Paper Citation Record · LEDGER

A Probabilistic Perspective on Model Collapse

As of 8 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 2 inbound Pith citation observations for arXiv:2505.13947.

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

pith.paper-citation-record.v1
2505.13947 v2

Coverage vector

measured 27 of 27 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T15:45:24.159183Z

measured 29 of 29 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-04T09:18:34.794717Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-11T02:30:54.341729Z

Reference resolution

27 of 27 outbound references displayed

verified exact0
verified fuzzy13
unresolved14
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ca8ee8ee-8164-45c1-9f82-54e44b840def · outbound

This paper cites GPT-4 Technical Report.

A Probabilistic Perspective on Model Collapse GPT-4 Technical Report

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-07T15:45:20.314272Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 33b5ba3e-df53-452b-8d6a-7cfabd526fbd · outbound

This paper cites Self-consuming generative models go MAD.

A Probabilistic Perspective on Model Collapse Self-consuming generative models go MAD

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:45:29.264149Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 10cd2a32-fb2a-4523-92bd-1d1f8aee2a90 · outbound

This paper cites Psi (digamma) function.

A Probabilistic Perspective on Model Collapse Psi (digamma) function

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:45:28.835289Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 465a38e2-fe76-4a39-b396-5f2dbf8b2eb7 · outbound

This paper cites On the stability of iterative retraining of generative models on their own data.

A Probabilistic Perspective on Model Collapse On the stability of iterative retraining of generative models on their own data

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:45:28.367779Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e41c29f7-1173-4fef-9450-f8414af132f0 · outbound

This paper cites Approximating the cumulative distribution function of the normal distribution.

A Probabilistic Perspective on Model Collapse Approximating the cumulative distribution function of the normal distribution

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:45:27.906704Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 526e8be8-b1d5-465c-b57b-25a12cc4031a · outbound

This paper cites Universality of the $\pi^2/6$ Pathway in Avoiding Model Collapse.

A Probabilistic Perspective on Model Collapse Universality of the $\pi^2/6$ Pathway in Avoiding Model Collapse

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-07T15:45:21.266742Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1e52b666-1d8c-4c9d-b2e2-aab7e7ce2f26 · outbound

This paper cites Bias reduction of maximum likelihood estimates.

A Probabilistic Perspective on Model Collapse Bias reduction of maximum likelihood estimates

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:45:27.564767Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5dbdd7b0-d826-4465-bf39-b4ce41cb1951 · outbound

This paper cites Donoho, and Sanmi Koyejo.

A Probabilistic Perspective on Model Collapse Donoho, and Sanmi Koyejo

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-07T15:45:21.501874Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 600e9328-7576-47e6-9695-cd063f5846ad · outbound

This paper cites Exponential tail bounds for chisquared random variables.

A Probabilistic Perspective on Model Collapse Exponential tail bounds for chisquared random variables

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:45:27.177455Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7a7d97b3-f3d2-4b89-9309-b51e751e4701 · outbound

This paper cites Recursive Learning Without Collapse: A Weighting-Based Stabilization Framework.

A Probabilistic Perspective on Model Collapse Recursive Learning Without Collapse: A Weighting-Based Stabilization Framework

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-07T15:45:21.706368Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cb8a96d5-be5d-4f7c-a0bc-960a4eac417d · outbound

This paper cites Probability inequalities for sums of bounded random variables.

A Probabilistic Perspective on Model Collapse Probability inequalities for sums of bounded random variables

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-07T15:45:21.826612Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4f1b9741-282d-4743-a3f1-f71b6d564368 · outbound

This paper cites Collapse or Thrive? Perils and Promises of Synthetic Data in a Self-Generating World.

A Probabilistic Perspective on Model Collapse Collapse or Thrive? Perils and Promises of Synthetic Data in a Self-Generating World

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-07T15:45:21.950378Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4c55f32b-2e6c-427b-862f-6c0b5dc7e1e7 · outbound

This paper cites Gaussian copula marginal regression.

A Probabilistic Perspective on Model Collapse Gaussian copula marginal regression

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-07T15:45:22.064839Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9965a5cc-ab4b-4dd9-81a9-9a46482d34f7 · outbound

This paper cites Inequalities for the incomplete gamma function.

A Probabilistic Perspective on Model Collapse Inequalities for the incomplete gamma function

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:45:26.834857Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 798849d7-978b-499d-ac68-29181c3b57be · outbound

This paper cites The synthetic data vault.

A Probabilistic Perspective on Model Collapse The synthetic data vault

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:45:26.604759Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2b0cedce-0c33-4922-b059-b2bedd9adad5 · outbound

This paper cites The non-central 2-and f-distribution and their applications.

A Probabilistic Perspective on Model Collapse The non-central 2-and f-distribution and their applications

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:45:26.342025Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7a76c744-1043-4f96-bd68-c43895c90356 · outbound

This paper cites Position: Model Collapse Does Not Mean What You Think.

A Probabilistic Perspective on Model Collapse Position: Model Collapse Does Not Mean What You Think

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-07T15:45:22.534821Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a16bf4e3-9d08-47a2-ab58-04fc89bd5957 · outbound

This paper cites The Curse of Recursion: Training on Generated Data Makes Models Forget.

A Probabilistic Perspective on Model Collapse The Curse of Recursion: Training on Generated Data Makes Models Forget

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-07T15:45:22.645684Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 39d040f7-bff3-45ed-a1bb-aa1a78bb6a25 · outbound

This paper cites Ai models collapse when trained on recursively generated data.

A Probabilistic Perspective on Model Collapse Ai models collapse when trained on recursively generated data

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:45:26.134747Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b0e40f13-2211-4e8f-8af4-68ef959409ac · outbound

This paper cites Edf statistics for goodness of fit and some comparisons.

A Probabilistic Perspective on Model Collapse Edf statistics for goodness of fit and some comparisons

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:45:25.775937Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 1a7b50ec-58cd-4510-bbce-7f7b03c59ec7 · outbound

This paper cites Energy statistics: A class of statistics based on distances.

A Probabilistic Perspective on Model Collapse Energy statistics: A class of statistics based on distances

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:45:25.484684Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 12679e38-f89e-4e40-86eb-8859458aebed · outbound

This paper cites Gemini: A Family of Highly Capable Multimodal Models.

A Probabilistic Perspective on Model Collapse Gemini: A Family of Highly Capable Multimodal Models

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-07T15:45:23.346716Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4928622a-a280-40f7-ac6f-05a7b93e9377 · outbound

This paper cites LLaMA: Open and Efficient Foundation Language Models.

A Probabilistic Perspective on Model Collapse LLaMA: Open and Efficient Foundation Language Models

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-07T15:45:23.478589Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fecd5b3b-c324-4dd6-a28a-32d40f48ce29 · outbound

This paper cites Position: Will we run out of data? limits of llm scaling based on human-generated data.

A Probabilistic Perspective on Model Collapse Position: Will we run out of data? limits of llm scaling based on human-generated data

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-07T15:45:23.614028Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8a212d12-1874-49a1-a2da-a6c6bb0357b8 · outbound

This paper cites A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity.

A Probabilistic Perspective on Model Collapse A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-07T15:45:23.914853Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3119c323-1bb2-48fe-aa2b-137fb83de921 · outbound

This paper cites Utility Theory of Synthetic Data Generation.

A Probabilistic Perspective on Model Collapse Utility Theory of Synthetic Data Generation

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-07T15:45:24.050813Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 967d38ae-cfed-41dc-91f2-b0df9cbc1465 · outbound

This paper cites On the non-asymptotic and sharp lower tail bounds of random variables.

A Probabilistic Perspective on Model Collapse On the non-asymptotic and sharp lower tail bounds of random variables

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:45:25.158565Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

Observation b35afada-8ee3-4a26-ad83-8c5a2ddb4acd · inbound

Escaping Model Collapse via Synthetic Data Verification: Near-term Improvements and Long-term Convergence cites this paper.

Escaping Model Collapse via Synthetic Data Verification: Near-term Improvements and Long-term Convergence A Probabilistic Perspective on Model Collapse

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-04T09:18:34.794717Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8c32c4bd-4f9e-4524-b883-1fe88f64f7d5 · inbound

Curated Synthetic Data Doesn't Have to Collapse: A Theoretical Study of Generative Retraining with Pluralistic Preferences cites this paper.

Curated Synthetic Data Doesn't Have to Collapse: A Theoretical Study of Generative Retraining with Pluralistic Preferences A Probabilistic Perspective on Model Collapse

Reference 103

Resolution: verified exact; arxiv_id, observed 2026-05-11T02:30:54.344648Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.