{"as_of":"2026-08-10T10:52:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:ff8a3528604d73529d5028f92efaf0bdb3ac0436fdb03f857183beff79c81884","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":8,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":8,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+00:00","state":"measured"},{"denominator":8,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":8,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-09T14:47:40.343242Z","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":"2026-06-30T12:04:38.769434Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2405.15459","last_updated":"2025-02-10T09:33:48Z","snapshot_observed_at":"2026-08-05T15:27:10.774229Z","submitted_at":"2024-05-24T11:34:31Z","title":"Repetita Iuvant: Data Repetition Allows SGD to Learn High-Dimensional Multi-Index Functions","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.15459","snapshot_observed_at":"2026-08-09T14:47:40.343242Z","title":"Repetita iuvant: Data repetition allows SGD to learn high-dimensional multi-index functions","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2502.01763","last_updated":"2025-02-03T19:08:32Z","snapshot_observed_at":"2026-08-09T22:04:26.139102Z","submitted_at":"2025-02-03T19:08:32Z","title":"On The Concurrence of Layer-wise Preconditioning Methods and Provable Feature Learning","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-09T14:47:40.343242Z"},"links":{"cited_paper":"/paper/2405.15459","citing_paper":"/paper/2502.01763"},"observation_digest":"sha256:e7bccfa78e3c41034c2576679a6f0f1bb5c2a7750ffebc3642441e4327ef79a4","observation_id":"10a1e903-c85c-402b-b5c9-ed75f1db0ffd","resolution":{"observed_at":"2026-08-09T14:47:40.343242Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.15459","last_updated":"2025-02-10T09:33:48Z","snapshot_observed_at":"2026-08-05T15:27:10.774229Z","submitted_at":"2024-05-24T11:34:31Z","title":"Repetita Iuvant: Data Repetition Allows SGD to Learn High-Dimensional Multi-Index Functions","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.15459","snapshot_observed_at":"2026-08-09T11:55:22.485129Z","title":"Repetita iuvant: Data repetition allows sgd to learn high-dimensional multi-index functions","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2502.02545","last_updated":"2025-06-10T17:55:07Z","snapshot_observed_at":"2026-08-09T11:45:25.723705Z","submitted_at":"2025-02-04T18:15:51Z","title":"Optimal Spectral Transitions in High-Dimensional Multi-Index Models","version":2},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-09T11:55:22.485129Z"},"links":{"cited_paper":"/paper/2405.15459","citing_paper":"/paper/2502.02545"},"observation_digest":"sha256:f7ea2428c08e79bbdb6d427a0d63749dd873377da9c4f8bca6ccf25a49a36480","observation_id":"7e5f4b3a-f9dd-4acf-8a26-1dd0705cb82b","resolution":{"observed_at":"2026-08-09T11:55:22.485129Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.15459","last_updated":"2025-02-10T09:33:48Z","snapshot_observed_at":"2026-08-05T15:27:10.774229Z","submitted_at":"2024-05-24T11:34:31Z","title":"Repetita Iuvant: Data Repetition Allows SGD to Learn High-Dimensional Multi-Index Functions","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.15459","snapshot_observed_at":"2026-08-08T15:34:16.569798Z","title":"Repetita iuvant: Data repetition allows SGD to learn high-dimensional multi-index functions","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2502.06443","last_updated":"2025-07-21T10:48:50Z","snapshot_observed_at":"2026-08-10T00:04:40.232039Z","submitted_at":"2025-02-10T13:19:30Z","title":"Low-dimensional Functions are Efficiently Learnable under Randomly Biased Distributions","version":2},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-08T15:34:16.569798Z"},"links":{"cited_paper":"/paper/2405.15459","citing_paper":"/paper/2502.06443"},"observation_digest":"sha256:7809f3a2a3a419b823fdaa0bcdd00680f96976b56f27a5b484576d03b10e2cdc","observation_id":"d891adcf-4063-4d6b-beea-bcf753a75f3a","resolution":{"observed_at":"2026-08-08T15:34:16.569798Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.15459","last_updated":"2025-02-10T09:33:48Z","snapshot_observed_at":"2026-08-05T15:27:10.774229Z","submitted_at":"2024-05-24T11:34:31Z","title":"Repetita Iuvant: Data Repetition Allows SGD to Learn High-Dimensional Multi-Index Functions","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.15459","snapshot_observed_at":"2026-08-07T14:40:54.390971Z","title":"Repetita iuvant: Data repetition allows SGD to learn high-dimensional multi-index functions","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.18346","last_updated":"2025-05-23T20:09:09Z","snapshot_observed_at":"2026-08-09T18:01:10.152830Z","submitted_at":"2025-05-23T20:09:09Z","title":"On the Mechanisms of Weak-to-Strong Generalization: A Theoretical Perspective","version":1},"reference_index":2023,"source":"pdf_text","source_observed_at":"2026-08-07T14:40:54.390971Z"},"links":{"cited_paper":"/paper/2405.15459","citing_paper":"/paper/2505.18346"},"observation_digest":"sha256:4dce9804085d129df7ad0b5486a3d179a34beff214e6df60094c4334030fa332","observation_id":"77158d68-8908-4806-9133-922debe71e6c","resolution":{"observed_at":"2026-08-07T14:40:54.390971Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.15459","last_updated":"2025-02-10T09:33:48Z","snapshot_observed_at":"2026-08-05T15:27:10.774229Z","submitted_at":"2024-05-24T11:34:31Z","title":"Repetita Iuvant: Data Repetition Allows SGD to Learn High-Dimensional Multi-Index Functions","version":2},"cited_work":{"arxiv_id":"2405.15459","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2405.15459","snapshot_observed_at":"2026-06-30T12:04:38.769434Z","title":"Repetita iuvant: Data repetition allows sgd to learn high-dimensional multi-index functions","venue":null,"work_id":"68174d3e-6f90-456c-82dd-528abfc6c8de","year":2024},"citing_paper":{"arxiv_id":"2605.14567","last_updated":"2026-05-14T08:37:28Z","snapshot_observed_at":"2026-08-03T00:46:36.800591Z","submitted_at":"2026-05-14T08:37:28Z","title":"Scaling Laws from Sequential Feature Recovery: A Solvable Hierarchical Model","version":1},"reference_index":166,"source":"arxiv_source","source_observed_at":"2026-05-15T01:39:21.733359Z"},"links":{"cited_paper":"/paper/2405.15459","citing_paper":"/paper/2605.14567"},"observation_digest":"sha256:77b4e14d29663b48216db75ffe276a60f77227192707a0e18286d08cb6f13aa7","observation_id":"90d0321a-5735-4f92-959a-e46a227a22f9","resolution":{"observed_at":"2026-05-15T01:39:38.361285Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.15459","last_updated":"2025-02-10T09:33:48Z","snapshot_observed_at":"2026-08-05T15:27:10.774229Z","submitted_at":"2024-05-24T11:34:31Z","title":"Repetita Iuvant: Data Repetition Allows SGD to Learn High-Dimensional Multi-Index Functions","version":2},"cited_work":{"arxiv_id":"2405.15459","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2405.15459","snapshot_observed_at":"2026-06-30T12:04:38.769434Z","title":"Repetita iuvant: Data repetition allows sgd to learn high-dimensional multi-index functions","venue":null,"work_id":"68174d3e-6f90-456c-82dd-528abfc6c8de","year":2024},"citing_paper":{"arxiv_id":"2605.15082","last_updated":"2026-05-14T17:05:30Z","snapshot_observed_at":"2026-08-08T06:36:12.447992Z","submitted_at":"2026-05-14T17:05:30Z","title":"Average Gradient Outer Product in kernel regression provably recovers the central subspace for multi-index models","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-15T03:10:20.833945Z"},"links":{"cited_paper":"/paper/2405.15459","citing_paper":"/paper/2605.15082"},"observation_digest":"sha256:6a194095e304cd22a2898c95c5397d173780448bc14ae68e2f23782d174d17d0","observation_id":"fd157416-7612-468c-82eb-d28254755e62","resolution":{"observed_at":"2026-05-15T03:14:53.232224Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.15459","last_updated":"2025-02-10T09:33:48Z","snapshot_observed_at":"2026-08-05T15:27:10.774229Z","submitted_at":"2024-05-24T11:34:31Z","title":"Repetita Iuvant: Data Repetition Allows SGD to Learn High-Dimensional Multi-Index Functions","version":2},"cited_work":{"arxiv_id":"2405.15459","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2405.15459","snapshot_observed_at":"2026-06-30T12:04:38.769434Z","title":"Repetita iuvant: Data repetition allows sgd to learn high-dimensional multi-index functions","venue":null,"work_id":"68174d3e-6f90-456c-82dd-528abfc6c8de","year":2024},"citing_paper":{"arxiv_id":"2605.24749","last_updated":"2026-05-23T22:00:38Z","snapshot_observed_at":"2026-08-06T08:15:51.837731Z","submitted_at":"2026-05-23T22:00:38Z","title":"How Neural Reward Models Learn Features for Policy Optimization: A Single-Index Analysis","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-30T12:00:53.639670Z"},"links":{"cited_paper":"/paper/2405.15459","citing_paper":"/paper/2605.24749"},"observation_digest":"sha256:f0018cdfc60ad963637fcde5a908660d0351bccbb4252da69d2f4e6acfd06170","observation_id":"3398e3d1-7dda-44d3-8b4e-544a0252fc96","resolution":{"observed_at":"2026-06-30T12:04:38.771038Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.15459","last_updated":"2025-02-10T09:33:48Z","snapshot_observed_at":"2026-08-05T15:27:10.774229Z","submitted_at":"2024-05-24T11:34:31Z","title":"Repetita Iuvant: Data Repetition Allows SGD to Learn High-Dimensional Multi-Index Functions","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.15459","snapshot_observed_at":"2026-08-04T23:35:23.380334Z","title":"arXiv preprint arXiv:2405.15459 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.01654","last_updated":"2026-08-03T03:44:13Z","snapshot_observed_at":"2026-08-09T17:21:50.028167Z","submitted_at":"2026-08-03T03:44:13Z","title":"Approximate Message Passing with Random Initialization for Phase Retrieval","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-04T23:35:23.380334Z"},"links":{"cited_paper":"/paper/2405.15459","citing_paper":"/paper/2608.01654"},"observation_digest":"sha256:da151f7bde664a7a9a2f75dfdb0b3c044d6cc8113942eee4f3fbbd0be78ae531","observation_id":"0d43a4f8-e80f-443b-a125-1d097146c688","resolution":{"observed_at":"2026-08-04T23:35:23.380334Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2405.15459/citation-record","integrity":"/paper/2405.15459/integrity","json":"/paper/2405.15459/citation-record.json","paper":"/paper/2405.15459"},"outbound":[],"paper":{"arxiv_id":"2405.15459","last_updated":"2025-02-10T09:33:48Z","latest_version":2,"primary_category":"stat.ML","snapshot_observed_at":"2026-08-05T15:27:10.774229Z","submitted_at":"2024-05-24T11:34:31Z","title":"Repetita Iuvant: Data Repetition Allows SGD to Learn High-Dimensional Multi-Index Functions"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"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":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 8 inbound Pith citation observations for arXiv:2405.15459."}