysis of

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-01T03:14:40.031214Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.