Paper Citation Record · LEDGER

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality

As of 19 August 2026, this Paper Citation Record lists 42 of 42 outbound references and 1 inbound Pith citation observation for arXiv:2506.22851.

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

pith.paper-citation-record.v1
2506.22851 v1

Coverage vector

measured 42 of 42 reference resolution

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measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-11T16:36:54.868502Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-11T16:36:54.985830Z

Reference resolution

42 of 42 outbound references displayed

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External citation measurements

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Outbound references

Observation 494c527a-8b8e-455d-ae06-4e8ef2b7ff1d · outbound

This paper cites Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the $L^p$-sense.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the $L^p$-sense

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:07:02.700622Z

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Observation 027dad35-6b5d-4b61-bf70-135743d01560 · outbound

This paper cites Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for space-time solutions of semilinear partial differential equations.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for space-time solutions of semilinear partial differential equations

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:07:02.480610Z

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Observation a0c32c02-dc4a-4b79-8673-b9635e785876 · outbound

This paper cites Overcoming the curse of dimensionality in the numerical approximation of high-dimensional semilinear elliptic partial differential equa- tions.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Overcoming the curse of dimensionality in the numerical approximation of high-dimensional semilinear elliptic partial differential equa- tions

Reference 3

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Observation bbed90e9-46fe-4a95-bf0e-9451f876f768 · outbound

This paper cites an unresolved cited work.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:07:07.350308Z

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Observation 561510d4-256c-4135-80f5-298e50d18825 · outbound

This paper cites Nonlinear Monte Carlo methods with polynomial runtime for Bellman equations of discrete time high-dimensional stochastic optimal control problems.Appl.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Nonlinear Monte Carlo methods with polynomial runtime for Bellman equations of discrete time high-dimensional stochastic optimal control problems.Appl

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:07:07.178720Z

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Observation d79dcab7-2dbe-49ee-a009-5f062029d9ed · outbound

This paper cites Nonlinear Monte Carlo methods with polynomial runtime for high-dimensional iterated nested expectations.

Reference 6

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Observation 0ee38b32-e015-4bf0-973d-5411139f78c1 · outbound

This paper cites Numerical simulations for full history recursive multilevel Picard approximations for systems of high-dimensional partial differential equations.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Numerical simulations for full history recursive multilevel Picard approximations for systems of high-dimensional partial differential equations

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:07:07.024233Z

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Observation c76d786e-349a-4bef-90cb-7595b907f874 · outbound

This paper cites Dynamic programming.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Dynamic programming

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:07:06.853661Z

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Observation b910f5c2-3ce8-4ec0-bd51-e57b2f6553be · outbound

This paper cites Reinforcement learning and optimal control.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Reinforcement learning and optimal control

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:07:06.699093Z

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Observation af0a7946-216a-45fd-8e25-859f3604e90f · outbound

This paper cites an unresolved cited work.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:07:06.523280Z

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Observation 7f0a7e42-7db2-42bf-8300-9144f8c06d44 · outbound

This paper cites an unresolved cited work.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Unresolved cited work

Reference 11

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Observation 3be293e7-f406-4860-a0a5-28adc45a0ec7 · outbound

This paper cites D., and W ang, Z.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality D., and W ang, Z

Reference 12

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Observation 7fc1e775-de8b-4e63-95b8-351c61298a7a · outbound

This paper cites Deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear partial differential equations.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear partial differential equations

Reference 13

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Observation 9fa12623-7a76-47de-9274-b7ac1df998cc · outbound

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Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Unresolved cited work

Reference 14

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Observation 4f845859-8fd0-4435-8c63-7a47828a60ed · outbound

This paper cites Multilevel Picard iterations for solving smooth semilinear parabolic heat equations.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Multilevel Picard iterations for solving smooth semilinear parabolic heat equations

Reference 15

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Observation 223a9ac2-7bc9-4222-889b-1983c8f74eed · outbound

This paper cites A theoretical analysis of deep Q-learning.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality A theoretical analysis of deep Q-learning

Reference 16

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Observation d251380b-03fa-4ca6-8a74-027a44a7f623 · outbound

This paper cites Generalised multilevel Picard approximations.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Generalised multilevel Picard approximations

Reference 17

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Observation 1279acbb-e947-415f-9600-56cd02ec3e06 · outbound

This paper cites Space-time error estimates for deep neural network approximations for differential equations.Adv.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Space-time error estimates for deep neural network approximations for differential equations.Adv

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:07:05.617656Z

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Observation 8fc47961-fe8f-44b5-a8d3-3eef77fac971 · outbound

This paper cites Deep neural network approximations for solutions of PDEs based on Monte Carlo algorithms.Partial Differ.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Deep neural network approximations for solutions of PDEs based on Monte Carlo algorithms.Partial Differ

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:07:05.494212Z

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Observation 2603c8c3-bf2e-46f9-9d91-a1815ef78b38 · outbound

This paper cites Overcoming the curse of dimen- sionality in the numerical approximation of parabolic partial differential equations with gradient-dependent nonlinearities.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Overcoming the curse of dimen- sionality in the numerical approximation of parabolic partial differential equations with gradient-dependent nonlinearities

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:07:05.370770Z

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Observation 521de22b-32fb-474a-bc8d-fbfc0a666e64 · outbound

This paper cites Multilevel Picard approximations for high-dimensional semilinear second-order PDEs with Lipschitz nonlinearities.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Multilevel Picard approximations for high-dimensional semilinear second-order PDEs with Lipschitz nonlinearities

Reference 21

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Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Unresolved cited work

Reference 22

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Observation 39d4a3e4-4404-4f6f-8407-2152237efc8b · outbound

This paper cites A., and von Wurstem- berger, P.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality A., and von Wurstem- berger, P

Reference 23

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Observation 609f0b94-273f-4ea7-97e2-8de8f1a71e35 · outbound

This paper cites Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:07:05.052517Z

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Observation cc510041-899f-4186-891b-c540a20cc023 · outbound

This paper cites Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks.

Reference 25

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Observation d0c58614-b662-4682-b017-62d83df3d5ab · outbound

This paper cites Multilevel Picard approximations of high- dimensional semilinear parabolic differential equations with gradient-dependent nonlinear- ities.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Multilevel Picard approximations of high- dimensional semilinear parabolic differential equations with gradient-dependent nonlinear- ities

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:07:04.892087Z

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Observation 949d1f35-5920-4973-b5df-527a7f0e8eb6 · outbound

This paper cites Mathematicalintroduction to deep learning: Methods, implementations, and theory, 2023.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Mathematicalintroduction to deep learning: Methods, implementations, and theory, 2023

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:07:04.770798Z

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Observation b36a07c3-2952-4a5b-a4f0-3bb514b15a11 · outbound

This paper cites Champion-level drone racing using deep reinforcement learning.Nature 620, 7976 (2023), 982–987.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Champion-level drone racing using deep reinforcement learning.Nature 620, 7976 (2023), 982–987

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:07:04.654138Z

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Observation 6d7a02e4-6d94-4d8c-accb-acdda074686f · outbound

This paper cites P., Hunt, J.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality P., Hunt, J

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:07:04.509380Z

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Observation 84672e67-622a-4e58-a393-559bf5f3dae5 · outbound

This paper cites A., Veness, J., Bellemare, M.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality A., Veness, J., Bellemare, M

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:07:04.351010Z

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Observation ba30e527-90c4-41af-89d1-34e3d8cfc449 · outbound

This paper cites an unresolved cited work.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Unresolved cited work

Reference 31

Resolution: verified exact; raw_fallback, observed 2026-08-06T22:07:02.247836Z

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Observation 67b2a63a-0dcb-4508-9e3b-d16907ef56d9 · outbound

This paper cites Rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of gradient-dependent semilinear heat equations.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of gradient-dependent semilinear heat equations

Reference 32

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:07:02.029498Z

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Observation d65431af-8b4a-4ba3-a54f-e7220c5b50cd · outbound

This paper cites Deep ReLU neural networks overcome the curse of dimensionality when approximating semilinear partial integro-differential equations.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Deep ReLU neural networks overcome the curse of dimensionality when approximating semilinear partial integro-differential equations

Reference 33

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:07:01.872809Z

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Observation ac626f5b-2af1-4c0b-97c3-985c058a29a8 · outbound

This paper cites A., and Wu, S.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality A., and Wu, S

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:07:04.193766Z

Source-reported events for the cited work

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Observation 05ead0d5-6eca-406c-878b-3c0afa052132 · outbound

This paper cites an unresolved cited work.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:07:04.027300Z

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Observation da857e18-169f-4537-bfda-7ffcdf316b42 · outbound

This paper cites The curse of dimension and a universal method for numer- ical integration.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality The curse of dimension and a universal method for numer- ical integration

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:07:03.830990Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 05ca9c43-c641-48a2-86c2-7907511815a7 · outbound

This paper cites Tractability of multivariate problems.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Tractability of multivariate problems

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:07:03.637227Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 38286d60-dc36-44eb-b7ef-88629912526b · outbound

This paper cites an unresolved cited work.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:07:03.471247Z

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Observation ec2b63dd-14aa-4189-8ebc-6d6317dd3610 · outbound

This paper cites an unresolved cited work.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality Unresolved cited work

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-06T22:07:01.364417Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 70269763-5f3d-4501-afa1-19a3dfbe7d18 · outbound

This paper cites J., Guez, A., Sifre, L., V an Den Driess- che, G., Schrittwieser, J., Antonoglou, I., Panneershel v am, V., Lanctot, M., et al.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality J., Guez, A., Sifre, L., V an Den Driess- che, G., Schrittwieser, J., Antonoglou, I., Panneershel v am, V., Lanctot, M., et al

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:07:03.267558Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 0a3d9598-3c9c-4441-8df7-8d0ae1181cd4 · outbound

This paper cites S., and Barto, A.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality S., and Barto, A

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:07:03.109345Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 705f09db-dcd1-4cf1-b931-af982ca7cb33 · outbound

This paper cites A finite-time analysis of Q-learning with neural network function approximation.

Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality A finite-time analysis of Q-learning with neural network function approximation

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:07:02.868743Z

Source-reported events for the cited work

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Pith citing papers

Observation 016a5011-45bf-40c8-96d6-89e3ebf884cd · inbound

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing cites this paper.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-08-11T16:36:54.992322Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.