Paper Citation Record · LEDGER

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks

As of 10 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 1 inbound Pith citation observation for arXiv:2502.02434.

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

pith.paper-citation-record.v1
2502.02434 v2

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-09T12:13:11.774889Z

measured 31 of 31 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-01T01:19:12.424654Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-01T13:05:44.267219Z

Reference resolution

30 of 30 outbound references displayed

verified exact6
verified fuzzy13
unresolved11
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 2453bbf1-d04c-4ad8-9ec3-c997933b4ccc · outbound

This paper cites XLB : A differentiable massively parallel lattice Boltzmann library in python.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks XLB : A differentiable massively parallel lattice Boltzmann library in python

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T12:13:12.743149Z

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 129f930e-2ea7-43a7-9c0e-cfad05356a02 · outbound

This paper cites Police : Provably optimal linear constraint enforcement for deep neural networks.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks Police : Provably optimal linear constraint enforcement for deep neural networks

Reference 2

Resolution: verified exact; arxiv_id_nonexistent, observed 2026-08-09T12:13:12.608346Z

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 37c0c941-44f5-4dd7-a910-b5d9adf8f122 · outbound

This paper cites Applied dynamic programming, volume 2050.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks Applied dynamic programming, volume 2050

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T12:13:12.733742Z

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 3fbe1a5d-539f-446b-bf1e-9f22bd447a23 · outbound

This paper cites Enforcing analytic constraints in neural networks emulating physical systems.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks Enforcing analytic constraints in neural networks emulating physical systems

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-09T12:13:11.683107Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3c025031-0650-440e-a744-2f02ee54ebfb · outbound

This paper cites Learning to Provably Satisfy High Relative Degree Constraints for Black-Box Systems.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks Learning to Provably Satisfy High Relative Degree Constraints for Black-Box Systems

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-08-09T12:13:12.448477Z

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 d589509a-75c1-4bfc-b690-c492a949c3ed · outbound

This paper cites POLICEd RL: Learning Closed-Loop Robot Control Policies with Provable Satisfaction of Hard Constraints.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks POLICEd RL: Learning Closed-Loop Robot Control Policies with Provable Satisfaction of Hard Constraints

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-09T12:13:11.693177Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ba93081f-bc37-41d3-92bf-23218dafdc5c · outbound

This paper cites Neural networks with physics-informed architectures and constraints for dynamical systems modeling.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks Neural networks with physics-informed architectures and constraints for dynamical systems modeling

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T12:13:12.725518Z

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 d4c772f1-5949-46d2-8932-e7170ffb3ef6 · outbound

This paper cites Addressing function approximation error in actor-critic methods.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks Addressing function approximation error in actor-critic methods

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-09T12:13:11.701496Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8efb4a9a-f7d5-40f3-8f23-f7db2e8046aa · outbound

This paper cites Aligning optimization trajectories with diffusion models for constrained design generation.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks Aligning optimization trajectories with diffusion models for constrained design generation

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T12:13:12.712988Z

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 fd0dad75-8e0a-4108-b6a5-ee1989b23704 · outbound

This paper cites Exact visualization of deep neural network geometry and decision boundary.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks Exact visualization of deep neural network geometry and decision boundary

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T12:13:12.704606Z

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 93a3354f-7e72-42a1-b76c-a1757a4ffe7d · outbound

This paper cites Splinecam: Exact visualization and characterization of deep network geometry and decision boundaries.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks Splinecam: Exact visualization and characterization of deep network geometry and decision boundaries

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T12:13:12.695694Z

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 5fd7eeb1-2e41-4791-bdcb-a58305e58702 · outbound

This paper cites CGD: Constraint-Guided Diffusion Policies for UAV Trajectory Planning.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks CGD: Constraint-Guided Diffusion Policies for UAV Trajectory Planning

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-09T12:13:11.713370Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 442438d2-9a69-4e3d-9e80-9fa849215b37 · outbound

This paper cites Imposing star-shaped hard constraints on the neural network output.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks Imposing star-shaped hard constraints on the neural network output

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T12:13:12.685847Z

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 06e20c11-944b-4e18-a8a5-7a0ea9df50fd · outbound

This paper cites Learning Constrained Optimization with Deep Augmented Lagrangian Methods.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks Learning Constrained Optimization with Deep Augmented Lagrangian Methods

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-09T12:13:11.719732Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5d165e36-1c8a-4627-9108-9335055b72ee · outbound

This paper cites End-to-End Constrained Optimization Learning: A Survey.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks End-to-End Constrained Optimization Learning: A Survey

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-09T12:13:11.723312Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 072d869c-53b8-4de1-a7a1-8cf59bd4d74f · outbound

This paper cites Characterizing possible failure modes in physics-informed neural networks.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks Characterizing possible failure modes in physics-informed neural networks

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T12:13:12.676384Z

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 d5196226-3c10-4319-ba22-0058213d1f07 · outbound

This paper cites an unresolved cited work.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-09T12:13:12.666652Z

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 7b0b512f-c1f8-4569-b2c9-56eb5d64eaf8 · outbound

This paper cites Lillo, M.H.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks Lillo, M.H

Reference 18

Resolution: verified exact; doi, observed 2026-08-09T12:13:11.816567Z

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 b39b46f9-4d6c-4315-9972-a4264ab94f2b · outbound

This paper cites an unresolved cited work.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-09T12:13:11.737609Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 667136c2-192b-4e0e-9b1b-87ac0da4c173 · outbound

This paper cites On the number of linear regions of deep neural networks.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks On the number of linear regions of deep neural networks

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T12:13:12.656311Z

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 8b5edf84-b60b-4c26-ae93-b574c1bd0cdb · outbound

This paper cites Transformers Can Do Bayesian Inference.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks Transformers Can Do Bayesian Inference

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-09T12:13:11.744274Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dfea8db8-d98b-4f90-826c-484b84a761d5 · outbound

This paper cites Generative optimization: A perspective on AI -enhanced problem solving in engineering.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks Generative optimization: A perspective on AI -enhanced problem solving in engineering

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-09T12:13:11.748462Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2674be86-4101-4419-a01e-14abdb646bcb · outbound

This paper cites Constrained optimization to train neural networks on critical and under-represented classes.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks Constrained optimization to train neural networks on critical and under-represented classes

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T12:13:12.647428Z

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 55b598b6-8359-4529-96de-c02eb728056d · outbound

This paper cites Provable editing of deep neural networks using parametric linear relaxation.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks Provable editing of deep neural networks using parametric linear relaxation

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T12:13:12.639198Z

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 ad89101f-9fd0-4026-ad9e-d2638b1e5688 · outbound

This paper cites Architecture-preserving provable repair of deep neural networks.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks Architecture-preserving provable repair of deep neural networks

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T12:13:12.629441Z

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 98f2d3d7-c0a1-4636-8c9c-92f462d54435 · outbound

This paper cites RAYEN: Imposition of Hard Convex Constraints on Neural Networks.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks RAYEN: Imposition of Hard Convex Constraints on Neural Networks

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-09T12:13:11.761159Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 016efb8b-0361-4c29-b38a-ab218225ec5a · outbound

This paper cites Leung, and Jun Wang.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks Leung, and Jun Wang

Reference 27

Resolution: verified exact; doi, observed 2026-08-09T12:13:11.801646Z

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 fa6f820f-8695-498f-8ce8-a6ae0a16d34d · outbound

This paper cites Physics-specialized neural network with hard constraints for solving multi-material diffusion problems.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks Physics-specialized neural network with hard constraints for solving multi-material diffusion problems

Reference 28

Resolution: verified exact; arxiv_id_nonexistent, observed 2026-08-09T12:13:12.132337Z

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 738a279b-44e2-49d1-a3c2-0c17d81e3dcf · outbound

This paper cites Fast and accurate bayesian optimization with pre-trained transformers for constrained engineering problems.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks Fast and accurate bayesian optimization with pre-trained transformers for constrained engineering problems

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T12:13:12.620451Z

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 f8b2d222-b590-4cd0-ba96-b5ae71636d53 · outbound

This paper cites Neural Fields with Hard Constraints of Arbitrary Differential Order.

mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks Neural Fields with Hard Constraints of Arbitrary Differential Order

Reference 30

Resolution: verified exact; local_arxiv, observed 2026-08-09T12:13:11.834282Z

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 f008e9b2-63f1-4d55-84a6-25d83e4aa5bc · inbound

ShardNet: Training Neural Controllers with Hard, Non-Convex Constraints cites this paper.

ShardNet: Training Neural Controllers with Hard, Non-Convex Constraints mPOLICE: Provable Enforcement of Multi-Region Affine Constraints in Deep Neural Networks

Reference 29

Resolution: verified exact; arxiv_id, observed 2026-07-01T13:05:44.269638Z

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.