Paper Citation Record · LEDGER

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry

As of 15 August 2026, this Paper Citation Record lists 68 of 68 outbound references and 7 inbound Pith citation observations for arXiv:2501.18915.

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

pith.paper-citation-record.v1
2501.18915 v2

Coverage vector

measured 68 of 68 reference resolution

Typed states for the displayed outbound observations.

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measured 75 of 75 standing notices

One-hop event checks from named stored sources.

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measured 7 of 7 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-03T23:41:26.610335Z

measured 1 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Reference resolution

68 of 68 outbound references displayed

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External citation measurements

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arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Outbound references

Observation 81c49474-0223-4ab5-9568-ebde931a88a7 · outbound

This paper cites write newline.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry write newline

Reference 1

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This paper cites and Heaton, A.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry and Heaton, A

Reference 2

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This paper cites Information geometry and its applications, volume 194.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Information geometry and its applications, volume 194

Reference 3

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This paper cites Singularities affect dynamics of learning in neuromanifolds.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Singularities affect dynamics of learning in neuromanifolds

Reference 4

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This paper cites Geometry and optimization of shallow polynomial networks.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Geometry and optimization of shallow polynomial networks

Reference 5

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This paper cites Understanding deep neural networks with rectified linear units.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Understanding deep neural networks with rectified linear units

Reference 6

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This paper cites On the optimization of deep networks: Implicit acceleration by overparameterization.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry On the optimization of deep networks: Implicit acceleration by overparameterization

Reference 7

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry and Lerario, A

Reference 8

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This paper cites Voronoi diagrams of algebraic varieties under polyhedral norms.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Voronoi diagrams of algebraic varieties under polyhedral norms

Reference 9

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This paper cites and Milman, P.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry and Milman, P

Reference 10

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This paper cites Rational neural networks.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Rational neural networks

Reference 11

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This paper cites Decomposition Polyhedra of Piecewise Linear Functions.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Decomposition Polyhedra of Piecewise Linear Functions

Reference 12

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This paper cites The real tropical geometry of neural networks for binary classification.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry The real tropical geometry of neural networks for binary classification

Reference 13

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This paper cites Metric Algebraic Geometry.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Metric Algebraic Geometry

Reference 14

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This paper cites Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges

Reference 15

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry and Vetter, U

Reference 16

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This paper cites Neuromanifolds.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Neuromanifolds

Reference 17

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This paper cites The maximum likelihood degree.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry The maximum likelihood degree

Reference 18

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry \"O ., Jamneshan, A., Mont \'u far, G., Sturmfels, B., and Venturello, L

Reference 19

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry and Smale, S

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Polynomial approximations to continuous functions

Reference 21

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Unresolved cited work

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry S., Hu, W., and Lee, J

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry and Harer, J

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry and Harris, J

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry I., Wu, C., and Yahl, T

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry and Carbin, M

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Intersection theory, volume 2

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Position: Categorical Deep Learning is an Algebraic Theory of All Architectures

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Hidden symmetries of relu networks

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Classes de faisceaux et theoreme de rimann-roch

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Topological Deep Learning: Going Beyond Graph Data

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry W., Marchetti, G

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry A., Jordan, M

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Neural tangent kernel: Convergence and generalization in neural networks

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry On the expressive power of deep polynomial neural networks

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry The geometry of the neuromanifold

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Geometry of linear convolutional networks

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Function space and critical points of linear convolutional networks

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Geometry of polynomial neural networks

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry and Sturmfels, B

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry L., Hillar, C

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Abide by the law and follow the flow: Conservation laws for gradient flows

Reference 45

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Low rank approximation: algorithms, implementation, applications, volume 906

Reference 46

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry The algebraic degree of the Wasserstein distance

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Sharp bounds for the number of regions of maxout networks and vertices of minkowski sums

Reference 49

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Approximation theory of the mlp model in neural networks

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry A note on different covering numbers in learning theory

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Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry and Hirsch, K

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Observation 170f5247-4409-49fb-8ccf-81e9f4d12ad2 · outbound

This paper cites Algebraic Complexity and Neurovariety of Linear Convolutional Networks.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Algebraic Complexity and Neurovariety of Linear Convolutional Networks

Reference 55

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This paper cites L., and Kohn, K.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry L., and Kohn, K

Reference 56

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:04:57.158009Z

Source-reported events for the cited work

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Observation 1350224c-316f-4c5b-96c3-4a14182ab998 · outbound

This paper cites Learning on a Razor's Edge: Identifiability and Singularity of Polynomial Neural Networks.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Learning on a Razor's Edge: Identifiability and Singularity of Polynomial Neural Networks

Reference 57

Resolution: verified exact; local_arxiv, observed 2026-08-09T22:04:26.755734Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 7eb8da01-2e58-443c-888b-eb82b3a699d4 · outbound

This paper cites Pure and spurious critical points: a geometric study of linear networks.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Pure and spurious critical points: a geometric study of linear networks

Reference 58

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:04:57.144071Z

Source-reported events for the cited work

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Observation db698673-57b2-4cb0-951f-6b09a15c4206 · outbound

This paper cites an unresolved cited work.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Unresolved cited work

Reference 59

Resolution: unresolved; raw_fallback, observed 2026-08-09T22:04:57.128791Z

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Observation 69440491-1665-4811-aede-f538311f0e77 · outbound

This paper cites Attention is all you need.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Attention is all you need

Reference 60

Resolution: unresolved; no resolver link, observed 2026-08-09T22:04:26.653383Z

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Observation b0ba68e3-6d35-4b5c-8c16-ad5d6aa5da6f · outbound

This paper cites Algebraic geometry and statistical learning theory, volume 25.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Algebraic geometry and statistical learning theory, volume 25

Reference 61

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:04:57.104700Z

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Observation 98a8222e-bf00-4f70-b677-3e55ba668c70 · outbound

This paper cites On the volume of tubes.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry On the volume of tubes

Reference 62

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:04:57.088700Z

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Observation 86f84e97-7b55-4c3e-bb27-985ecc494bbd · outbound

This paper cites Gradient dynamics of shallow univariate relu networks.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Gradient dynamics of shallow univariate relu networks

Reference 63

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:04:57.074330Z

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Observation bb982a42-849d-4b6e-8633-77f363c348f2 · outbound

This paper cites and Comte, G.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry and Comte, G

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:04:57.058842Z

Source-reported events for the cited work

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Observation c5019cde-5db1-4b53-9f21-0befad94c6ec · outbound

This paper cites Arbitrary-Depth Universal Approximation Theorems for Operator Neural Networks.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Arbitrary-Depth Universal Approximation Theorems for Operator Neural Networks

Reference 65

Resolution: verified exact; local_arxiv, observed 2026-08-09T22:04:26.734525Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation e1f28ff8-3dbc-498e-b451-8c44ffb9573c · outbound

This paper cites Tropical geometry of deep neural networks.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry Tropical geometry of deep neural networks

Reference 66

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:04:57.044497Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 6052bb30-8a86-496c-a088-79792fe201dd · outbound

This paper cites and Kileel, J.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry and Kileel, J

Reference 67

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T22:04:57.030213Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 29066d01-464b-437e-99de-70b5f8a35532 · outbound

This paper cites A survey on model compression for large language models.

Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry A survey on model compression for large language models

Reference 68

Resolution: unresolved; no resolver link, observed 2026-08-09T22:04:26.689658Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 23192e91-d0ec-4225-bdbe-46355382193e · inbound

Minimal Filling Architectures of Polynomial Neural Networks: Counterexamples, Frontier Search, and Defects cites this paper.

Minimal Filling Architectures of Polynomial Neural Networks: Counterexamples, Frontier Search, and Defects Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-05-12T02:26:16.441003Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation c12a4018-36d8-47dd-8c57-13921e3b53f6 · inbound

Minimal Filling Architectures of Polynomial Neural Networks: Counterexamples, Frontier Search, and Defects cites this paper.

Minimal Filling Architectures of Polynomial Neural Networks: Counterexamples, Frontier Search, and Defects Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-06-30T22:45:06.757470Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 24e0150b-010b-4199-8c11-d407bbb176ac · inbound

Copositive Matrices with Ordered Off-Diagonal Entries cites this paper.

Copositive Matrices with Ordered Off-Diagonal Entries Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry

Reference 299

Resolution: verified exact; arxiv_id, observed 2026-05-20T17:23:35.933539Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 10a4702b-eb7b-4c95-8bb6-a17b0fb7d778 · inbound

Conservation Laws from Data Symmetry in Neural Networks cites this paper.

Conservation Laws from Data Symmetry in Neural Networks Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry

Reference 32

Resolution: verified exact; arxiv_id, observed 2026-07-03T04:27:36.905816Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 3d21324a-39cc-4f62-985d-fe30f458b52d · inbound

Algebraic Networks and Architectural Degenerations cites this paper.

Algebraic Networks and Architectural Degenerations Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry

Reference 23

Resolution: verified exact; arxiv_id, observed 2026-07-03T23:29:02.689092Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation e8ea9427-681c-4ff8-9bc0-65845632f01a · inbound

Patnaik-Pearson intrinsic dimension for internal representations of neural networks cites this paper.

Patnaik-Pearson intrinsic dimension for internal representations of neural networks Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry

Reference 20

Resolution: verified exact; arxiv_id, observed 2026-07-04T02:59:25.625124Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b99231dc-61bc-47bf-b853-6eb20260ef0c · inbound

Patnaik-Pearson intrinsic dimension for internal representations of neural networks cites this paper.

Patnaik-Pearson intrinsic dimension for internal representations of neural networks Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry

Reference 20

Resolution: verified exact; arxiv_id, observed 2026-07-03T23:49:02.127901Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.