Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-05-20T12:12:01.073779Z
Paper Citation Record · LEDGER
The Symmetries of Three-Layer ReLU Networks
As of 7 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 1 inbound Pith citation observation for arXiv:2605.18319.
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 2026-08-07T06:34:17.273281+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-07-12T01:11:50.444218Z
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
27 of 27 outbound references displayed
- verified exact1
- verified fuzzy15
- unresolved11
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation f1d0a37a-bf3a-4818-9ab3-c18b08aecfcd · outbound
This paper cites Daniel Kunin, Javier Sagastuy-Brena, Surya Ganguli, Daniel LK Yamins, and Hidenori Tanaka.
The Symmetries of Three-Layer ReLU Networks Daniel Kunin, Javier Sagastuy-Brena, Surya Ganguli, Daniel LK Yamins, and Hidenori Tanaka
Reference 1
- Resolution
- verified exact
- doi, observed 2026-05-20T12:13:15.775474Z
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 bc1652a7-4a39-4faa-b5da-1ce14fdcd79c · outbound
This paper cites an unresolved cited work.
The Symmetries of Three-Layer ReLU Networks Unresolved cited work
Reference 2
- Resolution
- unresolved
- raw_fallback, observed 2026-05-20T12:13:16.619270Z
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 410a42e6-5668-47cc-ad45-d82f3b7d0234 · outbound
This paper cites an unresolved cited work.
The Symmetries of Three-Layer ReLU Networks Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-05-20T12:13:16.620979Z
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 d094b2a2-155a-4903-80e7-d64cb2481840 · outbound
This paper cites For a polyhedral complex C in Rd and k≤d we denote by Ck the set of k-dimensional polyhedra in C.
The Symmetries of Three-Layer ReLU Networks For a polyhedral complex C in Rd and k≤d we denote by Ck the set of k-dimensional polyhedra in C
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-20T12:13:16.615322Z
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 a58e6b97-f4bb-44f3-aaaa-790bf1972792 · outbound
This paper cites an unresolved cited work.
The Symmetries of Three-Layer ReLU Networks Unresolved cited work
Reference 5
- Resolution
- unresolved
- raw_fallback, observed 2026-05-20T12:13:16.611679Z
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 4b2b207d-38c3-4b30-81c6-1c3e387aff41 · outbound
This paper cites We denote the set of generic parameters by ˜ΘA ⊆Θ A.
The Symmetries of Three-Layer ReLU Networks We denote the set of generic parameters by ˜ΘA ⊆Θ A
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-20T12:13:16.613444Z
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 e193e576-4e45-453c-ab45-fa148d42d6ca · outbound
This paper cites In particular,H∩R= aff(σ 1)∩R.
The Symmetries of Three-Layer ReLU Networks In particular,H∩R= aff(σ 1)∩R
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-20T12:13:16.617518Z
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 f19def0c-ac57-4372-b6df-5dc38202629d · outbound
This paper cites In particular, H∩R= aff(σ)∩R.
The Symmetries of Three-Layer ReLU Networks In particular, H∩R= aff(σ)∩R
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-20T12:13:16.656475Z
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 e116a008-4944-467c-8f64-7cd4b2967f18 · outbound
This paper cites an unresolved cited work.
The Symmetries of Three-Layer ReLU Networks Unresolved cited work
Reference 9
- Resolution
- unresolved
- raw_fallback, observed 2026-05-20T12:13:16.658373Z
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 2b5a580b-1162-4e56-b564-b55e1eb02a31 · outbound
This paper cites Proof of Theorem 2.
The Symmetries of Three-Layer ReLU Networks Proof of Theorem 2
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-20T12:13:16.648948Z
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 fe68bc04-8fcf-48de-9111-df0511806a53 · outbound
This paper cites an unresolved cited work.
The Symmetries of Three-Layer ReLU Networks Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-05-20T12:13:16.645523Z
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 72069e2a-abae-4cd2-9be9-6e45a3edd92d · outbound
This paper cites k}, 0ifj∈ {k+ 1.
The Symmetries of Three-Layer ReLU Networks k}, 0ifj∈ {k+ 1
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-20T12:13:16.643837Z
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 763500af-d5e1-4642-9340-14b86fe4f436 · outbound
This paper cites an unresolved cited work.
The Symmetries of Three-Layer ReLU Networks Unresolved cited work
Reference 13
- Resolution
- unresolved
- raw_fallback, observed 2026-05-20T12:13:16.647279Z
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 fc1470c2-3321-4480-b388-ae9d264fe6a2 · outbound
This paper cites Thus k=|N vis|and the assignment mapϕrestricted toN vis is a permutation.
The Symmetries of Three-Layer ReLU Networks Thus k=|N vis|and the assignment mapϕrestricted toN vis is a permutation
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-20T12:13:16.650756Z
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 bada8592-a166-4b27-a1af-a952970887f5 · outbound
This paper cites ThusN can =∅.
The Symmetries of Three-Layer ReLU Networks ThusN can =∅
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-20T12:13:16.640271Z
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 f686be68-3bca-4663-b0f2-d7af3d902628 · outbound
This paper cites an unresolved cited work.
The Symmetries of Three-Layer ReLU Networks Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-05-20T12:13:16.636659Z
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 56ce6386-36bd-4f5a-a796-8d37813cbb3b · outbound
This paper cites an unresolved cited work.
The Symmetries of Three-Layer ReLU Networks Unresolved cited work
Reference 17
- Resolution
- unresolved
- raw_fallback, observed 2026-05-20T12:13:16.634818Z
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 b0b59b39-c8a8-48ee-bf2d-2667c79bdde9 · outbound
This paper cites an unresolved cited work.
The Symmetries of Three-Layer ReLU Networks Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-05-20T12:13:16.638431Z
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 f334ed77-2bc4-48e4-8b26-d413c44b3f5c · outbound
This paper cites Proof of Theorem 6.LetJ= [n]\[k].
The Symmetries of Three-Layer ReLU Networks Proof of Theorem 6.LetJ= [n]\[k]
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-20T12:13:16.642112Z
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 42316b32-7368-4af1-b23c-b9d6a0fab888 · outbound
This paper cites an unresolved cited work.
The Symmetries of Three-Layer ReLU Networks Unresolved cited work
Reference 20
- Resolution
- unresolved
- raw_fallback, observed 2026-05-20T12:13:16.652415Z
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 84717f0e-e514-429d-8774-1f17cb8d3a6b · outbound
This paper cites Moreover, it holds that z(2,η) i (x)≤W (2) ij [y+t] + +b (2,η) i =b (2,η) i =b (2) i −tW (2) ij ≤0.
The Symmetries of Three-Layer ReLU Networks Moreover, it holds that z(2,η) i (x)≤W (2) ij [y+t] + +b (2,η) i =b (2,η) i =b (2) i −tW (2) ij ≤0
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-20T12:13:16.654571Z
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 05577505-982c-45b3-af7d-e7e5b6e20760 · outbound
This paper cites Moreover, it holds that z(2,θ) i (x)≤W (2) ij [y]+ +b (2) i =b (2) i ≤0.
The Symmetries of Three-Layer ReLU Networks Moreover, it holds that z(2,θ) i (x)≤W (2) ij [y]+ +b (2) i =b (2) i ≤0
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-20T12:13:16.630853Z
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 c6eb6cb3-51d8-4d98-9d2a-c50eac2eaa06 · outbound
This paper cites In all four cases, a(2,η) i (x) =a (2,θ) i (x), and thus η∈ ˜S(θ).
The Symmetries of Three-Layer ReLU Networks In all four cases, a(2,η) i (x) =a (2,θ) i (x), and thus η∈ ˜S(θ)
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-20T12:13:16.626637Z
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 885b4641-497a-4656-9233-ebef24d63e5e · outbound
This paper cites an unresolved cited work.
The Symmetries of Three-Layer ReLU Networks Unresolved cited work
Reference 24
- Resolution
- unresolved
- raw_fallback, observed 2026-05-20T12:13:16.629093Z
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 5ffb52b5-4694-4883-9120-b3c3939ab9b4 · outbound
This paper cites The statements follow from established results on hyperplane arrangements (see, e.g., Orlik and Terao, 1992, Chapter 2).
The Symmetries of Three-Layer ReLU Networks The statements follow from established results on hyperplane arrangements (see, e.g., Orlik and Terao, 1992, Chapter 2)
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-20T12:13:16.633056Z
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 ab58344d-bc68-438b-8244-e30ebe84fd9b · outbound
This paper cites If P∩B j(θ)̸=∅ , then the facet P∩B j(θ) is parallel to a first-layer hyperplaneH i ∈ H 1(θ)if and only ifS 1(P) ={i}.
The Symmetries of Three-Layer ReLU Networks If P∩B j(θ)̸=∅ , then the facet P∩B j(θ) is parallel to a first-layer hyperplaneH i ∈ H 1(θ)if and only ifS 1(P) ={i}
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-20T12:13:16.622923Z
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 acc2e083-06c5-4d0b-b41b-3b4c9559da36 · outbound
This paper cites linear evidence.
The Symmetries of Three-Layer ReLU Networks linear evidence
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-20T12:13:16.624716Z
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.
Pith citing papers
Observation 9cd6e4e2-04eb-4282-ab38-cd209c4bc771 · 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 Symmetries of Three-Layer ReLU Networks
Reference 22
- Resolution
- unresolved
- no resolver link, observed 2026-07-12T01:11:50.444218Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.