Paper Citation Record · LEDGER

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise

As of 11 August 2026, this Paper Citation Record lists 49 of 49 outbound references and 0 inbound Pith citation observations for arXiv:2607.19173.

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

pith.paper-citation-record.v1
2607.19173 v1

Coverage vector

measured 49 of 49 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-01T13:17:15.746822Z

measured 49 of 49 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+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

49 of 49 outbound references displayed

verified exact0
verified fuzzy0
unresolved48
parse uncertain1
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation bc727a27-f6c4-4642-a425-cd96100bf66f · outbound

This paper cites an unresolved cited work.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:10.524691Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 874494a7-03b9-4b32-b946-b1d7bfed37bf · outbound

This paper cites Universal Differential Equations for Scientific Machine Learning.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Universal Differential Equations for Scientific Machine Learning

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:10.637426Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 217d0a04-ebfd-46e0-8711-fe3ca993592b · outbound

This paper cites Cohen, Christoph Reisinger, and Sheng Wang.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Cohen, Christoph Reisinger, and Sheng Wang

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:10.760499Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 832fa82b-ffdf-447b-a671-668ff0cf6d31 · outbound

This paper cites FP-Diffusion: Improving score-based diffusion models by enforcing the underlying score Fokker–Planck equation.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise FP-Diffusion: Improving score-based diffusion models by enforcing the underlying score Fokker–Planck equation

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:10.903314Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 566d4e11-2519-4e93-9ba6-817c13d4c917 · outbound

This paper cites Neural controlled differential equations for irregular time series.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Neural controlled differential equations for irregular time series

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:10.947729Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cd0c7ddb-f085-4678-bd1f-012aad982470 · outbound

This paper cites an unresolved cited work.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:11.039496Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f92aba39-90aa-487f-8599-92847b61adf8 · outbound

This paper cites Neural SDEs as infinite-dimensional GANs.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Neural SDEs as infinite-dimensional GANs

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:11.135479Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a8e3de92-1447-43a6-833a-b9a9499e425e · outbound

This paper cites an unresolved cited work.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:11.256043Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 30f7ee20-7737-4383-bbf6-f2c66a7dac7d · outbound

This paper cites Denoising diffusion probabilistic models.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Denoising diffusion probabilistic models

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:11.348589Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cd0406dd-3662-4aa2-b82f-751c45e6d7e1 · outbound

This paper cites Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:11.504342Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6a6253c6-4d36-461a-9dcc-65784fe6f1ec · outbound

This paper cites an unresolved cited work.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:11.595047Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 71eafc62-d4e1-4086-89b7-a07a2edba64b · outbound

This paper cites Kloeden and Eckhard Platen.Numerical Solution of Stochastic Differential Equations.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Kloeden and Eckhard Platen.Numerical Solution of Stochastic Differential Equations

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:11.741636Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6dc0a4d8-cbe8-42f4-abb1-8f09bffaebde · outbound

This paper cites Trajectory flow matching with applications to clinical time series modelling.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Trajectory flow matching with applications to clinical time series modelling

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:11.807335Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c8c32c27-fac0-4066-84f7-e4ffd7d491db · outbound

This paper cites Naesseth.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Naesseth

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:11.924863Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 67be4053-ce5c-40c2-af18-47fb31103886 · outbound

This paper cites Neural SDE: Stabilizing Neural ODE Networks with Stochastic Noise.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Neural SDE: Stabilizing Neural ODE Networks with Stochastic Noise

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:12.035540Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2a1e8b96-e932-44be-b35d-cbd142aa29fd · outbound

This paper cites an unresolved cited work.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:12.153494Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6528ec76-f48c-4cd3-9218-04db78dc7e98 · outbound

This paper cites Neural jump-diffusion temporal point processes.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Neural jump-diffusion temporal point processes

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:12.253388Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5fe976d5-c724-4fab-be67-25e5652ca941 · outbound

This paper cites an unresolved cited work.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Unresolved cited work

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:12.340418Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3526b9a6-44d5-4e34-847c-73132bada531 · outbound

This paper cites Convergence and stability analysis of neural stochastic differential equations with poisson jumps.Chaos, Solitons & Fractals, 2026.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Convergence and stability analysis of neural stochastic differential equations with poisson jumps.Chaos, Solitons & Fractals, 2026

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:12.454737Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5d50eb78-bb13-4733-adc7-35daf495168b · outbound

This paper cites Variational inference with normalizing flows.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Variational inference with normalizing flows

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:12.572253Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cac22092-a281-4a53-bde3-b1d5fb088703 · outbound

This paper cites Karniadakis.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Karniadakis

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:12.702750Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1349e508-97a0-4e71-83d0-45f831d2707a · outbound

This paper cites Williams, Ioannis G.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Williams, Ioannis G

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:12.832603Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 78effdad-e991-4ce4-8765-1270848a4d61 · outbound

This paper cites A differential geometric approach to nonlinear filtering: The projection filter.IEEE Transactions on Automatic Control, 43(2):247– 252, 1998.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise A differential geometric approach to nonlinear filtering: The projection filter.IEEE Transactions on Automatic Control, 43(2):247– 252, 1998

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:12.945373Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c16ccc37-4d6f-47de-9e9c-1ba7d4b17fd2 · outbound

This paper cites Approximate nonlinear filtering by projection on exponential manifolds of densities.Bernoulli, 5(3):495–534, 1999.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Approximate nonlinear filtering by projection on exponential manifolds of densities.Bernoulli, 5(3):495–534, 1999

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:13.054739Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 39bb80a6-77fa-4eea-8b99-c16c325b6d3a · outbound

This paper cites an unresolved cited work.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Unresolved cited work

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:13.136616Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f5f08949-5f21-4939-9b14-f5ad1fe23dc6 · outbound

This paper cites Approximate solution of the Fokker–Planck–Kolmogorov equation.Probabilistic Engineering Mechanics, 17(4):369–384, 2002.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Approximate solution of the Fokker–Planck–Kolmogorov equation.Probabilistic Engineering Mechanics, 17(4):369–384, 2002

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:13.260493Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation da25e122-87ba-4dee-a0e5-289d135a6a87 · outbound

This paper cites Gingold and Joseph J.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Gingold and Joseph J

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:13.404748Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d476a57f-c738-449e-b3ed-9c8741aeffa2 · outbound

This paper cites an unresolved cited work.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Unresolved cited work

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:13.514744Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2607abce-6f5b-4db1-9278-f4c5c2657a98 · outbound

This paper cites an unresolved cited work.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Unresolved cited work

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:13.624739Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 094d25e1-8626-45ba-9be9-d70125719f14 · outbound

This paper cites On the construction and comparison of difference schemes.SIAM Journal on Numerical Analysis, 5(3):506–517, 1968.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise On the construction and comparison of difference schemes.SIAM Journal on Numerical Analysis, 5(3):506–517, 1968

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:13.711762Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e415efa1-0c31-4ca3-b90b-fc86afacb313 · outbound

This paper cites Rousseeuw and Christophe Croux.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Rousseeuw and Christophe Croux

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:13.778803Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 19f5723d-56d8-484e-a5c0-1001f39d7d7e · outbound

This paper cites an unresolved cited work.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Unresolved cited work

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:13.891755Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 021292bb-9700-427e-aac8-d0f8525cae58 · outbound

This paper cites Neural SDEs as a Unified Approach to Continuous-Domain Sequence Modeling.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Neural SDEs as a Unified Approach to Continuous-Domain Sequence Modeling

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:13.986691Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d0c30a01-c218-4d60-9006-e9d52a128add · outbound

This paper cites Decoupled Weight Decay Regularization.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Decoupled Weight Decay Regularization

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:14.136639Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 04dc2300-e6fa-4e47-bc9b-b4d7a26d04ca · outbound

This paper cites American Mathematical Society and Oxford University Press, 2000.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise American Mathematical Society and Oxford University Press, 2000

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:14.244744Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3eafa0e7-6b8c-4945-9a10-c1ad63db3161 · outbound

This paper cites Singularity structures and impacts on parameter estimation in finite mixtures of distributions.SIAM Journal on Mathematics of Data Science, 1(4):730–758, 2019.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Singularity structures and impacts on parameter estimation in finite mixtures of distributions.SIAM Journal on Mathematics of Data Science, 1(4):730–758, 2019

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:14.364744Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 622ef860-f523-4aeb-a754-ff398defd35d · outbound

This paper cites Dempster, Nan M.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Dempster, Nan M

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:14.556989Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a775f2b3-7807-4065-a876-70eba22ad951 · outbound

This paper cites From molecular dynamics to brownian dynamics.Proceedings.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise From molecular dynamics to brownian dynamics.Proceedings

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:14.667941Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 96bb288a-d428-4d3f-9678-b8a5b12897c7 · outbound

This paper cites an unresolved cited work.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Unresolved cited work

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:14.749417Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e1f54f8f-ea25-4f61-b20e-fcf98f2defcb · outbound

This paper cites Consequently,G K becomes a stratified space rather than a smooth manifold [36].

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Consequently,G K becomes a stratified space rather than a smooth manifold [36]

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:14.914499Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0196b799-3eff-4b29-975f-087af3de5ad4 · outbound

This paper cites an unresolved cited work.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Unresolved cited work

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:15.055378Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 03199cee-db84-43cf-8dff-7d6d9128d98d · outbound

This paper cites Proof sketch.Permuting Gaussian components leaves the mixture density unchanged.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Proof sketch.Permuting Gaussian components leaves the mixture density unchanged

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:15.266651Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 04d313a8-5c06-4a44-ae67-97439f3dabe9 · outbound

This paper cites an unresolved cited work.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Unresolved cited work

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:15.386207Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a8b01988-af41-4790-9f53-cdb552ac869e · outbound

This paper cites an unresolved cited work.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Unresolved cited work

Reference 44

Resolution: parse uncertain; no resolver link, observed 2026-08-01T13:17:15.481998Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fef5933c-4311-4494-8305-eb1cc0ea6e17 · outbound

This paper cites an unresolved cited work.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Unresolved cited work

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:15.544634Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6adf4855-bdac-432a-b4ba-1203cd5fad1d · outbound

This paper cites 18 C Lifted Dynamics This appendix provides theoretical justification for the approximations underlying Neural Kolmogorov Equations.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise 18 C Lifted Dynamics This appendix provides theoretical justification for the approximations underlying Neural Kolmogorov Equations

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:15.590215Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4bf659a0-d985-4fc1-9fcd-62dea503b3cb · outbound

This paper cites an unresolved cited work.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Unresolved cited work

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:15.638169Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f55405fa-aec3-4068-b5b1-fd0ca6a6a21c · outbound

This paper cites an unresolved cited work.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Unresolved cited work

Reference 48

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:15.686504Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3c4a0d0d-41a5-4757-9a61-3893236df089 · outbound

This paper cites Throughout this section, we assume f∈C 3 b (Rd,R d), a:=gg ⊤ ∈C 2 b (Rd,R d×d), and that all jump measures possess finite third moments.

Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise Throughout this section, we assume f∈C 3 b (Rd,R d), a:=gg ⊤ ∈C 2 b (Rd,R d×d), and that all jump measures possess finite third moments

Reference 49

Resolution: unresolved; no resolver link, observed 2026-08-01T13:17:15.746822Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.