Paper Citation Record · LEDGER

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs

As of 10 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 3 inbound Pith citation observations for arXiv:2507.08486.

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

pith.paper-citation-record.v1
2507.08486 v1

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T18:32:23.663701Z

measured 40 of 40 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T12:54:27.036188Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-16T05:50:40.294424Z

Reference resolution

37 of 37 outbound references displayed

verified exact2
verified fuzzy29
unresolved6
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External citation measurements

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Outbound references

Observation f23cbdf1-55fa-4d1b-bf0a-93f8e58afa17 · outbound

This paper cites Control on the manifolds of mappings with a view to the deep learning.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs Control on the manifolds of mappings with a view to the deep learning

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:32:31.625330Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 5465c824-bf9d-4cc2-bf4d-9d68ca03d275 · outbound

This paper cites Lectures in Mathematics ETH Zürich.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs Lectures in Mathematics ETH Zürich

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:32:31.418628Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e2adf178-c285-487f-bdd1-665798a6734d · outbound

This paper cites Springer, Cham, 2014.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs Springer, Cham, 2014

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:32:31.256450Z

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Observation be987f64-1707-42db-a717-00f6222e3339 · outbound

This paper cites Understanding the training of infinitely deep and wide resnets with conditional optimal transport, 2024.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs Understanding the training of infinitely deep and wide resnets with conditional optimal transport, 2024

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:32:31.002992Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation ce66dcd0-7eac-4c09-a6e7-712d57667423 · outbound

This paper cites Bertsekas and Steven E.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs Bertsekas and Steven E

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:32:30.738239Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 5cd39be6-19ed-46a8-9ea1-c3101839253a · outbound

This paper cites Weighted Csiszár-Kullback-Pinsker inequalities and applications to trans- portation inequalities.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs Weighted Csiszár-Kullback-Pinsker inequalities and applications to trans- portation inequalities

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:32:30.565759Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 48ff62f0-bcaf-4422-b410-fbe20c2e761d · outbound

This paper cites A measure theoretical approach to the mean-field maximum principle for training NeurODEs.Nonlinear Anal., 227:Paper No.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs A measure theoretical approach to the mean-field maximum principle for training NeurODEs.Nonlinear Anal., 227:Paper No

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:32:30.415784Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation d3c0d71c-e4fc-4104-9014-bec85f96194e · outbound

This paper cites Stable solutions in potential mean field game systems.NoDEA Nonlinear Differential Equations Appl., 25(1):Paper No.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs Stable solutions in potential mean field game systems.NoDEA Nonlinear Differential Equations Appl., 25(1):Paper No

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:32:30.142203Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 529b1734-eab4-45f4-9ca3-c51ce182b965 · outbound

This paper cites Springer, New York, 2019.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs Springer, New York, 2019

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:32:29.863527Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 22734b0e-0dfa-4f6e-8b34-3aa98ed6c984 · outbound

This paper cites Birkhäuser Boston, Inc., Boston, MA, 2004.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs Birkhäuser Boston, Inc., Boston, MA, 2004

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-06T18:32:21.922138Z

Source-reported events for the cited work

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Observation b62f42ea-f709-4d5e-b812-fd61df7cbca2 · outbound

This paper cites Princeton University Press, Princeton, NJ, 2019.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs Princeton University Press, Princeton, NJ, 2019

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:32:29.673043Z

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Observation 78f6b6f5-c042-4378-a9f1-025c6c873a36 · outbound

This paper cites Sharp convergence rates for mean field control in the region of strong regularity.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs Sharp convergence rates for mean field control in the region of strong regularity

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-06T18:32:22.082999Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 11c7c4fc-326c-41e4-af7b-f62b31536ce9 · outbound

This paper cites Souganidis.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs Souganidis

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:32:29.220031Z

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Observation 23d3b6ad-a4a0-42ed-ab90-4fd2f2209b11 · outbound

This paper cites Springer, 2018.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs Springer, 2018

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:32:28.871498Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 4fef0e93-cbdc-4cfe-be47-684f590f66b5 · outbound

This paper cites On the global convergence of gradient descent for over-parameterized models using optimal transport.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs On the global convergence of gradient descent for over-parameterized models using optimal transport

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:32:28.597358Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 9d08c2c5-37e3-4cd1-b242-303e473379ff · outbound

This paper cites The feature speed formula: a flexible approach to scale hyper-parameters of deep neural networks.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs The feature speed formula: a flexible approach to scale hyper-parameters of deep neural networks

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:32:28.427033Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation fd326b13-f2ba-42f0-b645-3ff5143b034b · outbound

This paper cites Asymptotic Analysis of Deep Residual Networks.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs Asymptotic Analysis of Deep Residual Networks

Reference 17

Resolution: verified exact; local_arxiv, observed 2026-08-06T18:32:23.893440Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 7c2a683c-673b-4090-b412-008c587ac9ed · outbound

This paper cites Deep neural networks, generic universal interpolation, and controlled odes.SIAM Journal on Mathematics of Data Science, 2(3):901–919, 2020.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs Deep neural networks, generic universal interpolation, and controlled odes.SIAM Journal on Mathematics of Data Science, 2(3):901–919, 2020

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:32:28.307262Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 207b4310-3b43-4654-b176-d7dc945acf8d · outbound

This paper cites Overparameterization of deep resnet: zero loss and mean-field analysis.Journal of machine learning research, 23(48):1–65, 2022.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs Overparameterization of deep resnet: zero loss and mean-field analysis.Journal of machine learning research, 23(48):1–65, 2022

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:32:28.166328Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation d54ca4b5-adce-416b-a596-3847d4c0eb02 · outbound

This paper cites A proposal on machine learning via dynamical systems.Commun.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs A proposal on machine learning via dynamical systems.Commun

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:32:27.898505Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 9eb5343a-3ad4-4aa4-9533-b92a1972eb0c · outbound

This paper cites A mean-field optimal control formulation of deep learning.Res.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs A mean-field optimal control formulation of deep learning.Res

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:32:27.562414Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation a1bdb753-01a7-4d39-b45b-6904937d6c38 · outbound

This paper cites A gradient flow on control space with rough initial condition, 2024.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs A gradient flow on control space with rough initial condition, 2024

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:32:27.247982Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 108a9743-df90-48bc-916e-4553f254614b · outbound

This paper cites Stable architectures for deep neural networks.Inverse Problems, 34(1):014004, 22, 2018.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs Stable architectures for deep neural networks.Inverse Problems, 34(1):014004, 22, 2018

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:32:26.961646Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 39e16b8f-8ff0-4c72-b08e-cbe90833310f · outbound

This paper cites Deep residual learning for image recognition.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs Deep residual learning for image recognition

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-06T18:32:22.956549Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b3c5362f-dfbc-4675-ad72-5ec9427a41e5 · outbound

This paper cites Mean-field Langevin System, Optimal Control and Deep Neural Networks.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs Mean-field Langevin System, Optimal Control and Deep Neural Networks

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-08-06T18:32:23.778071Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 7f8cfa7e-0fc2-450e-ada2-b8cd73366893 · outbound

This paper cites A convergence result of a continuous model of deep learning via a \L{}ojasiewicz--Simon inequality.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs A convergence result of a continuous model of deep learning via a \L{}ojasiewicz--Simon inequality

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-06T18:32:23.061524Z

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Unavailable: canonical work link unavailable.

Observation d83503f1-9fd1-40c1-949b-ed10f2f825e1 · outbound

This paper cites Approximation of continuous functions on rd by linear combinations of shifted rotations of a sigmoid function with and without scaling.Neural Networks, 5(1):105–115, 1992.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs Approximation of continuous functions on rd by linear combinations of shifted rotations of a sigmoid function with and without scaling.Neural Networks, 5(1):105–115, 1992

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:32:26.661457Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation da169348-3a94-43c2-956e-8a7980f76c7e · outbound

This paper cites Mean-Field Neural ODEs via Relaxed Optimal Control.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs Mean-Field Neural ODEs via Relaxed Optimal Control

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-06T18:32:23.164699Z

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Observation 5ce1b054-7090-4878-afb9-991b13e8b8e4 · outbound

This paper cites A general characterization of the mean field limit for stochastic differential games.Probab.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs A general characterization of the mean field limit for stochastic differential games.Probab

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:32:26.323647Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation cb0af2db-74e6-4ce3-b3d4-027efc847870 · outbound

This paper cites Deep learning via dynamical systems: an approximation perspective.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs Deep learning via dynamical systems: an approximation perspective

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:32:25.989701Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f25f76b4-a80d-470f-8077-e512df197f45 · outbound

This paper cites Cours au collège de france, equations aux dérivées partielles et applications.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs Cours au collège de france, equations aux dérivées partielles et applications

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:32:25.750410Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 2e71d897-7164-47c7-b837-7d158f836235 · outbound

This paper cites A mean field analysis of deep resnet and beyond: Towards provably optimization via overparameterization from depth.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs A mean field analysis of deep resnet and beyond: Towards provably optimization via overparameterization from depth

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:32:25.400205Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 552529de-bd04-4a79-9ca5-45cc0804b264 · outbound

This paper cites A mean field view of the landscape of two-layer neural networks.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs A mean field view of the landscape of two-layer neural networks

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:32:25.029678Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation be8707fc-094a-4986-ac41-0e6d7ea8fb48 · outbound

This paper cites Local convergence rates for wasserstein gradient flows and mckean-vlasov equations with multiple stationary solutions, 2024.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs Local convergence rates for wasserstein gradient flows and mckean-vlasov equations with multiple stationary solutions, 2024

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:32:24.595124Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation ccdab250-9f6c-4c42-b100-9ceba63b2a8c · outbound

This paper cites Trainability and Accuracy of Neural Networks: An Interacting Particle System Approach.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs Trainability and Accuracy of Neural Networks: An Interacting Particle System Approach

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-06T18:32:23.541601Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 34383df6-3e37-4aa6-bd02-8c2eb3ca4bff · outbound

This paper cites Neural ode control for classification, approximation, and transport.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs Neural ode control for classification, approximation, and transport

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:32:24.309660Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 0deae14d-2f4f-4e04-b38a-e83f65e09c4e · outbound

This paper cites Deep learning approximation of diffeomorphisms via linear-control systems.Mathematical Control and Related Fields, 13(3):1226–1257, 2023.

Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs Deep learning approximation of diffeomorphisms via linear-control systems.Mathematical Control and Related Fields, 13(3):1226–1257, 2023

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:32:24.084746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Pith citing papers

Observation 4cfd6cda-7d1f-4e0a-8101-2706abd67d91 · inbound

From Sublinear to Linear: Local Convergence in Finite-Width Networks via Locally Polyak-Lojasiewicz Regions cites this paper.

From Sublinear to Linear: Local Convergence in Finite-Width Networks via Locally Polyak-Lojasiewicz Regions Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs

Reference 2015

Resolution: unresolved; no resolver link, observed 2026-08-06T12:54:27.036188Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 703629c9-66ee-4986-b142-b25eab433931 · inbound

Constructive conditional normalizing flows cites this paper.

Constructive conditional normalizing flows Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs

Reference 5

Resolution: verified exact; arxiv_id, observed 2026-05-16T05:50:40.296818Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 0590d328-7ed2-4ce2-a7b9-911e30ff9245 · inbound

Dropout and Random Gradient Masking Are Asymptotically Equivalent in Large ResNets cites this paper.

Dropout and Random Gradient Masking Are Asymptotically Equivalent in Large ResNets Genericity of Polyak-Lojasiewicz Inequalities for Entropic Mean-Field Neural ODEs

Reference 55

Resolution: unresolved; no resolver link, observed 2026-08-01T20:07:07.749632Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.