Paper Citation Record · LEDGER

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs

As of 20 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 0 inbound Pith citation observations for arXiv:2509.03056.

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

pith.paper-citation-record.v1
2509.03056 v2

Coverage vector

measured 43 of 43 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T16:37:56.659938Z

measured 43 of 43 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+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

43 of 43 outbound references displayed

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External citation measurements

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Outbound references

Observation a73aec0a-4534-46bf-b3ad-8b3199908af3 · outbound

This paper cites an unresolved cited work.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:37:57.297851Z

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Observation 62d4b188-3130-4576-919c-89bf78738aa1 · outbound

This paper cites On the Number of Linear Regions of Deep Neural Networks.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs On the Number of Linear Regions of Deep Neural Networks

Reference 2

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Observation e275e413-768d-4cf2-94f5-00f338f03761 · outbound

This paper cites Deep ReLU networks have surprisingly few activation patterns,.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Deep ReLU networks have surprisingly few activation patterns,

Reference 3

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Observation 0e396884-04bf-4af9-a349-d5829f521a2b · outbound

This paper cites Bounding and counting linear regions of deep neural networks,.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Bounding and counting linear regions of deep neural networks,

Reference 4

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Observation a0c98cc1-eee2-4757-9ae4-bff2e0102c37 · outbound

This paper cites The Geometry of ReLU Networks through the ReLU Transition Graph.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs The Geometry of ReLU Networks through the ReLU Transition Graph

Reference 5

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Observation acf8f92b-2181-4ed7-addd-4b88595f0341 · outbound

This paper cites On the second eigenvalue of a graph and a network flow problem,.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs On the second eigenvalue of a graph and a network flow problem,

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:37:57.267327Z

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Observation 60987502-3ec2-46a4-985a-2d2bfa1e4bb0 · outbound

This paper cites Expander graphs,.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Expander graphs,

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:37:57.258097Z

Source-reported events for the cited work

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Observation 33dda763-0c27-4324-876b-f22e75a06b6a · outbound

This paper cites Neural Tangent Kernel: Convergence and Generalization in Neural Networks.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Neural Tangent Kernel: Convergence and Generalization in Neural Networks

Reference 8

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Observation 1f6544aa-b484-4e9d-81cc-906a94b66e98 · outbound

This paper cites Facing Up to Arrangements: Face-Count Formulas for Partitions of Space by Hyperplanes.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Facing Up to Arrangements: Face-Count Formulas for Partitions of Space by Hyperplanes

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:37:57.247986Z

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Observation ef7b5cc2-0635-420e-94e8-116014d836db · outbound

This paper cites Understanding Deep Neural Networks with Rectified Linear Units.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Understanding Deep Neural Networks with Rectified Linear Units

Reference 10

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Observation e218984a-e1d9-4728-b382-abf00f55e2a0 · outbound

This paper cites Complexity of linear regions in deep networks,.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Complexity of linear regions in deep networks,

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:37:57.237443Z

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Observation 3eeab581-6f01-4a9c-8f49-c016f53e3759 · outbound

This paper cites On the expressive power of deep neural networks,.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs On the expressive power of deep neural networks,

Reference 12

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This paper cites Benefits of depth in neural networks.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Benefits of depth in neural networks

Reference 13

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This paper cites Notes on the number of linear regions of deep neural networks,.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Notes on the number of linear regions of deep neural networks,

Reference 14

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Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Unresolved cited work

Reference 15

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Observation c4fa7e6e-8843-4a47-ad67-731b06aaca76 · outbound

This paper cites Belkin, D.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Belkin, D

Reference 16

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This paper cites Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability

Reference 17

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Observation 41382ba8-6c5d-44a1-b104-fb0e5740ebf9 · outbound

This paper cites Ongie, A.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Ongie, A

Reference 18

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Observation 1fa1880f-9b38-4eb3-975f-ba406e287421 · outbound

This paper cites On the information bottleneck theory of deep learning,.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs On the information bottleneck theory of deep learning,

Reference 19

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Observation ce7b5607-f234-419c-bd07-e274267aa9eb · outbound

This paper cites Bianchini and F.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Bianchini and F

Reference 20

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This paper cites Ramanujan graphs,.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Ramanujan graphs,

Reference 21

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Observation c67e21e3-254c-4b8c-92c3-099577ce7eca · outbound

This paper cites The secret sharer: Evaluating and testing unintended memorization in neural networks,.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs The secret sharer: Evaluating and testing unintended memorization in neural networks,

Reference 22

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Observation 8110ae7b-4b0c-4b79-af1f-d0faf002571a · outbound

This paper cites A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs A Combinatorial Theory of Dropout: Subnetworks, Graph Geometry, and Generalization

Reference 23

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Observation 6951f56f-9266-4665-9ae5-056017967bb1 · outbound

This paper cites Flat minima,.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Flat minima,

Reference 24

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Observation 6d596a70-9d05-4337-8a57-e0e9209526be · outbound

This paper cites A PAC-Bayesian Approach to Spectrally-Normalized Margin Bounds for Neural Networks.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs A PAC-Bayesian Approach to Spectrally-Normalized Margin Bounds for Neural Networks

Reference 25

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Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Spectrally-normalized margin bounds for neural networks

Reference 26

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This paper cites Distance-Based Regularisation of Deep Networks for Fine-Tuning.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Distance-Based Regularisation of Deep Networks for Fine-Tuning

Reference 27

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Observation 4e4cec81-7a65-4667-9cb8-a6d74f30ada2 · outbound

This paper cites Visualizing the Loss Landscape of Neural Nets.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Visualizing the Loss Landscape of Neural Nets

Reference 28

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This paper cites Entropy-SGD: Biasing gradient descent into wide valleys,.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Entropy-SGD: Biasing gradient descent into wide valleys,

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:37:57.140896Z

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This paper cites Information-theoretic analysis of gen- eralization capability of learning algorithms.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Information-theoretic analysis of gen- eralization capability of learning algorithms

Reference 30

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This paper cites Deep Learning and the Information Bottleneck Principle.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Deep Learning and the Information Bottleneck Principle

Reference 31

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Observation 287684cc-4d7a-49a5-81ef-3648365a903b · outbound

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Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Unresolved cited work

Reference 32

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This paper cites Neural networks and principal component analysis: Learning from examples without local minima,.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Neural networks and principal component analysis: Learning from examples without local minima,

Reference 33

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Observation 56d1f92e-bd4d-4ee2-abc2-00931cc9fcfb · outbound

This paper cites Exponential expressivity in deep neural networks through transient chaos.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Exponential expressivity in deep neural networks through transient chaos

Reference 34

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This paper cites Towards Understanding the Role of Over-Parametrization in Generalization of Neural Networks.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Towards Understanding the Role of Over-Parametrization in Generalization of Neural Networks

Reference 35

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This paper cites On the number of variables to use in principal component regression,.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs On the number of variables to use in principal component regression,

Reference 36

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Observation 40c362ec-2fc0-4f45-a6d7-3a6072e42164 · outbound

This paper cites Neural Tangents: Fast and Easy Infinite Neural Networks in Python.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Neural Tangents: Fast and Easy Infinite Neural Networks in Python

Reference 37

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Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Geometric deep learning: Going beyond Euclidean data,

Reference 38

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Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Semi-Supervised Classification with Graph Convolutional Networks

Reference 39

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Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Unresolved cited work

Reference 40

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Observation 381143b3-23ba-4ec4-84a2-30ce03b066fa · outbound

This paper cites Interpreting Blackbox Models via Model Extraction.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Interpreting Blackbox Models via Model Extraction

Reference 41

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This paper cites Interpretable Deep Learning under Fire.

Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs Interpretable Deep Learning under Fire

Reference 42

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Observation affae9a0-1b1e-4523-b8cc-09e1f004412a · outbound

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Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs PyTorch: An imperative style, high- performance deep learning library,

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:37:57.060623Z

Source-reported events for the cited work

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