{"as_of":"2026-08-23T22:02:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:f801bb6749b676c5c4f5fbd2f405741ba1371a9c7a162506293cd0be29308b6c","coverage":[{"denominator":58,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":58,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T11:07:55.759990Z","state":"measured"},{"denominator":58,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":58,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-23T06:30:58.430688+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2412.15911/citation-record","integrity":"/paper/2412.15911/integrity","json":"/paper/2412.15911/citation-record.json","paper":"/paper/2412.15911"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T11:07:56.862120Z","title":"Priors for infinite networks,","venue":null,"work_id":"a66a2ad3-2600-4994-9e70-824531e427d7","year":1996},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.478316Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:11fe875be052015ac9b8dfdb99114cd0881eab278dc13df9bb6cc254bd6655ef","observation_id":"0c8379e5-ece2-41da-ae94-bcd7f6b5cc6f","resolution":{"observed_at":"2026-08-11T11:07:56.871278Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.846172Z","title":"Introduction to gaussian processes,","venue":null,"work_id":"8bde22c0-80fb-45ab-a7ae-2e3c5e9a5b00","year":1998},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.486285Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:a0f433e3487d18c5edd197bdbca79d142859de01031fbba09817acbd00c0a481","observation_id":"3ba14c24-8078-406b-acf7-b1e55e25477c","resolution":{"observed_at":"2026-08-11T11:07:56.852250Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.827638Z","title":"Computing with infinite networks,","venue":null,"work_id":"bd3a220a-0a05-4d63-8baa-ab5594b3cc60","year":1996},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.490758Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:b0c3054f80ae8d8aef2a25747bbb2816efe0cbb91ce8aa35c167358f2f74b472","observation_id":"c04cbcff-eec2-4600-a1fc-5320ba9e7e8c","resolution":{"observed_at":"2026-08-11T11:07:56.833464Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.811184Z","title":"Gaussian process behaviour in wide deep neural networks,","venue":null,"work_id":"ef0da7c8-55cd-4abd-a76e-c4ccbadbdd1e","year":2018},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.494929Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:d010541177313bc2ce38c6e915deee86556f8a24abd17596ee67510af01cfe5d","observation_id":"e6ec0818-37f6-4194-8b15-3c8645741f9e","resolution":{"observed_at":"2026-08-11T11:07:56.817332Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.793306Z","title":"Deep neural networks as gaussian processes,","venue":null,"work_id":"17d50b0c-d80a-4aa8-a7e7-b81f4224b85b","year":2018},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.499285Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:5987fce8dd2c30b53eb71e2615968c863fe12dbd85e47c27227371b5c0e9c716","observation_id":"775232dd-4583-4fb6-b1ad-25980775d166","resolution":{"observed_at":"2026-08-11T11:07:56.800192Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.770312Z","title":"On exact computation with an infinitely wide neural net,","venue":null,"work_id":"c051d193-fe9d-4641-ac47-69b06861051a","year":2019},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.503383Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:2da9765e5187e4ca712d450ee87334beded1fec58a7fd5767ca5f9a302703e39","observation_id":"c2614208-6c15-4c6a-a0dd-0cfd4d399c91","resolution":{"observed_at":"2026-08-11T11:07:56.779268Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.749205Z","title":"On lazy training in differentiable programming,","venue":null,"work_id":"aa86a26c-ae06-4195-b390-3f9d5927cb8d","year":2019},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.507816Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:cb901eae68863284e4c5c580ccabe60ee1ee1c15b0784a6073d5962f04caea25","observation_id":"4727aac4-ed5a-4842-bd6e-161031a53eea","resolution":{"observed_at":"2026-08-11T11:07:56.758582Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.731928Z","title":"Why bigger is not always better: on finite and infinite neural networks,","venue":null,"work_id":"adcdb8dd-9af3-4e31-acac-3226d9723a4b","year":2020},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.511935Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:9cd75839ac1bb5dae7268b8f640b737f52b335693b42df944193f2fccb0e9f3f","observation_id":"f92f3fc9-f045-4d75-b8d3-5ef00d89143c","resolution":{"observed_at":"2026-08-11T11:07:56.738925Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2307.06092","last_updated":"2024-06-17T12:51:09Z","snapshot_observed_at":"2026-08-18T08:22:42.387398Z","submitted_at":"2023-07-12T11:35:37Z","title":"Quantitative CLTs in Deep Neural Networks","version":5},"cited_work":{"arxiv_id":"2307.06092","doi":null,"metadata_source":"pith","pith_arxiv_id":"2307.06092","snapshot_observed_at":"2026-08-11T11:07:56.138331Z","title":"Quantitative CLTs in Deep Neural Networks","venue":"cs.LG","work_id":"eedbcd1e-adf4-4f82-bfc3-02789f0a4c49","year":2023},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.515726Z"},"links":{"cited_paper":"/paper/2307.06092","citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:a54b0b11df83d423062e61e227d8787f87c34151a3aae379266ceb53be4aaf2f","observation_id":"9a4c9826-5717-413d-9eb6-4fc5732ca9e3","resolution":{"observed_at":"2026-08-11T11:07:56.146468Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.716067Z","title":"Deep convolutional networks as shallow gaussian processes,","venue":null,"work_id":"dc3ed229-290e-4243-98d1-7dc2853c9b3a","year":2019},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.522757Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:7919c96a4e5ce0978f89eedb33770c652da6d98945f87523a4cde710725ae244","observation_id":"c99a14bc-39a7-46b2-9641-bf00e6b6c8a9","resolution":{"observed_at":"2026-08-11T11:07:56.720246Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.700373Z","title":"Bayesian deep convolutional networks with many channels are gaussian processes,","venue":null,"work_id":"d3e2c74f-6b80-486f-82d5-e34ae0628aab","year":2019},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.528317Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:73d0a3864446d22e97012ea0f665ca1de90fa3396c63083ca0135ff6cc373d2c","observation_id":"90d2db70-7611-41f6-a1ea-c63f4c92f53b","resolution":{"observed_at":"2026-08-11T11:07:56.704948Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.687965Z","title":"Tensor programs i: Wide feedforward or recurrent neural networks of any architecture are gaussian processes,","venue":null,"work_id":"1bc33fe0-5545-4119-acc6-028d0b1d1e23","year":2019},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.533214Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:a126d1825bf212592aaaee1375da369af223a175fe359718ba3e467720cd3554","observation_id":"99193631-b713-4512-a413-38020aed4aea","resolution":{"observed_at":"2026-08-11T11:07:56.692528Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1301.3605","last_updated":"2013-03-08T19:42:37Z","snapshot_observed_at":"2026-08-15T18:34:40.390994Z","submitted_at":"2013-01-16T07:23:19Z","title":"Feature Learning in Deep Neural Networks - Studies on Speech Recognition Tasks","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1301.3605","snapshot_observed_at":"2026-08-11T11:07:55.539069Z","title":"Feature learning in deep neural networks-studies on speech recognition tasks,","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.539069Z"},"links":{"cited_paper":"/paper/1301.3605","citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:54eed301a9bf5dbcbf824923974d6030cc47a64a27f9edbddbd4c33c5a0d3d88","observation_id":"872b91e7-d51d-4454-a53b-4e6a518480f8","resolution":{"observed_at":"2026-08-11T11:07:55.539069Z","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":"2026-08-11T11:07:56.675957Z","title":"Learning sparse features can lead to overfitting in neural networks,","venue":null,"work_id":"b172c6d5-558f-46af-a252-684cd0319194","year":2022},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.543919Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:c96ee2e2f82282752c3120ac8d726fe1511fb025e399cd9aa795dceabdfd515a","observation_id":"a0f6b646-23c7-4593-8691-a6a7d1a39157","resolution":{"observed_at":"2026-08-11T11:07:56.680453Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.660577Z","title":"Inversion dynamics of class manifolds in deep learning reveals tradeoffs underlying generalization,","venue":null,"work_id":"0a175d4d-63d3-4a24-b61a-ca674b525d30","year":2024},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.548603Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:505eef5c8ad04499a01b439c627a5696882ad06584e33d5a3b104b3bab0d6680","observation_id":"4b363c2b-0474-4879-a97e-bd74a91d548e","resolution":{"observed_at":"2026-08-11T11:07:56.665489Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.19353","last_updated":"2025-06-27T14:20:12Z","snapshot_observed_at":"2026-08-18T07:43:11.532774Z","submitted_at":"2024-07-28T00:07:20Z","title":"Spring-block theory of feature learning in deep neural networks","version":4},"cited_work":{"arxiv_id":"2407.19353","doi":null,"metadata_source":"pith","pith_arxiv_id":"2407.19353","snapshot_observed_at":"2026-08-11T11:07:56.103397Z","title":"Spring-block theory of feature learning in deep neural networks","venue":"cond-mat.dis-nn","work_id":"18e1c276-bb9a-4fcf-951e-22e18089e0b1","year":2024},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.552966Z"},"links":{"cited_paper":"/paper/2407.19353","citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:0bf830bff6beeb527354177377daffcf9f28dfc8e97f343223ba967beb919aa8","observation_id":"69357a89-7ecd-4714-a98b-0335ad45631c","resolution":{"observed_at":"2026-08-11T11:07:56.108433Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:55.557295Z","title":"A mean field view of the landscape of two- layer neural networks,","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.557295Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:9fca8effa1e0df56019c315929001f6392be0fd0ff4c9e7b90e3666d5e9ab4a6","observation_id":"69da8f1b-7dbf-4bee-b579-56138445c3e2","resolution":{"observed_at":"2026-08-11T11:07:55.557295Z","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":"2026-08-11T11:07:56.645804Z","title":"On the global convergence of gradient descent for over-parameterized models using optimal transport,","venue":null,"work_id":"d3574f50-dede-4df1-8d31-6dd97573820e","year":2018},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.561679Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:d6bdc62f20366febfb361434fbddfa284328401c2d63890ba432f0f4416f0084","observation_id":"99661d17-e796-4f23-9953-7aa4a29578b2","resolution":{"observed_at":"2026-08-11T11:07:56.651352Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:55.566273Z","title":"Mean field analysis of neural networks: A law of large numbers,","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.566273Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:0b02e902c9a52eb178339ef8152cb759ecc48df0591b1da4b1acd20a1c860d0a","observation_id":"5fc9eb2d-8c48-4459-9449-e7f4abcd9eaf","resolution":{"observed_at":"2026-08-11T11:07:55.566273Z","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":"2026-08-11T11:07:56.623691Z","title":"Parameters as interacting particles: long time convergence and asymptotic error scaling of neural networks,","venue":null,"work_id":"a41822fe-779c-45a7-88b6-6e6f8743e9ee","year":2018},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.571684Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:4fcd80240bf174f5dac371b840303dd4ad4e0c78cab06af14df4eb6512d08912","observation_id":"a32db8ed-55f2-49db-a975-bfdb19f7f0a8","resolution":{"observed_at":"2026-08-11T11:07:56.628828Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.606841Z","title":"Tensor programs iv: Feature learning in infinite-width neural networks,","venue":null,"work_id":"b56534e8-b108-4b6b-9d6b-77b7df017d4c","year":2021},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.578322Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:7161740d7a1dc11ce4339b1a0ba1017044f3ccd80f1b90280f9f2c3c533889f5","observation_id":"01e519de-f876-4490-a67e-c5120c6f3b41","resolution":{"observed_at":"2026-08-11T11:07:56.611597Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.583609Z","title":"What can be learnt with wide convolutional neural networks?","venue":null,"work_id":"410e250f-0d84-4818-b70c-269431351073","year":2023},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.584264Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:0d157e6963085abce7115ab908f5de444a8670ccd0e7d79dbe1631943d4708a3","observation_id":"5e7032b6-57cf-4427-8df1-8211ecb37e3f","resolution":{"observed_at":"2026-08-11T11:07:56.592949Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.568235Z","title":"Locality defeats the curse of dimensionality in convolutional teacher-student scenarios,","venue":null,"work_id":"53bafa36-2f8b-423c-b27f-c437f218fd6d","year":2021},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.588824Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:7625db1da1b3d65817edbf977a7e1dd8f11c7e64e664b8a23a25d099a7466da5","observation_id":"3bd8a695-20e6-4a7a-bb71-0c86a9e4bcfb","resolution":{"observed_at":"2026-08-11T11:07:56.572531Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2108.13097","last_updated":"2023-05-25T07:46:00Z","snapshot_observed_at":"2026-08-18T09:52:27.466112Z","submitted_at":"2021-08-30T10:07:37Z","title":"A theory of representation learning gives a deep generalisation of kernel methods","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.13097","snapshot_observed_at":"2026-08-11T11:07:55.593123Z","title":"A theory of representation learning in deep neural networks gives a deep generalisation of kernel methods,","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.593123Z"},"links":{"cited_paper":"/paper/2108.13097","citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:ad07b32cdb79514ac446c708259119605e9dba31b905b2633713a92d15dea07f","observation_id":"e8277e92-853d-4950-81ca-ad49cc848948","resolution":{"observed_at":"2026-08-11T11:07:55.593123Z","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":"2026-08-11T11:07:56.542849Z","title":"Statistical mechanics of deep linear neural networks: The backpropagating kernel renormalization,","venue":null,"work_id":"7ff44a48-aadf-4bcc-9a39-c6ec0f97d3d3","year":2021},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.597826Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:27f185f6575ddf383eb7ebe2c7e844af5bf228b493ce2fbfa82c5c7e3bab5b23","observation_id":"4e05c480-0a7b-4b40-9067-3b8c9f90e1bf","resolution":{"observed_at":"2026-08-11T11:07:56.553254Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.521502Z","title":"A statistical mechanics framework for bayesian deep neural networks beyond the infinite-width limit,","venue":null,"work_id":"9578dcd8-fc5c-494b-9ff2-8d12644e634a","year":2023},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.603035Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:8ec00ba67fc46770bb55977b141d8dc7b92bd582236c297a609a263a2575664a","observation_id":"28428393-155d-46ef-b48d-c73e655cf78b","resolution":{"observed_at":"2026-08-11T11:07:56.527423Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2307.11807","last_updated":"2023-07-21T17:22:04Z","snapshot_observed_at":"2026-08-19T08:46:53.291447Z","submitted_at":"2023-07-21T17:22:04Z","title":"Local Kernel Renormalization as a mechanism for feature learning in overparametrized Convolutional Neural Networks","version":1},"cited_work":{"arxiv_id":"2307.11807","doi":null,"metadata_source":"pith","pith_arxiv_id":"2307.11807","snapshot_observed_at":"2026-08-11T11:07:56.044921Z","title":"Local Kernel Renormalization as a mechanism for feature learning in overparametrized Convolutional Neural Networks","venue":"cs.LG","work_id":"8e64486e-f61a-492b-9857-b26d40c330b8","year":2023},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.607289Z"},"links":{"cited_paper":"/paper/2307.11807","citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:706fd2aaa61be458c45ef2b00a9d906cab5f095e856f3177d3484f34bf4308e0","observation_id":"a7d166d9-4138-4daf-b1f0-8d391f82bb7b","resolution":{"observed_at":"2026-08-11T11:07:56.052005Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.07168","last_updated":"2024-07-09T18:14:18Z","snapshot_observed_at":"2026-08-16T13:35:39.784764Z","submitted_at":"2024-07-09T18:14:18Z","title":"Statistical mechanics of transfer learning in fully-connected networks in the proportional limit","version":1},"cited_work":{"arxiv_id":"2407.07168","doi":null,"metadata_source":"pith","pith_arxiv_id":"2407.07168","snapshot_observed_at":"2026-08-11T11:07:56.021627Z","title":"Statistical mechanics of transfer learning in fully-connected networks in the proportional limit","venue":"cond-mat.dis-nn","work_id":"9d81e2da-bcd4-45af-bf58-5e0f23643d4d","year":2024},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.611707Z"},"links":{"cited_paper":"/paper/2407.07168","citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:2bfa783a167398662decf03cc032b051ca3088582d12c74b65cbf8739ba1c7f4","observation_id":"bc0dd8f2-f5f1-4405-995a-3818390e5dab","resolution":{"observed_at":"2026-08-11T11:07:56.027577Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.504048Z","title":"Predictive power of a bayesian effective action for fully connected one hidden layer neural networks in the proportional limit,","venue":null,"work_id":"ab43a804-6ba8-4041-a7d5-6995828144ca","year":2024},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.615587Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:90c0fadd94d145ec55c87e9d363890046c1c1b4fe1608f0aa6093f274536044e","observation_id":"bc3ea0fb-4ffb-434a-ba34-ac0734350769","resolution":{"observed_at":"2026-08-11T11:07:56.509660Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.487344Z","title":"Critical feature learning in deep neural networks,","venue":null,"work_id":"643130b5-86bd-4857-a3b9-967ae568e16c","year":2024},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.619677Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:1e1f63529473d5291edd08dd2fa245a67a45ee4692ed1d9cab2f401a933346f0","observation_id":"b1fcd274-6e66-4d15-a608-700ac48ccade","resolution":{"observed_at":"2026-08-11T11:07:56.491615Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2409.13904","last_updated":"2025-01-14T23:31:03Z","snapshot_observed_at":"2026-08-16T13:16:44.339042Z","submitted_at":"2024-09-20T21:20:04Z","title":"High-dimensional learning of narrow neural networks","version":2},"cited_work":{"arxiv_id":"2409.13904","doi":null,"metadata_source":"pith","pith_arxiv_id":"2409.13904","snapshot_observed_at":"2026-08-11T11:07:55.997527Z","title":"High-dimensional learning of narrow neural networks","venue":"stat.ML","work_id":"d56cec33-efe5-40d3-9068-71e7f2010400","year":2024},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.626154Z"},"links":{"cited_paper":"/paper/2409.13904","citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:da8d52eb9f6e2c93e2038921772ed2928db093d0127aa015a267822600d7f1fe","observation_id":"04d173b3-d4de-445b-bba5-f5de52fb654b","resolution":{"observed_at":"2026-08-11T11:07:56.003846Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2307.05635","last_updated":"2023-07-11T08:30:50Z","snapshot_observed_at":"2026-08-16T15:17:11.728671Z","submitted_at":"2023-07-11T08:30:50Z","title":"Fundamental limits of overparametrized shallow neural networks for supervised learning","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2307.05635","snapshot_observed_at":"2026-08-11T11:07:55.635467Z","title":"Fundamental limits of overparametrized shallow neural networks for supervised learning,","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.635467Z"},"links":{"cited_paper":"/paper/2307.05635","citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:85ebbc8816771947c739f0e81581e1fc9691a39ce42271e1de682f19a491c1be","observation_id":"a4dfe96f-c605-4401-b771-35e62fedd58f","resolution":{"observed_at":"2026-08-11T11:07:55.635467Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.15926","last_updated":"2024-12-08T02:29:42Z","snapshot_observed_at":"2026-08-18T20:34:06.759127Z","submitted_at":"2024-05-24T20:34:18Z","title":"Dissecting the Interplay of Attention Paths in a Statistical Mechanics Theory of Transformers","version":2},"cited_work":{"arxiv_id":"2405.15926","doi":null,"metadata_source":"pith","pith_arxiv_id":"2405.15926","snapshot_observed_at":"2026-08-11T11:07:55.940372Z","title":"Dissecting the Interplay of Attention Paths in a Statistical Mechanics Theory of Transformers","venue":"cs.LG","work_id":"4f048740-1b43-4128-8b07-0a55d8876c25","year":2024},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.642161Z"},"links":{"cited_paper":"/paper/2405.15926","citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:ee2e293c7933b4c25211d60b158b9d72fdd30777b78127e141f396ddf2ed63ca","observation_id":"e87164da-48ce-4707-9682-10947a8ea106","resolution":{"observed_at":"2026-08-11T11:07:55.947112Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1412.6980","last_updated":"2017-01-30T01:27:54Z","snapshot_observed_at":"2026-08-17T19:26:44.032537Z","submitted_at":"2014-12-22T13:54:29Z","title":"Adam: A Method for Stochastic Optimization","version":9},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1412.6980","snapshot_observed_at":"2026-08-11T11:07:55.649034Z","title":"Adam: A method for stochastic optimization,","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.649034Z"},"links":{"cited_paper":"/paper/1412.6980","citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:30c66d20d8f27e5885c1a556ae3812e8146547084eabd891a16d198e010ab8e7","observation_id":"7ee29d04-fea0-430f-a271-74e5ebce7413","resolution":{"observed_at":"2026-08-11T11:07:55.649034Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1807.05118","last_updated":"2018-07-13T15:00:17Z","snapshot_observed_at":"2026-08-19T20:35:38.129629Z","submitted_at":"2018-07-13T15:00:17Z","title":"Tune: A Research Platform for Distributed Model Selection and Training","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1807.05118","snapshot_observed_at":"2026-08-11T11:07:55.653928Z","title":"Tune: A research platform for distributed model selection and training,","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.653928Z"},"links":{"cited_paper":"/paper/1807.05118","citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:24cd7927a8c38936cfef51ba9045491785cbdbb17ec19d21d382bb26cc611e1e","observation_id":"af1dae00-aacc-474b-b3c7-0ce3e38a55ff","resolution":{"observed_at":"2026-08-11T11:07:55.653928Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2406.03260","last_updated":"2025-06-16T11:42:27Z","snapshot_observed_at":"2026-08-16T13:45:53.778542Z","submitted_at":"2024-06-05T13:37:42Z","title":"Feature learning in finite-width Bayesian deep linear networks with multiple outputs and convolutional layers","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2406.03260","snapshot_observed_at":"2026-08-11T11:07:55.659929Z","title":"Feature learning in finite-width bayesian deep linear networks with multiple outputs and convolutional layers,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.659929Z"},"links":{"cited_paper":"/paper/2406.03260","citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:ec04b1a29ca08d718f05de3fa5025d6f0367a3faaf8762d08b5cc5c3df340b4e","observation_id":"efa5fcd3-4305-4089-bc31-b05dc39fe038","resolution":{"observed_at":"2026-08-11T11:07:55.659929Z","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":"2026-08-11T11:07:56.470965Z","title":"The generalization error of random features regression: Precise asymptotics and the double descent curve,","venue":null,"work_id":"446fb2e3-898c-44ca-9629-12c8626225f1","year":2019},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.664567Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:c01c266968cbf386ff3080129ed968eab2dd6e3791db751963061c94c63f54ac","observation_id":"4d338472-4fda-405b-8cda-2c26343084fe","resolution":{"observed_at":"2026-08-11T11:07:56.476268Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.455695Z","title":"Generalisation error in learning with random features and the hidden manifold model,","venue":null,"work_id":"8c461fed-65fa-4390-b85c-de78eda3f46f","year":2021},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.669123Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:ee73f56de6bc1f1b65b1725902c71bee87cf50bae42e41a3cc809d7762b40030","observation_id":"f0c855eb-c656-43f8-b9da-0d65013af849","resolution":{"observed_at":"2026-08-11T11:07:56.460942Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2402.10164","last_updated":"2025-01-31T17:16:17Z","snapshot_observed_at":"2026-08-16T14:18:13.036959Z","submitted_at":"2024-02-15T18:09:41Z","title":"Random features and polynomial rules","version":2},"cited_work":{"arxiv_id":"2402.10164","doi":null,"metadata_source":"pith","pith_arxiv_id":"2402.10164","snapshot_observed_at":"2026-08-11T11:07:55.847669Z","title":"Random features and polynomial rules","venue":"cond-mat.dis-nn","work_id":"9a62a8c3-bd6c-40c1-afa8-1570dbc0adac","year":2024},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.674408Z"},"links":{"cited_paper":"/paper/2402.10164","citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:98c2f71d875d71eff391212bb8d6d0f4acef94c9574518a775cb3ccf6b871da6","observation_id":"c72997ee-2105-49ac-9010-9f3a5a0509f8","resolution":{"observed_at":"2026-08-11T11:07:55.855113Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.438863Z","title":"Universal mean-field upper bound for the generalization gap of deep neural networks,","venue":null,"work_id":"c7faa28c-baf2-4c7f-be8a-dbcb8a7d8949","year":2022},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.679457Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:44e48abc7b5a305a09d8e3b7bfd852792aebfd58075734b7e80d754cc846a4ff","observation_id":"d26300a7-0779-4d6a-9cc6-1f92926a2daa","resolution":{"observed_at":"2026-08-11T11:07:56.445487Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.420299Z","title":"Central limit theorems for non-linear functionals of gaussian fields,","venue":null,"work_id":"070520ab-1fb6-4e5f-b057-5baefc5251da","year":1983},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.683391Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:50ca0113f3df6c31f410758a958019ffeb0c237eccad12472dbe8f8fa31cb1c0","observation_id":"ffc01b2a-2be9-4a22-9421-892aa3d80ad8","resolution":{"observed_at":"2026-08-11T11:07:56.429826Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.402676Z","title":"Quantitative Breuer-Major theorems,","venue":null,"work_id":"4ad36f29-6e72-47e5-868d-c4308cd96ab6","year":2010},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.687696Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:70fbe40b281839acb28b8984c22f9a11b9c57ce86a7dbd1e62bf34a9fc978476","observation_id":"9e961856-458f-4c72-9814-d36685b56725","resolution":{"observed_at":"2026-08-11T11:07:56.408035Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.386475Z","title":"A smaller subset of 10 easily classified classes from imagenet,","venue":null,"work_id":"6de2ec1a-4f40-43b2-a90f-bb0ddc6ac5c5","year":null},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.692015Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:987ca4ddda0ab0bdd04ae1e940866d790993152fd9ab936860c38c4ecde2ec58","observation_id":"fd3ea558-cd03-42ce-8a4c-88278c421940","resolution":{"observed_at":"2026-08-11T11:07:56.391917Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.366617Z","title":"Finite versus infinite neural networks: an empirical study,","venue":null,"work_id":"1c043a84-fae1-4eb7-b8c4-b0107e10d1b5","year":2020},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.697492Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:8839f49afe7d7d42720148ff8d0c9a161fabd47e8697ebf5e3df5be9d3b99984","observation_id":"79a4267b-8d72-489a-b188-c8ec90c70521","resolution":{"observed_at":"2026-08-11T11:07:56.372830Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:55.701142Z","title":"Representations and generalization in artificial and brain neural networks,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.701142Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:36c22a4e8870b289a02e8887ad25c3fb455a8e5180602f4cf078e58bf7a8895c","observation_id":"fe45e1c5-f643-4e06-9de3-8c4f26659121","resolution":{"observed_at":"2026-08-11T11:07:55.701142Z","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":"2026-08-11T11:07:56.348479Z","title":"A self consistent theory of gaussian processes captures feature learning effects in finite cnns,","venue":null,"work_id":"692535ea-5e89-4faa-9e42-1fad6c115982","year":2021},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.705039Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:01ef0cd4e2ac344f7ce1c0ea7580e4c8be981716561cac8d686c90b7f143d523","observation_id":"5c9c13a8-0399-4341-9866-0d5780440eb2","resolution":{"observed_at":"2026-08-11T11:07:56.353517Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.332186Z","title":"Separation of scales and a thermodynamic description of feature learning in some cnns,","venue":null,"work_id":"08f14fb3-2550-4232-9f1b-9e689f103875","year":2023},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.709017Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:445f41bc8f76dc5e846bf7c89599a64dde1027edc69339a0d61265be98d96770","observation_id":"68f6db5c-48f2-4f22-86d9-31848cfbeafd","resolution":{"observed_at":"2026-08-11T11:07:56.337059Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.16630","last_updated":"2024-05-26T17:08:04Z","snapshot_observed_at":"2026-08-16T21:16:40.007433Z","submitted_at":"2024-05-26T17:08:04Z","title":"Bayesian Inference with Deep Weakly Nonlinear Networks","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.16630","snapshot_observed_at":"2026-08-11T11:07:55.713007Z","title":"Bayesian inference with deep weakly nonlinear networks,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.713007Z"},"links":{"cited_paper":"/paper/2405.16630","citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:a73857b147ebb3c40c3523e2d09bea5800bc9d67c4ac47f7f41dc556b36591b9","observation_id":"93717ad5-c0c6-4cf6-9d7c-20dda17bc3a6","resolution":{"observed_at":"2026-08-11T11:07:55.713007Z","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":"2026-08-11T11:07:55.717403Z","title":"Data- driven emergence of convolutional structure in neural networks,","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.717403Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:0a47f3f77846701e25d1c90b5e5da918901bf41b794376efb98be1c7011436c5","observation_id":"365194d3-29d7-4390-9a97-e69e5051d9f3","resolution":{"observed_at":"2026-08-11T11:07:55.717403Z","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":"2026-08-11T11:07:56.311264Z","title":"Moment bounds and central limit theorems for gaussian subordinated arrays,","venue":null,"work_id":"faee37ed-cd52-4724-b634-88b1a3dc5aaf","year":2013},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.721086Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:dbf7e3e7cc4e40d6086040c2f8afcb23a7f2a3381657a6320e0581b6237c890d","observation_id":"dcc2434f-daa5-4523-b6d8-2df65ab07dbb","resolution":{"observed_at":"2026-08-11T11:07:56.319275Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.297097Z","title":"Multivariate normal approximation using stein’s method and malliavin calculus,","venue":null,"work_id":"6102bc47-80d5-489f-984e-970c581526b0","year":2008},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.725334Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:cc809a71fbc4bedf585594e17de00bf2b0ca7cb60cccfae702f6da1e23d43cd5","observation_id":"e1bb4951-c352-4d1e-bac2-08aebff7f7ba","resolution":{"observed_at":"2026-08-11T11:07:56.302546Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.268358Z","title":"An integral which occurs in statistics,","venue":null,"work_id":"24d95153-be8f-49cd-b414-0d4bc99b2cf6","year":1933},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.730403Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:d269c994e25187b486e7e1bb95f652b9d973ace1783f3aa66c65a72cc1847efd","observation_id":"a5910337-4bf8-4783-b9a1-6ea6e998e57c","resolution":{"observed_at":"2026-08-11T11:07:56.278821Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.251547Z","title":"Kernel shape renormalization in bayesian shallow networks: a gaussian process perspective,","venue":null,"work_id":"54e718b7-e4b7-4af0-82a8-0435c317340d","year":2024},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.738129Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:ef93a02a0d2de27381965ce7ec500950effbd0849864adedfe82ed6faaef90c6","observation_id":"0598f304-1572-4068-bae5-7277baf17464","resolution":{"observed_at":"2026-08-11T11:07:56.258771Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.222004Z","title":null,"venue":null,"work_id":"c2bcdd52-ec32-4e45-9656-032dd1e9d3c2","year":2020},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.743158Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:5cbc0daa3bd1395451694ce2112cf9dccbff194faeac1f3e4347305f16b81fc8","observation_id":"633ff120-b92f-4579-90a0-fc005c27eddc","resolution":{"observed_at":"2026-08-11T11:07:56.227391Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.208497Z","title":"Heermann, Monte Carlo Simulation in Statistical Physics (Springer Berlin Heidelberg, 2002)","venue":null,"work_id":"0e1cd17f-bd0b-4a1b-aee1-9473b07f9761","year":2002},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.747339Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:775de7f57b63a6be3a322e07ba6c2fb4a1193b7909bd4819abf39ab554d820b7","observation_id":"097e7d5b-b09d-468a-bc0a-1a419c1e5e30","resolution":{"observed_at":"2026-08-11T11:07:56.213099Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.192722Z","title":"Monte carlo errors with less errors,","venue":null,"work_id":"6d433d78-5c48-460f-b623-5ab9a20adae8","year":2004},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.751952Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:7a13cec9f1b933137c679aff871b7bdbfaddf4799988a98adf34415038345c33","observation_id":"01cd80e3-8fff-4e4c-96c4-a6adc4d5c4a4","resolution":{"observed_at":"2026-08-11T11:07:56.198556Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.173954Z","title":"EfficientNet: Rethinking model scaling for convolutional neural networks,","venue":null,"work_id":"e847e0fe-6d14-4e9c-9fa8-5cb0614307a9","year":2019},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.755816Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:985d858d657f732ff61acc5586a060541279d1066e5ac3a3311648edab4937b3","observation_id":"735172a9-be5b-4ca7-af9e-6d4f194213d0","resolution":{"observed_at":"2026-08-11T11:07:56.178802Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-11T11:07:56.158788Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden layer networks","venue":null,"work_id":"1e027d56-ab93-4703-b4eb-1d4f6d99561c","year":2009},"citing_paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-11T11:07:55.759990Z"},"links":{"citing_paper":"/paper/2412.15911"},"observation_digest":"sha256:07cea3735318ab3e8982176553be4bfa50a9712419f8e69c4c98505587aafc10","observation_id":"6d13d31d-5eef-4ddd-bbb6-5a9d0814243f","resolution":{"observed_at":"2026-08-11T11:07:56.164275Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.15911","last_updated":"2024-12-20T14:01:16Z","latest_version":1,"primary_category":"cond-mat.dis-nn","snapshot_observed_at":"2026-08-18T03:55:44.495283Z","submitted_at":"2024-12-20T14:01:16Z","title":"Kernel shape renormalization explains output-output correlations in finite Bayesian one-hidden-layer networks"},"reference_resolution":{"displayed":58,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":12,"verified_exact":7,"verified_fuzzy":39},"total_outbound_references":58},"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":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"thesis":"As of 23 August 2026, this Paper Citation Record lists 58 of 58 outbound references and 0 inbound Pith citation observations for arXiv:2412.15911."}