{"as_of":"2026-08-05T03:01:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:2e83ec1444524cf01a0a72dc6117a8ea465ffebc13a436e99871ca8ae5de4060","coverage":[{"denominator":43,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":43,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-18T22:55:08.245141Z","state":"measured"},{"denominator":46,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":46,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-04T06:34:03.388597+00:00","state":"measured"},{"denominator":3,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":3,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T18:25:45.421473Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-06-30T08:14:26.101219Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2508.12121","snapshot_observed_at":"2026-08-03T18:25:45.421473Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.05790","last_updated":"2026-07-15T06:37:33Z","snapshot_observed_at":"2026-08-03T18:25:41.532388Z","submitted_at":"2025-12-05T15:16:59Z","title":"Learnability Window in Gated Recurrent Neural Networks","version":9},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-03T18:25:45.421473Z"},"links":{"cited_paper":"/paper/2508.12121","citing_paper":"/paper/2512.05790"},"observation_digest":"sha256:a9c40eeae8c493bf5bba3d46e328cc38a450c7a93ac87d7f44f48ce8aabcfda0","observation_id":"e1068dd9-3aea-4276-823d-b096244f2c99","resolution":{"observed_at":"2026-08-03T18:25:45.421473Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"cited_work":{"arxiv_id":"2508.12121","doi":null,"metadata_source":"pith","pith_arxiv_id":"2508.12121","snapshot_observed_at":"2026-06-30T08:14:26.101219Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","venue":"cs.LG","work_id":"a2b41990-7355-45b2-b880-2ede6b7ec5dc","year":2025},"citing_paper":{"arxiv_id":"2606.29519","last_updated":"2026-07-17T10:08:43Z","snapshot_observed_at":"2026-08-02T10:13:00.721203Z","submitted_at":"2026-06-28T17:30:36Z","title":"Anti-Collapse Dynamics and the Emergence of Multi-Time-Scale Learning in Recurrent Neural Networks","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-06-30T07:34:39.700429Z"},"links":{"cited_paper":"/paper/2508.12121","citing_paper":"/paper/2606.29519"},"observation_digest":"sha256:e612dbbb49d96a09b00d151bc23d89795e3c94ce960e6b92c8939ef2bd420094","observation_id":"8c846844-d4ea-46a4-b9d5-2f313eddab1b","resolution":{"observed_at":"2026-06-30T08:14:26.102657Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2508.12121","snapshot_observed_at":"2026-08-02T09:43:28.106394Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.29519","last_updated":"2026-07-17T10:08:43Z","snapshot_observed_at":"2026-08-02T10:13:00.721203Z","submitted_at":"2026-06-28T17:30:36Z","title":"Anti-Collapse Dynamics and the Emergence of Multi-Time-Scale Learning in Recurrent Neural Networks","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-02T09:43:28.106394Z"},"links":{"cited_paper":"/paper/2508.12121","citing_paper":"/paper/2606.29519"},"observation_digest":"sha256:d425bf815271fd559c6490533a855a3c37cafee5da9f30d961df7107a2266055","observation_id":"edc7a33d-a7a7-4e92-8b53-f3a711caeeb9","resolution":{"observed_at":"2026-08-02T09:43:28.106394Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2508.12121/citation-record","integrity":"/paper/2508.12121/integrity","json":"/paper/2508.12121/citation-record.json","paper":"/paper/2508.12121"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"On the difficulty of training recurrent neural networks","venue":null,"work_id":"91cb2012-8113-45e1-bfc1-61fd7b15f03f","year":2013},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:2a5b3cebd9fb0db195e66f52cf2f5ebea308133aff9697039c701ae9e2d3e7ee","observation_id":"f211771f-7512-44e2-a660-ad19331a9a46","resolution":{"observed_at":"2026-05-18T22:56:53.997392Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Recurrent neural networks: vanishing and exploding gradients are not the end of the story","venue":null,"work_id":"651bf28a-4bdc-47d5-b346-bcc45a47589f","year":2024},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:79326df540be06b0957b78707342b3cd841a3c5976635265464d440a049a0f66","observation_id":"b04674ce-2a6f-49f5-b892-b626668664cf","resolution":{"observed_at":"2026-05-18T22:56:53.961041Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Random orthogonal additive filters: A solution to the van- ishing/exploding gradient of deep neural networks","venue":null,"work_id":"292faf82-e0b7-422d-8c48-96dda17820ca","year":2025},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:8c9bb77af462784407c0d7b86f04bc54feb20a4df86e672e23777fd99240f89f","observation_id":"c6ae864d-1c90-4376-8935-a5cb9c19e88c","resolution":{"observed_at":"2026-05-18T22:56:53.950867Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2111.00396","last_updated":"2022-08-05T17:54:38Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2021-10-31T03:32:18Z","title":"Efficiently Modeling Long Sequences with Structured State Spaces","version":3},"cited_work":{"arxiv_id":"2111.00396","doi":"10.48550/arxiv.2111.00396","metadata_source":"pith","pith_arxiv_id":"2111.00396","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Efficiently Modeling Long Sequences with Structured State Spaces","venue":"cs.LG","work_id":"4150b761-b8bf-4d9b-a2f8-cb2d1b73d378","year":2021},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"cited_paper":"/paper/2111.00396","citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:6cad7c090488accb2c305a5c3bc23f92e7eb60e61a2e395a6721f42d1cbda80c","observation_id":"e6d22542-8151-4df5-ae76-52756d9d8565","resolution":{"observed_at":"2026-05-18T22:56:53.090297Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Combining recurrent, convolutional, and continuous-time models with linear state space layers","venue":null,"work_id":"325cb993-d7b2-409c-9687-d1157b009bea","year":2021},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:33ed7fa5e80a0812f19765df8362e9a97f140177d48135c71f1a39ae76239e65","observation_id":"ab352fa3-20e6-40a8-9b50-34272b635a27","resolution":{"observed_at":"2026-05-18T22:56:53.973062Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"The- oretical foundations of deep selective state-space models","venue":null,"work_id":"d7b2c9c3-14da-40a6-9df5-2ebd1afddca5","year":2024},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:28eb6e851690d036e8ab83675fbd3871d29eadfc0949108424f3ddadf0c6e870","observation_id":"89bd8fea-3be9-4a9d-b57e-69649a622e17","resolution":{"observed_at":"2026-05-18T22:56:53.980207Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Wide neural networks of any depth evolve as linear models under gradient descent","venue":null,"work_id":"1cc32b39-57be-4c39-8d76-72f200bd828b","year":2019},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:bd45dc4ceccf6b63eb31faf56496c8e15d8da6966642eb3ca3093d76424be9c4","observation_id":"353fbccc-3a5a-4265-9870-719e2930951f","resolution":{"observed_at":"2026-05-18T22:56:53.953965Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1312.6120","last_updated":"2014-02-19T17:26:57Z","snapshot_observed_at":"2026-08-01T19:05:53.906854Z","submitted_at":"2013-12-20T20:24:00Z","title":"Exact solutions to the nonlinear dynamics of learning in deep linear neural networks","version":3},"cited_work":{"arxiv_id":"1312.6120","doi":"10.48550/arxiv.1312.6120","metadata_source":"pith","pith_arxiv_id":"1312.6120","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Exact solutions to the nonlinear dynamics of learning in deep linear neural networks","venue":"cs.NE","work_id":"adbbf9c7-c3a4-4cb7-9a00-c98b12f8a315","year":2013},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"cited_paper":"/paper/1312.6120","citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:43e04b53af67207f397845b789f33d04bf030d4485e65f15f08321e4a721c78a","observation_id":"c0efe837-4a93-46e3-ab53-02b0dbafa55b","resolution":{"observed_at":"2026-05-18T22:56:53.084512Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-07-11T04:49:31.258619+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-11T04:49:31.258619+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Orthogonal recurrent neural networks with scaled Cayley transform","venue":null,"work_id":"ad2fbc79-a7ec-4bd4-82a8-1f53f85a4579","year":2018},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:eb2494d3e2acc95afdb08d3dc35c418553d89bd25e9ef15d7a5bc9a4227af5d7","observation_id":"a7a4674d-9409-4c65-9015-6225c241fbf7","resolution":{"observed_at":"2026-05-18T22:56:53.957522Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Efficient or- thogonal parametrisation of recurrent neural networks using householder reflections","venue":null,"work_id":"309731e0-7a79-49d5-9d32-c74c31a33ca6","year":2017},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:518f3bf2b44331b5557f8c9ef6a49f15ff45680767c3c628013fca5614e8cfc4","observation_id":"b2501153-d220-4620-88bd-d34509dee70b","resolution":{"observed_at":"2026-05-18T22:56:53.964088Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Unitary evolution recurrent neural networks","venue":null,"work_id":"46f268f7-d4a5-4d60-b5b0-6eda4c2124d3","year":2016},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:d4e5fdd0daa35c24103bfdf63adabed8140fe2051dde048a5ca420dfc995db17","observation_id":"89e192ec-57cc-4f6e-8682-a8480b528a2b","resolution":{"observed_at":"2026-05-18T22:56:53.947692Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Full- capacity unitary recurrent neural networks","venue":null,"work_id":"e290f487-6c20-4557-ab6e-b88058424c0c","year":2016},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:fe76b1b35fe4a66f0425d6683bc4d5248bb8f47c66337368404aa473d0abb655","observation_id":"a40be806-1602-4e3d-85d3-7e30a81bc8e8","resolution":{"observed_at":"2026-05-18T22:56:53.990267Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"On orthogonality and learning recurrent networks with long term dependencies","venue":null,"work_id":"28fb374f-227e-41bc-bd4c-d846efdefe46","year":2017},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:ec8118a439458912e1f62e2bbbd334fbea1002a2d8e3e936f8d405f1dfba3819","observation_id":"0db2ed53-b035-4913-b059-f03d2f72a607","resolution":{"observed_at":"2026-05-18T22:56:53.983744Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2006.12070","last_updated":"2021-04-24T03:31:59Z","snapshot_observed_at":"2026-07-06T09:31:19.187163Z","submitted_at":"2020-06-22T08:44:52Z","title":"Lipschitz Recurrent Neural Networks","version":3},"cited_work":{"arxiv_id":"2006.12070","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2006.12070","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Lipschitz recurrent neural networks","venue":null,"work_id":"55c4a84d-c52e-471c-add9-99292693d715","year":2006},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"cited_paper":"/paper/2006.12070","citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:44fac07bfec2d094e3ad7acbe5748a97accfe3bc22ae20c830f4dc7436bad987","observation_id":"7a2c8a29-b131-44ae-9f13-e440692ce421","resolution":{"observed_at":"2026-05-18T22:56:53.079495Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1905.12080","last_updated":"2019-10-28T13:13:02Z","snapshot_observed_at":"2026-07-06T07:56:14.335105Z","submitted_at":"2019-05-28T20:41:27Z","title":"Non-normal Recurrent Neural Network (nnRNN): learning long time dependencies while improving expressivity with transient dynamics","version":2},"cited_work":{"arxiv_id":"1905.12080","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1905.12080","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Non-normal recurrent neural network (nnrnn): learning long time dependencies while improving expressivity with transient dynamics","venue":null,"work_id":"7368d721-cf17-45ee-8bc9-e39eab07d2c3","year":1905},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"cited_paper":"/paper/1905.12080","citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:8393180023e3a5002cff7907948f6b449c8636b65fd0205acf27bb1665c5d3ad","observation_id":"12354a7a-c443-46c9-add7-db0abbf01730","resolution":{"observed_at":"2026-05-18T22:56:53.095224Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"RNNs incrementally evolving on an equilibrium manifold: A panacea for vanishing and exploding gradients?","venue":null,"work_id":"cb248524-eddb-4b79-bae2-4a194897c4cd","year":2020},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:df3ab55b14ae9b9e06cd100aece751c9c8514fb2949a67a0aff55debeb70e620","observation_id":"d330ffd7-560d-4321-b3e1-4d8ceef26c46","resolution":{"observed_at":"2026-05-18T22:56:53.976737Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"AntisymmetricRNN: A dynamical system view on recurrent neural networks","venue":null,"work_id":"495ea835-5819-4980-8093-4e06b70ab522","year":2019},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:192ac7b048b0d45e4e69ea81c41e2944e97d18a5b0dc35d219603e446e702486","observation_id":"8d1c8dd4-881e-40a8-91f5-2efba6367df1","resolution":{"observed_at":"2026-05-18T22:56:54.001225Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Coupled oscillatory recurrent neural network (cornn): An accurate and (gradient) stable architecture for learning long time dependencies","venue":null,"work_id":"4185ee2e-0a21-47bf-85c9-8a852b855a67","year":2021},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:9239a8fccad7bba4a80b707cde4c0c7de75269373b617c536a34c1d65a424003","observation_id":"bbedf6cc-f1ec-468c-a22b-db747f5676f4","resolution":{"observed_at":"2026-05-18T22:56:53.993632Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2110.04744","last_updated":"2022-02-25T15:20:52Z","snapshot_observed_at":"2026-08-05T00:16:23.373749Z","submitted_at":"2021-10-10T09:43:02Z","title":"Long Expressive Memory for Sequence Modeling","version":2},"cited_work":{"arxiv_id":"2110.04744","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2110.04744","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Long expressive memory for sequence modeling","venue":null,"work_id":"df9c65e6-741b-4814-8e9e-d5fc631ef101","year":2021},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"cited_paper":"/paper/2110.04744","citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:e2e0e32c5af563f4644c0f8770dad508d98d0a0c3cf8d3d9350ff3374d7b46bd","observation_id":"4e2291be-a2df-45a6-9663-7cd79c39ca20","resolution":{"observed_at":"2026-05-18T22:56:53.074205Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"A clockwork RNN","venue":null,"work_id":"c39ed2d8-51f5-4752-a59a-70ec05fd1a65","year":2014},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:1ff43fa2d375c3915d2db6e4fc610fd3ca13a9703b7f6b9a525b3a52f4626024","observation_id":"5f5ae107-cb6f-4051-9efc-de1f65970b89","resolution":{"observed_at":"2026-05-18T22:56:53.966771Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Dynamical isometry and a mean field theory of RNNs: Gating enables signal propagation in recurrent neural networks","venue":null,"work_id":"beb620f7-54fb-4ef0-a9bf-9b495558e05c","year":2018},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:25715536b9792b3eae45fe214228e5bf41bf38360b01f2254a232a45a7f9e07f","observation_id":"bad1cee6-5426-4d86-a6e2-cc46b044d718","resolution":{"observed_at":"2026-05-18T22:56:53.969804Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1901.08987","last_updated":"2019-05-24T01:10:22Z","snapshot_observed_at":"2026-07-06T07:29:06.755132Z","submitted_at":"2019-01-25T17:05:54Z","title":"Dynamical Isometry and a Mean Field Theory of LSTMs and GRUs","version":2},"cited_work":{"arxiv_id":"1901.08987","doi":null,"metadata_source":"pith","pith_arxiv_id":"1901.08987","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Dynamical Isometry and a Mean Field Theory of LSTMs and GRUs","venue":"cs.LG","work_id":"88356995-bfb4-4a5a-847c-a3a4c5c6cd59","year":2019},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"cited_paper":"/paper/1901.08987","citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:dc06564f6973807a6f352dab54e7722737e004cda5aba4b1d0d253b0ebe2a16a","observation_id":"8dd79e26-8867-4b9f-aabd-89214dd38094","resolution":{"observed_at":"2026-05-18T22:56:53.069687Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Resurrecting the sigmoid in deep learning through dynamical isometry: theory and practice","venue":null,"work_id":"8ce5f68f-54db-4fa0-988e-bd16f37291a6","year":2017},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:3d319f8559f7b0c4cd0858415a8759b590f11854fb41a4fd86272917e2caf1f1","observation_id":"1c583dac-2a54-4bc5-a826-04117f3f28f3","resolution":{"observed_at":"2026-05-18T22:56:54.005528Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Gating revisited: Deep multi-layer rnns that can be trained","venue":null,"work_id":"d29d72c1-7c14-40fa-a874-4843aa7c85ce","year":2022},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:6dbd869481a82c412fbb4ae2a4815a684542857219ec12fe30eea9af812d761d","observation_id":"a19ec61c-b24f-495b-ab85-d61518182afb","resolution":{"observed_at":"2026-05-18T22:56:53.986888Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1804.04849","last_updated":"2018-09-13T10:55:56Z","snapshot_observed_at":"2026-07-06T06:33:15.714029Z","submitted_at":"2018-04-13T09:18:17Z","title":"The unreasonable effectiveness of the forget gate","version":3},"cited_work":{"arxiv_id":"1804.04849","doi":null,"metadata_source":"pith","pith_arxiv_id":"1804.04849","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"The unreasonable effectiveness of the forget gate","venue":"cs.NE","work_id":"c602c7b5-d501-4f21-a073-f5fab7892bd2","year":2018},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"cited_paper":"/paper/1804.04849","citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:e18d765d2bee45a613cd939c30841c26796f82b7d54c68a44a470f1eaf967ed4","observation_id":"89ae9eda-c50a-44a6-bcc4-cd46fd8e4dd3","resolution":{"observed_at":"2026-05-18T22:56:53.060486Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Theory of gating in recurrent neural networks","venue":null,"work_id":"0643983e-de84-4e9b-8b9c-2d94d132caf2","year":2022},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:f9de4233047512cc9cd2dc9932d120d1f2e1ed947eb5bb46463dcce846a307ce","observation_id":"d87d8ffc-b123-478b-81e9-df3a48681389","resolution":{"observed_at":"2026-05-18T22:56:53.902763Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Gates create slow modes in recurrent neural networks","venue":null,"work_id":"2c38036a-6f10-49e0-8fee-3fab3a79f2a8","year":2020},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:d134317dd00de4bab294261e84a9958ef8162782a3a0aa505bca92392fb58d9d","observation_id":"17afe4e7-845f-4888-89f3-3101bdd7a3a9","resolution":{"observed_at":"2026-05-18T22:56:53.944547Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Adaptive time scales in recurrent neural networks","venue":null,"work_id":"ed6bf7dd-50ae-42ba-9aab-d3c12a7a5a02","year":2020},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:19bbd8c1e8addf2c92ec37ce629364bb77c773e3426c7eb2c28f83a7be30b5ff","observation_id":"5cc43551-6de6-40fe-815c-7aa5d37dbb13","resolution":{"observed_at":"2026-05-18T22:56:53.917922Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Can recurrent neural networks warp time?","venue":null,"work_id":"bb6158f3-7f47-43fe-bb33-29a52d59d7d0","year":2018},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:aa22a4f5c5602833add03d45aad610705c770c83d3cd885cab8506ef1c1a9830","observation_id":"73957f23-c072-4b76-924b-7c8d6b249f21","resolution":{"observed_at":"2026-05-18T22:56:53.905972Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Optimization and applications of echo state networks with leaky-integrator neurons","venue":null,"work_id":"4eae42e3-91c3-4972-a889-94f609f2e760","year":2007},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:16da9af8c4a8f88a8dfd4a775c01fd3ff92ef4bb9dff61bd71449a1da672ec9d","observation_id":"23967350-2931-43ef-8aba-86f86dcab035","resolution":{"observed_at":"2026-05-18T22:56:53.938082Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Backpropagation through time: what it does and how to do it","venue":null,"work_id":"062b7dae-ef17-449f-a23f-c0eb21e65519","year":1990},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:a7036b0df4cd23463c465e6057db632e63326abf937d04b44e23618abe08dbc7","observation_id":"7090d4ae-ec89-419f-abfc-2fc7c27aa5ca","resolution":{"observed_at":"2026-05-18T22:56:53.941358Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1609.04747","last_updated":"2017-06-15T13:21:04Z","snapshot_observed_at":"2026-08-04T02:05:40.539691Z","submitted_at":"2016-09-15T17:32:34Z","title":"An overview of gradient descent optimization algorithms","version":2},"cited_work":{"arxiv_id":"1609.04747","doi":"10.48550/arxiv.1609.04747","metadata_source":"pith","pith_arxiv_id":"1609.04747","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"An overview of gradient descent optimization algorithms","venue":"cs.LG","work_id":"840f481e-6e07-4454-8939-95804142c46d","year":2016},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"cited_paper":"/paper/1609.04747","citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:63a68830fe26b0e678eb2e2aa55b13c3b6eedadcc9f9bdc6f575f45ee9700d4b","observation_id":"730947af-0410-46c0-9408-74d179ea8f72","resolution":{"observed_at":"2026-05-18T22:56:53.055492Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-01T05:08:09.422576+00:00","source":"crossref_status_cache"},{"observed_at":"2026-08-01T05:08:09.422576+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-07-06T16:22:38.582822Z","title":"Long short-term memory","venue":null,"work_id":"c0deeb3f-6ea9-435c-bccc-90ae1a94f872","year":1997},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:0c5998ece40f4450d7f76611d50294ad1692778376a38cc787926c923ca09752","observation_id":"3e85532c-0cec-4a35-9f16-2ade2bd70d20","resolution":{"observed_at":"2026-05-18T22:56:53.896308Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1406.1078","last_updated":"2014-09-03T00:25:02Z","snapshot_observed_at":"2026-07-06T03:45:28.546418Z","submitted_at":"2014-06-03T17:47:08Z","title":"Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation","version":3},"cited_work":{"arxiv_id":"1406.1078","doi":"10.48550/arxiv.1406.1078","metadata_source":"pith","pith_arxiv_id":"1406.1078","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation","venue":"cs.CL","work_id":"af085a26-bb72-4b1a-8e38-107776555081","year":2014},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"cited_paper":"/paper/1406.1078","citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:0f3435cd09134ee33ba922e66a43b4da5db42c57d54846536c37ede6766596f5","observation_id":"984688a7-b763-4b09-ba5b-0f19434a5e2c","resolution":{"observed_at":"2026-05-18T22:56:53.065155Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-07-16T20:21:34.843836+00:00","source":"crossref_status_cache"},{"observed_at":"2026-07-16T20:21:34.843836+00:00","source":"openalex_status_cache"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Attention is all you need","venue":null,"work_id":"eab8352b-f1d2-4404-b528-775ac299dab8","year":2017},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:2162fc2c9c22e57d746613dfd2b252117e8a9b2752a791287d80003a93a5640c","observation_id":"e0c2a609-5360-4eb3-9f6f-be4c1a489cf6","resolution":{"observed_at":"2026-05-18T22:56:53.934686Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"913c54dd-d3e6-4054-a1ce-641e7efc2784","year":2008},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:1fbeb59dbae84d58f1e18c34d8474706ba28666e3717c85bf135751c7c3c73e4","observation_id":"75f61c9b-f7f2-44f5-abd9-1df708be0d1e","resolution":{"observed_at":"2026-05-18T22:56:53.899257Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"ff36225a-040f-4014-ad04-c8c67c86561f","year":2003},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:b4fff286ea5aa0d919d93e819a39e3823cfaeca5f7f68ae2d92959be552d8f07","observation_id":"89e8ea66-6c92-4451-9652-eaaee10f62c4","resolution":{"observed_at":"2026-05-18T22:56:53.931569Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1412.6980","last_updated":"2017-01-30T01:27:54Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2014-12-22T13:54:29Z","title":"Adam: A Method for Stochastic Optimization","version":9},"cited_work":{"arxiv_id":"1412.6980","doi":"10.1002/mrm.28086","metadata_source":"pith","pith_arxiv_id":"1412.6980","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Adam: A Method for Stochastic Optimization","venue":"cs.LG","work_id":"1910796d-9b52-4683-bf5c-de9632c1028b","year":2014},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"cited_paper":"/paper/1412.6980","citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:575744efd437fb83327bde7a3718462986ec36063598fd84cef07d9f48badb8d","observation_id":"bb086ed9-e410-49fa-aca4-e6ef37c8d7a8","resolution":{"observed_at":"2026-05-18T22:56:53.050661Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"Since the space is finite-dimensional, all norms are equivalent","venue":null,"work_id":"7e61fc3d-166e-4bc8-89b0-43a08aa6a589","year":null},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:77b44dfe40f82a391093460b2239e5c553f042318fcecb026c6dd2f1e8e6555e","observation_id":"87eec651-35c7-4f25-a325-c8bba785b83e","resolution":{"observed_at":"2026-05-18T22:56:53.928285Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"The direction of perturbation E in (57) is now the tuple E ≡ (B1, B2","venue":null,"work_id":"fdae0f45-d8ea-44d2-b762-a9b15c960158","year":null},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:620fca971232112eb5aa4179baf52f24b29fef3be072e986fa596666c83b81ba","observation_id":"5643366b-19e2-4810-9da2-4e00990d4b73","resolution":{"observed_at":"2026-05-18T22:56:53.921153Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"We now apply the product rule (58) to Fn by setting g(ε) = Fn−1(ε), h (ε) = An + εBn","venue":null,"work_id":"6c9c635d-4842-4d53-9853-dc497e02cf64","year":null},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:3906b94bf09e5a854e8014dc3fafab942824cfe7bed11394936f7cb357db5fbb","observation_id":"530c547d-5771-4def-a316-a88ad32a6611","resolution":{"observed_at":"2026-05-18T22:56:53.910271Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"6fd8e123-6c73-40b1-987f-07b8e349a720","year":null},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:54c33d50f1d4379b195474d12b0a943b4cb2e4ab19cf076be5f55e0aa5ad5464","observation_id":"b0b41e47-471e-4ece-83ef-0d7ec1e64cfc","resolution":{"observed_at":"2026-05-18T22:56:53.924650Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+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":"2026-06-05T21:23:00.469572Z","title":"In the main text, Bj represents gate-induced corrections, which are typically low-norm compared to the dominant dynamics in Aj","venue":null,"work_id":"5b5b7beb-57a2-4a55-abe7-a9db1f742d96","year":null},"citing_paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks","version":5},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-05-18T22:55:08.245141Z"},"links":{"citing_paper":"/paper/2508.12121"},"observation_digest":"sha256:3f5ee433063549d46b6571802931192c1d7b5eff0ae465bd8bfd292b76fbd827","observation_id":"b4a15046-73c8-4970-9fed-49c45013aad8","resolution":{"observed_at":"2026-05-18T22:56:53.914409Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2508.12121","last_updated":"2026-04-21T17:54:21Z","latest_version":5,"primary_category":"cs.LG","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-08-16T18:19:34Z","title":"Time-Scale Coupling Between States and Parameters in Recurrent Neural Networks"},"reference_resolution":{"displayed":43,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":10,"verified_fuzzy":30},"total_outbound_references":43},"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":"2026-08-04T06:34:03.388597+00:00","source":"crossref"},{"observed_at":"2026-08-04T06:33:57.428241+00:00","source":"retraction_watch"}],"thesis":"As of 5 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 3 inbound Pith citation observations for arXiv:2508.12121."}