{"as_of":"2026-08-14T15:16:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:155ce538677af33f2522d78cd2afcfcda1b9416fac920e2f957d699cc8f175b1","coverage":[{"denominator":27,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":27,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T15:45:24.159183Z","state":"measured"},{"denominator":29,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":29,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T09:18:34.794717Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-11T02:30:54.341729Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.13947","snapshot_observed_at":"2026-08-04T09:18:34.794717Z","title":"A probabilistic perspective on model collapse.arXiv preprint arXiv:2505.13947,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2510.16657","last_updated":"2026-07-16T03:25:47Z","snapshot_observed_at":"2026-08-08T15:16:56.011041Z","submitted_at":"2025-10-18T22:39:39Z","title":"Escaping Model Collapse via Synthetic Data Verification: Near-term Improvements and Long-term Convergence","version":3},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-04T09:18:34.794717Z"},"links":{"cited_paper":"/paper/2505.13947","citing_paper":"/paper/2510.16657"},"observation_digest":"sha256:e92bafd0912e05e2336fff0f245e280a2f89461621edf6ca6ebdebc476363580","observation_id":"b35afada-8ee3-4a26-ad83-8c5a2ddb4acd","resolution":{"observed_at":"2026-08-04T09:18:34.794717Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse","version":2},"cited_work":{"arxiv_id":"2505.13947","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2505.13947","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"arXiv preprint arXiv:2505.13947 , year=","venue":null,"work_id":"64bda749-cd48-4289-8b7c-b54529e9cc57","year":null},"citing_paper":{"arxiv_id":"2605.07724","last_updated":"2026-06-03T12:55:17Z","snapshot_observed_at":"2026-08-13T10:43:02.284944Z","submitted_at":"2026-05-08T13:27:23Z","title":"Curated Synthetic Data Doesn't Have to Collapse: A Theoretical Study of Generative Retraining with Pluralistic Preferences","version":1},"reference_index":103,"source":"arxiv_source","source_observed_at":"2026-05-11T02:30:14.693348Z"},"links":{"cited_paper":"/paper/2505.13947","citing_paper":"/paper/2605.07724"},"observation_digest":"sha256:bcd4da98c980224efe120e7b2804acef7b289a7f2c5e07b86fa657254cff3ec7","observation_id":"8c32c4bd-4f9e-4524-b883-1fe88f64f7d5","resolution":{"observed_at":"2026-05-11T02:30:54.344648Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2505.13947/citation-record","integrity":"/paper/2505.13947/integrity","json":"/paper/2505.13947/citation-record.json","paper":"/paper/2505.13947"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2303.08774","last_updated":"2024-03-04T06:01:33Z","snapshot_observed_at":"2026-08-07T07:30:12.213965Z","submitted_at":"2023-03-15T17:15:04Z","title":"GPT-4 Technical Report","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2303.08774","snapshot_observed_at":"2026-08-07T15:45:20.314272Z","title":"Gpt-4 technical report","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse","version":2},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-07T15:45:20.314272Z"},"links":{"cited_paper":"/paper/2303.08774","citing_paper":"/paper/2505.13947"},"observation_digest":"sha256:3d9449303d1c74ec04a536c70a52ca03747fec451bc386e4cacfdfeacba38a6e","observation_id":"ca8ee8ee-8164-45c1-9f82-54e44b840def","resolution":{"observed_at":"2026-08-07T15:45:20.314272Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:45:29.017820Z","title":"Self-consuming generative models go MAD","venue":null,"work_id":"062085db-e75c-4f28-92ff-f04f3698d610","year":2024},"citing_paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse","version":2},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-07T15:45:20.541505Z"},"links":{"citing_paper":"/paper/2505.13947"},"observation_digest":"sha256:3fd517b85d4757038e069b5a8bd6cf4a3c4f22d32d45d67005b53726870dc40f","observation_id":"33b5ba3e-df53-452b-8d6a-7cfabd526fbd","resolution":{"observed_at":"2026-08-07T15:45:29.264149Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:45:28.633915Z","title":"Psi (digamma) function","venue":null,"work_id":"627fbedc-1392-4f55-8dbb-d5e27ba7d105","year":1976},"citing_paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse","version":2},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-07T15:45:20.644739Z"},"links":{"citing_paper":"/paper/2505.13947"},"observation_digest":"sha256:88885356a51c9ef33d5c79478fcb9968ea2114975b856fb8b1f57a0caa999315","observation_id":"10cd2a32-fb2a-4523-92bd-1d1f8aee2a90","resolution":{"observed_at":"2026-08-07T15:45:28.835289Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:45:28.114225Z","title":"On the stability of iterative retraining of generative models on their own data","venue":null,"work_id":"e0bc1896-632b-495c-ac56-68bf4dea75c8","year":2024},"citing_paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse","version":2},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-07T15:45:20.934951Z"},"links":{"citing_paper":"/paper/2505.13947"},"observation_digest":"sha256:f42c76d399eab46c7eb1d4b2944a6d620c7789e0debfa2651c25ea77476a2845","observation_id":"465a38e2-fe76-4a39-b396-5f2dbf8b2eb7","resolution":{"observed_at":"2026-08-07T15:45:28.367779Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:45:27.784930Z","title":"Approximating the cumulative distribution function of the normal distribution","venue":null,"work_id":"c7933495-3842-44a5-ae5a-6359f2892cfe","year":2007},"citing_paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse","version":2},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-07T15:45:21.074997Z"},"links":{"citing_paper":"/paper/2505.13947"},"observation_digest":"sha256:6af87684409569ea58fb0b6d5637fba51b122e685d571405a6fc8f4554c3641f","observation_id":"e41c29f7-1173-4fef-9450-f8414af132f0","resolution":{"observed_at":"2026-08-07T15:45:27.906704Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2410.22812","last_updated":"2024-10-30T08:44:10Z","snapshot_observed_at":"2026-08-14T07:27:04.350525Z","submitted_at":"2024-10-30T08:44:10Z","title":"Universality of the $\\pi^2/6$ Pathway in Avoiding Model Collapse","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.22812","snapshot_observed_at":"2026-08-07T15:45:21.266742Z","title":"Universality of the ^2/6 pathway in avoiding model collapse","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse","version":2},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-07T15:45:21.266742Z"},"links":{"cited_paper":"/paper/2410.22812","citing_paper":"/paper/2505.13947"},"observation_digest":"sha256:1a85fe183bc3b5acb8a7be89efee63ba8e044fbfd7a3c8bec979468e1433570b","observation_id":"526e8be8-b1d5-465c-b57b-25a12cc4031a","resolution":{"observed_at":"2026-08-07T15:45:21.266742Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:45:27.424745Z","title":"Bias reduction of maximum likelihood estimates","venue":null,"work_id":"b02f3c20-fba9-46a8-bcff-cdc47ef34703","year":1993},"citing_paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse","version":2},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-07T15:45:21.384890Z"},"links":{"citing_paper":"/paper/2505.13947"},"observation_digest":"sha256:b5f7b3ff7959178eb93d6be4eff8605eb0deab6b99b1e233d65aacb8d435082f","observation_id":"1e52b666-1d8c-4c9d-b2e2-aab7e7ce2f26","resolution":{"observed_at":"2026-08-07T15:45:27.564767Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:45:21.501874Z","title":"Donoho, and Sanmi Koyejo","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse","version":2},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-07T15:45:21.501874Z"},"links":{"citing_paper":"/paper/2505.13947"},"observation_digest":"sha256:c4a0848220faa40abedfb4491e005d07c2bd4f1ccb2167c831c6596d467e49c1","observation_id":"5dbdd7b0-d826-4465-bf39-b4ce41cb1951","resolution":{"observed_at":"2026-08-07T15:45:21.501874Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:45:27.074880Z","title":"Exponential tail bounds for chisquared random variables","venue":null,"work_id":"2b4965c2-ef7d-4e24-9a9b-de9a68a7c1ef","year":2021},"citing_paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse","version":2},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-07T15:45:21.605724Z"},"links":{"citing_paper":"/paper/2505.13947"},"observation_digest":"sha256:0cb29babf3d1290f814b44301f2f88339a7525695f910b1507632846125ed38f","observation_id":"600e9328-7576-47e6-9695-cd063f5846ad","resolution":{"observed_at":"2026-08-07T15:45:27.177455Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.18049","last_updated":"2026-07-02T02:49:00Z","snapshot_observed_at":"2026-08-07T17:50:35.725138Z","submitted_at":"2025-02-25T10:15:16Z","title":"Recursive Learning Without Collapse: A Weighting-Based Stabilization Framework","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.18049","snapshot_observed_at":"2026-08-07T15:45:21.706368Z","title":"Golden ratio weighting prevents model collapse","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse","version":2},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-07T15:45:21.706368Z"},"links":{"cited_paper":"/paper/2502.18049","citing_paper":"/paper/2505.13947"},"observation_digest":"sha256:97075a94685144215b90df31a28ac6714eef52fb1a6814271a82d91b58cb7dfb","observation_id":"7a7d97b3-f3d2-4b89-9309-b51e751e4701","resolution":{"observed_at":"2026-08-07T15:45:21.706368Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:45:21.826612Z","title":"Probability inequalities for sums of bounded random variables","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse","version":2},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-07T15:45:21.826612Z"},"links":{"citing_paper":"/paper/2505.13947"},"observation_digest":"sha256:5f1f47575f3b1b44ab56b32e781aec848e7057fea1100fe48f5e1728a1f2ce2f","observation_id":"cb8a96d5-be5d-4f7c-a0bc-960a4eac417d","resolution":{"observed_at":"2026-08-07T15:45:21.826612Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2410.16713","last_updated":"2025-03-17T21:14:46Z","snapshot_observed_at":"2026-08-12T22:17:53.808398Z","submitted_at":"2024-10-22T05:49:24Z","title":"Collapse or Thrive? Perils and Promises of Synthetic Data in a Self-Generating World","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.16713","snapshot_observed_at":"2026-08-07T15:45:21.950378Z","title":"Collapse or thrive? perils and promises of synthetic data in a self-generating world","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse","version":2},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-07T15:45:21.950378Z"},"links":{"cited_paper":"/paper/2410.16713","citing_paper":"/paper/2505.13947"},"observation_digest":"sha256:40258afa5e866906ac444a6adf7e19b17ee6126d017ad9bf3034da1950a5f1de","observation_id":"4f1b9741-282d-4743-a3f1-f71b6d564368","resolution":{"observed_at":"2026-08-07T15:45:21.950378Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:45:22.064839Z","title":"Gaussian copula marginal regression","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse","version":2},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-07T15:45:22.064839Z"},"links":{"citing_paper":"/paper/2505.13947"},"observation_digest":"sha256:92429e0f8189bfaf7a12c7178d1eb4e19dce57bf841b7a214d83705b64b51dee","observation_id":"4c55f32b-2e6c-427b-862f-6c0b5dc7e1e7","resolution":{"observed_at":"2026-08-07T15:45:22.064839Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:45:26.721650Z","title":"Inequalities for the incomplete gamma function","venue":null,"work_id":"b1e9a863-f560-4b0c-bdcc-d6539b721f23","year":2000},"citing_paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse","version":2},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-07T15:45:22.165125Z"},"links":{"citing_paper":"/paper/2505.13947"},"observation_digest":"sha256:6e296a98dee5c5d588ff12ab8ef299ecf75732579e0dfe4e1799db4166eaa484","observation_id":"9965a5cc-ab4b-4dd9-81a9-9a46482d34f7","resolution":{"observed_at":"2026-08-07T15:45:26.834857Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:45:26.465307Z","title":"The synthetic data vault","venue":null,"work_id":"dba306a0-3991-4b46-93b6-7873bb4457b9","year":2016},"citing_paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse","version":2},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-07T15:45:22.314963Z"},"links":{"citing_paper":"/paper/2505.13947"},"observation_digest":"sha256:d67d9574efe483a71b6974bec3988b225b25e920174507a527ce52027e8e90d0","observation_id":"798849d7-978b-499d-ac68-29181c3b57be","resolution":{"observed_at":"2026-08-07T15:45:26.604759Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:45:26.254746Z","title":"The non-central 2-and f-distribution and their applications","venue":null,"work_id":"e5a7f608-237a-4ca0-bf0d-eadf52cbad4d","year":1949},"citing_paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse","version":2},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-07T15:45:22.444747Z"},"links":{"citing_paper":"/paper/2505.13947"},"observation_digest":"sha256:143839aaf0e0ba0e500bf6b842fe98a7f983566ce53db52943cf44d10f969d03","observation_id":"2b0cedce-0c33-4922-b059-b2bedd9adad5","resolution":{"observed_at":"2026-08-07T15:45:26.342025Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2503.03150","last_updated":"2025-03-18T03:48:25Z","snapshot_observed_at":"2026-08-07T17:28:45.841852Z","submitted_at":"2025-03-05T03:47:17Z","title":"Position: Model Collapse Does Not Mean What You Think","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.03150","snapshot_observed_at":"2026-08-07T15:45:22.534821Z","title":"Position: Model collapse does not mean what you think","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse","version":2},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-07T15:45:22.534821Z"},"links":{"cited_paper":"/paper/2503.03150","citing_paper":"/paper/2505.13947"},"observation_digest":"sha256:e3bcc91249d0361843e7d727a30e51c4e2b7b5c5a572ba3e9bfb306d2dc71900","observation_id":"7a76c744-1043-4f96-bd68-c43895c90356","resolution":{"observed_at":"2026-08-07T15:45:22.534821Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2305.17493","last_updated":"2024-04-14T05:20:10Z","snapshot_observed_at":"2026-08-05T16:03:40.517679Z","submitted_at":"2023-05-27T15:10:41Z","title":"The Curse of Recursion: Training on Generated Data Makes Models Forget","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2305.17493","snapshot_observed_at":"2026-08-07T15:45:22.645684Z","title":"The curse of recursion: Training on generated data makes models forget","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse","version":2},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-07T15:45:22.645684Z"},"links":{"cited_paper":"/paper/2305.17493","citing_paper":"/paper/2505.13947"},"observation_digest":"sha256:96d6728263880b608152073dd660c397a693c747369b83c65a846a8048e05870","observation_id":"a16bf4e3-9d08-47a2-ab58-04fc89bd5957","resolution":{"observed_at":"2026-08-07T15:45:22.645684Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:45:25.895284Z","title":"Ai models collapse when trained on recursively generated data","venue":null,"work_id":"e6dc8ed4-238e-4d2b-8a71-a4848773220f","year":2024},"citing_paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse","version":2},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-07T15:45:22.744039Z"},"links":{"citing_paper":"/paper/2505.13947"},"observation_digest":"sha256:0615836a691b4f2349d0588530e61e6b41ab4e4a7a6a237fd33728c6b60b8409","observation_id":"39d040f7-bff3-45ed-a1bb-aa1a78bb6a25","resolution":{"observed_at":"2026-08-07T15:45:26.134747Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:45:25.665630Z","title":"Edf statistics for goodness of fit and some comparisons","venue":null,"work_id":"b65741b5-d5a7-44cb-a6d7-222a699448a2","year":1974},"citing_paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse","version":2},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-07T15:45:23.056482Z"},"links":{"citing_paper":"/paper/2505.13947"},"observation_digest":"sha256:09e65278a58e1be083e23c6f74ac5e106a3e0f761a5125c3ca4bbc4bff14b521","observation_id":"b0e40f13-2211-4e8f-8af4-68ef959409ac","resolution":{"observed_at":"2026-08-07T15:45:25.775937Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:45:25.375142Z","title":"Energy statistics: A class of statistics based on distances","venue":null,"work_id":"9fc3c50d-1147-4b2e-812a-104ef69531e0","year":2013},"citing_paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse","version":2},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-07T15:45:23.154802Z"},"links":{"citing_paper":"/paper/2505.13947"},"observation_digest":"sha256:4c5e907b30f4ea888cd03bf0e1c2e9db67a9d8480468d3d721bf41953d1f686c","observation_id":"1a7b50ec-58cd-4510-bbce-7f7b03c59ec7","resolution":{"observed_at":"2026-08-07T15:45:25.484684Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2312.11805","last_updated":"2025-05-09T21:04:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2023-12-19T02:39:27Z","title":"Gemini: A Family of Highly Capable Multimodal Models","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2312.11805","snapshot_observed_at":"2026-08-07T15:45:23.346716Z","title":"Gemini: a family of highly capable multimodal models","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse","version":2},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-07T15:45:23.346716Z"},"links":{"cited_paper":"/paper/2312.11805","citing_paper":"/paper/2505.13947"},"observation_digest":"sha256:b083a29c27a1e34ed780af6161295680bc464869dddc90f1a9c85e6f1b770cc8","observation_id":"12679e38-f89e-4e40-86eb-8859458aebed","resolution":{"observed_at":"2026-08-07T15:45:23.346716Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2302.13971","last_updated":"2023-02-27T17:11:15Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2023-02-27T17:11:15Z","title":"LLaMA: Open and Efficient Foundation Language Models","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2302.13971","snapshot_observed_at":"2026-08-07T15:45:23.478589Z","title":"Llama: Open and efficient foundation language models","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse","version":2},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-07T15:45:23.478589Z"},"links":{"cited_paper":"/paper/2302.13971","citing_paper":"/paper/2505.13947"},"observation_digest":"sha256:d9bec98a28947089fecf5b21f0c4baf264a7a936fec18d33bd31043eae124eb0","observation_id":"4928622a-a280-40f7-ac6f-05a7b93e9377","resolution":{"observed_at":"2026-08-07T15:45:23.478589Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:45:23.614028Z","title":"Position: Will we run out of data? limits of llm scaling based on human-generated data","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse","version":2},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-07T15:45:23.614028Z"},"links":{"citing_paper":"/paper/2505.13947"},"observation_digest":"sha256:2023b2dda907505695d19267f7c49346117fbd3aa1ae27919791e25629b315a3","observation_id":"fecd5b3b-c324-4dd6-a28a-32d40f48ce29","resolution":{"observed_at":"2026-08-07T15:45:23.614028Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:45:23.914853Z","title":"A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity","venue":null,"work_id":null,"year":1980},"citing_paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse","version":2},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-07T15:45:23.914853Z"},"links":{"citing_paper":"/paper/2505.13947"},"observation_digest":"sha256:562694c42f994b6c0b6abbcb415f7eefa89c311e0704fee92d1f8541aa5e3ffa","observation_id":"8a212d12-1874-49a1-a2da-a6c6bb0357b8","resolution":{"observed_at":"2026-08-07T15:45:23.914853Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2305.10015","last_updated":"2025-04-03T00:24:10Z","snapshot_observed_at":"2026-08-13T11:40:28.228869Z","submitted_at":"2023-05-17T07:49:16Z","title":"Utility Theory of Synthetic Data Generation","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2305.10015","snapshot_observed_at":"2026-08-07T15:45:24.050813Z","title":"Utility theory of synthetic data generation","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse","version":2},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-07T15:45:24.050813Z"},"links":{"cited_paper":"/paper/2305.10015","citing_paper":"/paper/2505.13947"},"observation_digest":"sha256:70bdc59a7fe9cd6565aaf8ddf77cba661ffa276d574fde0f854ef1c3e4d23087","observation_id":"3119c323-1bb2-48fe-aa2b-137fb83de921","resolution":{"observed_at":"2026-08-07T15:45:24.050813Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:45:25.077223Z","title":"On the non-asymptotic and sharp lower tail bounds of random variables","venue":null,"work_id":"b5821c65-66f6-4717-9fce-68a810baa6b3","year":2020},"citing_paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse","version":2},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-07T15:45:24.159183Z"},"links":{"citing_paper":"/paper/2505.13947"},"observation_digest":"sha256:29d206f10c915bf1bbc973251114a37b2291951fa1e66608cf4e5158547e6120","observation_id":"967d38ae-cfed-41dc-91f2-b0df9cbc1465","resolution":{"observed_at":"2026-08-07T15:45:25.158565Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2505.13947","last_updated":"2025-05-21T20:43:02Z","latest_version":2,"primary_category":"stat.ML","snapshot_observed_at":"2026-08-09T20:52:47.883417Z","submitted_at":"2025-05-20T05:25:29Z","title":"A Probabilistic Perspective on Model Collapse"},"reference_resolution":{"displayed":27,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":14,"verified_exact":0,"verified_fuzzy":13},"total_outbound_references":27},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 2 inbound Pith citation observations for arXiv:2505.13947."}