Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T16:28:38.100097Z
Paper Citation Record · LEDGER
Toric geometry of ReLU neural networks
As of 23 August 2026, this Paper Citation Record lists 13 of 13 outbound references and 1 inbound Pith citation observation for arXiv:2509.05894.
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 2026-08-23T06:30:58.430688+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-06-28T12:26:10.454497Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-07-02T01:16:24.156397Z
Reference resolution
13 of 13 outbound references displayed
- verified exact0
- verified fuzzy10
- unresolved3
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 1bfd4b2e-9215-4669-a416-de219d0f4cbf · outbound
This paper cites Understanding deep neural networks with rectified linear units.
Toric geometry of ReLU neural networks Understanding deep neural networks with rectified linear units
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:28:38.870327Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 9fcdd3d3-874b-4cb2-9f43-65f657e574da · outbound
This paper cites Better neural network expressivity: subdividing the simplex.arXiv preprint arXiv:2505.14338, 2025.
Toric geometry of ReLU neural networks Better neural network expressivity: subdividing the simplex.arXiv preprint arXiv:2505.14338, 2025
Reference 2
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T16:28:37.892441Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a4a915e8-2646-458c-b51f-2d9685ab9e2e · outbound
This paper cites American Mathematical Soc., 2011.
Toric geometry of ReLU neural networks American Mathematical Soc., 2011
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:28:38.852381Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 21074f35-ef0c-4858-992f-5b18e79e0dd6 · outbound
This paper cites Activation degree thresholds and expressiveness of polynomial neural networks.
Toric geometry of ReLU neural networks Activation degree thresholds and expressiveness of polynomial neural networks
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:28:38.834344Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation b58a9ff4-6e5a-4ee7-aa94-8748506c7b83 · outbound
This paper cites On transversality of bent hyperplane ar- rangements and the topological expressiveness of relu neural networks.SIAM Journal on Applied Algebra and Geometry, 6(2):216–242, 2022.
Toric geometry of ReLU neural networks On transversality of bent hyperplane ar- rangements and the topological expressiveness of relu neural networks.SIAM Journal on Applied Algebra and Geometry, 6(2):216–242, 2022
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:28:38.748654Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 05cafa5d-ac36-480f-bca8-4583eb90cfc1 · outbound
This paper cites Lower Bounds on the Depth of Integral ReLU Neural Networks via Lattice Polytopes.
Toric geometry of ReLU neural networks Lower Bounds on the Depth of Integral ReLU Neural Networks via Lattice Polytopes
Reference 6
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T16:28:37.998632Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 761eeaec-fc22-4edd-944d-6f4795491981 · outbound
This paper cites Towards lower bounds on the depth of relu neural networks.SIAM Journal on Discrete Math- ematics, 37(2):997–1029, 2023.
Toric geometry of ReLU neural networks Towards lower bounds on the depth of relu neural networks.SIAM Journal on Discrete Math- ematics, 37(2):997–1029, 2023
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:28:38.600213Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 52696fe2-aded-4d69-a946-061239b246af · outbound
This paper cites Geometry of polynomial neural networks.Algebraic Statistics, 15(2):295–328, 2024.
Toric geometry of ReLU neural networks Geometry of polynomial neural networks.Algebraic Statistics, 15(2):295–328, 2024
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:28:38.581295Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation fe624dc3-004d-49dd-9483-31f913681ed8 · outbound
This paper cites American Mathematical Society, 2021.
Toric geometry of ReLU neural networks American Mathematical Society, 2021
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:28:38.444376Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 9f3f6ce9-7954-4403-a64e-7e1addfc8b61 · outbound
This paper cites Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry.
Toric geometry of ReLU neural networks Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry
Reference 10
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T16:28:38.020965Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation efcafec0-8eca-4bcf-85b9-f97197e3a9ac · outbound
This paper cites Approximation theory of the mlp model in neural networks.Acta Nu- merica, 8:143–195, 1999.
Toric geometry of ReLU neural networks Approximation theory of the mlp model in neural networks.Acta Nu- merica, 8:143–195, 1999
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:28:38.343553Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation ca13f8f0-c01e-484b-ba2d-91f4692ec156 · outbound
This paper cites Generalization of hinging hyperplanes.IEEE Trans- actions on Information Theory, 51(12):4425–4431, 2005.
Toric geometry of ReLU neural networks Generalization of hinging hyperplanes.IEEE Trans- actions on Information Theory, 51(12):4425–4431, 2005
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:28:38.326935Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 501ad357-6782-4053-9efd-9c84b4790d5d · outbound
This paper cites Tropical geometry of deep neu- ral networks.
Toric geometry of ReLU neural networks Tropical geometry of deep neu- ral networks
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T16:28:38.308663Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Pith citing papers
Observation 991f3b3e-73ec-49fd-8071-6e7c284e6cc6 · inbound
On the fibers and semi-algebraicity of ReLU neuromanifolds cites this paper.
On the fibers and semi-algebraicity of ReLU neuromanifolds Toric geometry of ReLU neural networks
Reference 37
- Resolution
- verified exact
- arxiv_id, observed 2026-07-02T01:16:24.159341Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.