{"as_of":"2026-08-09T08:15:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:f2e59196a38641d5fea0ea9f30934e1b856cba76bcc625d952bb2f63e767b4b6","coverage":[{"denominator":44,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":44,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T01:00:39.989192Z","state":"measured"},{"denominator":45,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":45,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-21T21:13:24.267454Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-21T21:14:22.034596Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"cited_work":{"arxiv_id":"2506.12284","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2506.12284","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Grokalign: Geometric character- isation and acceleration of grokking.arXiv preprint arxiv:2506.12284","venue":null,"work_id":"e192de51-2259-4e3c-88be-a48371bd46df","year":null},"citing_paper":{"arxiv_id":"2510.04930","last_updated":"2026-05-18T15:03:38Z","snapshot_observed_at":"2026-07-06T22:31:49.574184Z","submitted_at":"2025-10-06T15:40:36Z","title":"Egalitarian Gradient Descent: A Simple Approach to Accelerated Grokking","version":3},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-21T21:13:24.267454Z"},"links":{"cited_paper":"/paper/2506.12284","citing_paper":"/paper/2510.04930"},"observation_digest":"sha256:5858f8a2f29ee8f5e55881fa8e4c9e2b73a71636e85a29da22cf0e6f47abcf6a","observation_id":"654b7e58-2fcf-4e26-bdbd-ae857e5dd4b0","resolution":{"observed_at":"2026-05-21T21:14:22.037868Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2506.12284/citation-record","integrity":"/paper/2506.12284/integrity","json":"/paper/2506.12284/citation-record.json","paper":"/paper/2506.12284"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T01:00:36.638337Z","title":"Lecun, L","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:36.638337Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:02d4f59c50855e540b508f96bd5afe757ac044a6d4a7cba2bb4c5a391f3c5a67","observation_id":"61c268fd-ddac-46a3-b142-2fc896a19431","resolution":{"observed_at":"2026-08-07T01:00:36.638337Z","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":"2026-08-07T01:00:44.971841Z","title":"SplineCam: Exact Visualization and Characterization of Deep Network Geometry and Decision Boundaries","venue":null,"work_id":"325272ea-5b3d-4bbc-ac97-0b7925dc2bde","year":2023},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:36.744463Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:f92fd60f1d9694ad78aaa81828121eea6868db74d39ed10501b9efa79c24f001","observation_id":"0f82bf01-18f0-490a-b8d3-a8a39f584d6b","resolution":{"observed_at":"2026-08-07T01:00:45.099731Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:44.702862Z","title":"Aazhang, and Richard Baraniuk","venue":null,"work_id":"941c4d35-4601-4595-b8bd-8def6e0e97b5","year":2019},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:36.852789Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:acccceac6816d7cb466310b88f6de78d95b4179a26da982acc32d6c6df3021bc","observation_id":"6c1bfda6-7729-4ddd-894d-a9969490e372","resolution":{"observed_at":"2026-08-07T01:00:44.806886Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2201.02177","last_updated":"2022-01-06T18:43:37Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2022-01-06T18:43:37Z","title":"Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2201.02177","snapshot_observed_at":"2026-08-07T01:00:36.935473Z","title":"Grokking: Gen- eralization Beyond Overfitting on Small Algorithmic Datasets, January 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:36.935473Z"},"links":{"cited_paper":"/paper/2201.02177","citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:c936e83df87c31f1a17871f85a3eb8fa3c74fbb69056ec50e491fd2bb5e8fbba","observation_id":"f77666c4-5a2b-4562-b1d0-2c159416a354","resolution":{"observed_at":"2026-08-07T01:00:36.935473Z","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":"2026-08-07T01:00:44.477059Z","title":"Loss landscape geometry reveals stagewise development of transformers","venue":null,"work_id":"c7b42395-95dd-4fdb-b346-0d6ab2da6b6e","year":2024},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:37.082546Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:d10d29c4962647ace93e9825485d53ebf3a79edd2777e394ada2da4785d7e7e9","observation_id":"1d4a8afa-e03b-4965-9aa4-da40e96d8206","resolution":{"observed_at":"2026-08-07T01:00:44.552782Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:44.303414Z","title":"Michaud, and Max Tegmark","venue":null,"work_id":"0f54c278-e6f5-4ee1-90a4-a5248839c595","year":2022},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:37.140937Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:9ad723ffe09cb270537106915339350f1e38d2f32e829e8379adc7caff0571a1","observation_id":"313b284b-d6df-4535-8eb1-4739908b4456","resolution":{"observed_at":"2026-08-07T01:00:44.395208Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:44.016849Z","title":"Deep Networks Always Grok and Here is Why","venue":null,"work_id":"6fad1e96-c4ee-4982-9dbd-de915ec189ab","year":2024},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:37.215115Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:1b06a1c94eb7803e9e8acafb30178596a38df1c849c52ec864c5d37abc46464d","observation_id":"91292880-dcab-4148-ad56-913abbc18e9b","resolution":{"observed_at":"2026-08-07T01:00:44.143231Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:43.911899Z","title":"Robustness may be at odds with accuracy","venue":null,"work_id":"1f823757-f8ad-435b-b586-026151c6e1a9","year":2019},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:37.318347Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:086d86056433112c8e9baaebc7e9252aec29493a48c75dfdf26df94bb69526c8","observation_id":"94a9626e-1f0b-4b26-a0a0-62453201e453","resolution":{"observed_at":"2026-08-07T01:00:43.960791Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:43.739386Z","title":"Theoretically Principled Trade-off between Robustness and Accuracy","venue":null,"work_id":"9d11e51a-aa03-4837-99c3-ff6ef84dbc3e","year":2019},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:37.393110Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:41cc02c4294b7e8457e0202e07e077c2b4bc7d5804a2d6b560084f684e7490ea","observation_id":"eb5571d9-5c39-4cc4-bc45-758cd82ef463","resolution":{"observed_at":"2026-08-07T01:00:43.821867Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:43.591210Z","title":"Lee, and Wei Hu","venue":null,"work_id":"10c8a85e-d6e3-4a14-8b1c-a9720b5df21b","year":2024},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:37.501161Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:3543a62b10b65e42b8ccf9d2c38910e60c412f68e81c5a27dbfdf010d3a4b6e0","observation_id":"0044ab35-2852-4e9b-9d6e-a9226f3f5644","resolution":{"observed_at":"2026-08-07T01:00:43.651868Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:43.425304Z","title":"Grokking as a First Order Phase Transition in Two Layer Networks","venue":null,"work_id":"d536674c-8926-49ab-ad2b-b79fd911e23b","year":2024},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:37.538709Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:1fd254022713b3bc945efd0ea8b50000dbdce7eedff75697686190df31039ee1","observation_id":"a1a5923a-dc69-4a0e-935b-526e5a255775","resolution":{"observed_at":"2026-08-07T01:00:43.512411Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:43.252259Z","title":"Gershman, and Cengiz Pehlevan","venue":null,"work_id":"9119570e-8ee2-4591-af68-90b4ce2afe6d","year":2024},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:37.595273Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:51cc65cdb11b8dfcd1ae1df5a2475c9c9f3d808cf9808786775745c470440de5","observation_id":"d64ce499-b4dc-4d4b-8917-6d6d3f007565","resolution":{"observed_at":"2026-08-07T01:00:43.333008Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:43.113918Z","title":"Neural tangent kernel: convergence and generalization in neural networks","venue":null,"work_id":"4ff1722d-2411-4e04-8d7c-df02980ace8c","year":2018},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:37.701378Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:695af4d3e9ece59f3a52204f0554c04e9c487fff8cb27b14f079ae673801ff5c","observation_id":"20b5bfb7-2e49-4ad5-ac00-e436b91f47ea","resolution":{"observed_at":"2026-08-07T01:00:43.179572Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:43.044246Z","title":"Separation of scales and a thermodynamic description of feature learning in some CNNs","venue":null,"work_id":"78f7fa7c-5f14-4972-9863-d22af6742ba2","year":2023},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:37.776108Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:64302ef2b7d5a7249ef56ba22b34bad811e13b80378e745f46edaa179cc38307","observation_id":"439c74a6-6ab0-465d-83e9-efd3c8f2385d","resolution":{"observed_at":"2026-08-07T01:00:43.076588Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:42.960757Z","title":"Progress measures for grokking via mechanistic interpretability","venue":null,"work_id":"1567e46c-9b29-4064-a763-ae213b1c826d","year":2022},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:37.853544Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:c2b794293d94b2eaf7637cf0b72ce3371ae9afca921f10885e04c03a147ab92c","observation_id":"6432fb5f-bac5-4adb-8563-28059039aa23","resolution":{"observed_at":"2026-08-07T01:00:42.993054Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2309.02390","last_updated":"2023-09-05T17:00:24Z","snapshot_observed_at":"2026-08-02T05:47:38.281400Z","submitted_at":"2023-09-05T17:00:24Z","title":"Explaining grokking through circuit efficiency","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2309.02390","snapshot_observed_at":"2026-08-07T01:00:37.893406Z","title":"Explaining grokking through circuit efficiency, September 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:37.893406Z"},"links":{"cited_paper":"/paper/2309.02390","citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:0dadfe204859b0bd1f1d79ea29031d99b11958f2f19d274294b73f16366b3029","observation_id":"d0df5cde-9239-44cc-98c1-c205df3ec890","resolution":{"observed_at":"2026-08-07T01:00:37.893406Z","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":"2026-08-07T01:00:42.890648Z","title":"Contractive auto- encoders: explicit invariance during feature extraction","venue":null,"work_id":"42bce89c-ebb5-4d29-b370-915a5d3866fe","year":2011},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:37.962595Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:6e526ad05aea02da23e05b2651dfd931bc18482be45374c812c9d085c2b7c79a","observation_id":"9b23fbed-7f1a-409f-bdb3-f3527825eb38","resolution":{"observed_at":"2026-08-07T01:00:42.926573Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:42.802489Z","title":"Improving DNN Robustness to Adversarial Attacks Using Jacobian Regularization","venue":null,"work_id":"ea36fb6a-bbea-48e8-8122-8a8d1f98e56c","year":2018},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:38.044726Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:3994a9d8c84b88bc89e33712eb846dd9eb5ed7be855a30354f129059b77af4cb","observation_id":"2cb6df73-5df0-4b57-9654-fe66e1ac03c5","resolution":{"observed_at":"2026-08-07T01:00:42.850646Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1908.02729","last_updated":"2019-08-07T17:04:26Z","snapshot_observed_at":"2026-08-02T17:37:17.740273Z","submitted_at":"2019-08-07T17:04:26Z","title":"Robust Learning with Jacobian Regularization","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1908.02729","snapshot_observed_at":"2026-08-07T01:00:38.112185Z","title":"Roberts, and Sho Yaida","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:38.112185Z"},"links":{"cited_paper":"/paper/1908.02729","citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:442c26617b272d00715d477bf9925006a283af614ea3d48ce1af644eb85cca44","observation_id":"cf405871-487c-41af-9b42-a358361baee8","resolution":{"observed_at":"2026-08-07T01:00:38.112185Z","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":"2026-08-07T01:00:42.725778Z","title":"On the Connection Between Adversarial Robustness and Saliency Map Interpretability","venue":null,"work_id":"0aae92e4-a84c-4d1b-b0e5-d8440b72596a","year":2019},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:38.187918Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:0ef613ecce6eba90f05ae6caea043d2722c3a745f5c33fb81ac641fbe0654e39","observation_id":"961e3384-f150-4ac9-94e6-387f6075448d","resolution":{"observed_at":"2026-08-07T01:00:42.768520Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:42.649355Z","title":"Jacobian adversarially regularized networks for robustness","venue":null,"work_id":"0f4b7380-c29d-42ba-9aac-dd1baed3a4a3","year":2020},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:38.292747Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:31cff5b0d46ac91f259c1f52fa17f395da50968b7044ce3b85fc2575b216c472","observation_id":"6151c10e-ae9e-43a6-878f-7ee9547def91","resolution":{"observed_at":"2026-08-07T01:00:42.677292Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:42.560665Z","title":"Training invariances and the low-rank phenomenon: beyond linear networks","venue":null,"work_id":"333cc3fb-1d2d-4f69-9c52-2a3624134dfa","year":2022},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:38.340812Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:042a63d411379a5cfd2b82a0465ec8f221e28a580678237e07ec04af3a06b1fe","observation_id":"2ec44cca-eb61-4937-a655-eb08ba35c973","resolution":{"observed_at":"2026-08-07T01:00:42.596851Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:42.449643Z","title":"The low-rank simplicity bias in deep networks","venue":null,"work_id":"b89cce7b-d2cb-4720-97bd-c515b2d2b5d8","year":2023},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:38.434994Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:f1f7cfacd1216a2577ef2628747e8130afd7bc7064109725ec274941a18e41fc","observation_id":"5f231a57-4564-47cb-8e38-cd48db196bb7","resolution":{"observed_at":"2026-08-07T01:00:42.503464Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:42.327217Z","title":"Implicit Regularization Towards Rank Minimization in ReLU Networks","venue":null,"work_id":"27d335a7-5045-4229-a069-049ec6dedaaa","year":2023},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:38.513479Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:efa99c755997547a119ad3057604c188d57f964450b55d285fd2c17de7ebbac6","observation_id":"3bae733b-1915-4947-bf4d-faf8b39bd422","resolution":{"observed_at":"2026-08-07T01:00:42.406491Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:42.259649Z","title":"Rank minimization, alignment and weight decay in neural networks","venue":null,"work_id":"5709eb70-0c33-4c99-a7da-2c9e9deff811","year":2024},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:38.620505Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:ea424a18e37f95ad72e1262eec3dc4fe8c3216b964b7ec1915f1ce2002fa4b20","observation_id":"84f0806f-2391-4880-bbbc-deaf3dd753d0","resolution":{"observed_at":"2026-08-07T01:00:42.280354Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:42.154808Z","title":"Siegel, Aparna Gupte, and Tomaso A","venue":null,"work_id":"2b8576b2-7069-4ce8-adff-3bbc8bab902a","year":2025},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:38.658016Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:6a284be0cbe8fab1407cca809e0042578018dbe3e36e3e1ae281e1852db20805","observation_id":"1467b0fd-60ec-4798-addf-b9c8f1d087f9","resolution":{"observed_at":"2026-08-07T01:00:42.207037Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2104.00219","last_updated":"2021-04-01T03:04:40Z","snapshot_observed_at":"2026-07-06T10:55:35.273705Z","submitted_at":"2021-04-01T03:04:40Z","title":"Fast Jacobian-Vector Product for Deep Networks","version":1},"cited_work":{"arxiv_id":"2104.00219","doi":null,"metadata_source":"pith","pith_arxiv_id":"2104.00219","snapshot_observed_at":"2026-08-07T01:00:40.207016Z","title":"Fast Jacobian-Vector Product for Deep Networks","venue":"cs.LG","work_id":"0573c6cd-1f17-46b6-911f-f83185524caa","year":2021},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:38.763686Z"},"links":{"cited_paper":"/paper/2104.00219","citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:df2bc031e744ab6afe77b6d60551c05acfe76048a131b0c134e8f0110e609e20","observation_id":"cf228774-692d-4cc4-95b2-7cd757d9118b","resolution":{"observed_at":"2026-08-07T01:00:40.269490Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:42.044698Z","title":"A Spline Theory of Deep Learning","venue":null,"work_id":"a9d995d6-ba27-46c3-aaff-d8f57411673a","year":2018},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:38.813785Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:7a90e0eb16c33f2863248cc4a4b77df0430ed65e4bc89621ffd85c944576c34c","observation_id":"de0871b4-5b2e-4e0c-b945-13965019ebcd","resolution":{"observed_at":"2026-08-07T01:00:42.092963Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:38.882637Z","title":"Decoupled weight decay regularization","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:38.882637Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:b4a72b2e0a4e4a3c6cae19912d14ba821340a07caed50826de425232daf43adf","observation_id":"39b56b07-4ab8-4bd8-9564-8dcad5b53fc4","resolution":{"observed_at":"2026-08-07T01:00:38.882637Z","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":"2026-08-07T01:00:41.954644Z","title":"Gu and Luca Rigazio","venue":null,"work_id":"69ba7d3c-2107-4c83-aada-dafd57501e57","year":2014},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:38.963534Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:8b04532821c3e6916ad0fae3e10ca6d7f6b62cf6497ecff9e273e4d1326d9c42","observation_id":"9a0be4cd-594e-470f-aacc-9377d18bc3e2","resolution":{"observed_at":"2026-08-07T01:00:41.991765Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:41.840926Z","title":"A closer look at accuracy vs","venue":null,"work_id":"6bcf37b0-246f-4253-b9e5-a39169db7d43","year":2020},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:39.069675Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:0dafbd93d144d3151a88f2824d55e5ce5d5e9cefc6a95e92c1adac2b848fab3f","observation_id":"5196ae04-d5f3-4181-a09e-247832e8436e","resolution":{"observed_at":"2026-08-07T01:00:41.896428Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.20233","last_updated":"2024-06-05T15:12:00Z","snapshot_observed_at":"2026-07-06T18:22:48.671656Z","submitted_at":"2024-05-30T16:35:30Z","title":"Grokfast: Accelerated Grokking by Amplifying Slow Gradients","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.20233","snapshot_observed_at":"2026-08-07T01:00:39.136957Z","title":"Grokfast: Accelerated Grokking by Amplifying Slow Gradients, June 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:39.136957Z"},"links":{"cited_paper":"/paper/2405.20233","citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:b430dcfba946d3ac3a7f58ec7f95938d61e443483076003ce5567997a52ed4a1","observation_id":"243c6626-68d3-4329-a7fe-6c6bf0bd8918","resolution":{"observed_at":"2026-08-07T01:00:39.136957Z","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":"2026-08-07T01:00:41.727818Z","title":"On Lazy Training in Differentiable Programming","venue":null,"work_id":"a8e496b3-fc64-4f93-bdbd-49ee9569a5de","year":2019},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:39.215482Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:b9b4da90db03b7c91d3624cb6cf4fe9e7221ea95dd42cb006a3b8d9590675f81","observation_id":"ba6dcd7e-5881-4dbe-9b6f-00e4455bd547","resolution":{"observed_at":"2026-08-07T01:00:41.789909Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:41.611239Z","title":"Lee, Edward Moroshko, Pedro Savarese, Itay Golan, Daniel Soudry, and Nathan Srebro","venue":null,"work_id":"bdc0a47d-2e5c-49ad-be2e-011a0dac044b","year":2020},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:39.303943Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:9fb76502fad656a0a98dbc09b50fc246ade7f60e424056712fb9085cd18ae370","observation_id":"a966e09c-ffac-4786-85c5-6ba472d3651a","resolution":{"observed_at":"2026-08-07T01:00:41.668125Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:41.487880Z","title":"Lee, Nathan Srebro, and Daniel Soudry","venue":null,"work_id":"1a3c616c-5438-4a3f-914f-836058214119","year":2020},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:39.359011Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:71e51c36ed25234f7ec06e0ca093e79cfeef586945d8d6b76df4c1bcc49f38ba","observation_id":"4a1b7bf3-ea4d-4a9a-b129-75a7e5a14a24","resolution":{"observed_at":"2026-08-07T01:00:41.564125Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:41.317957Z","title":"Let me grok for you: Accelerating grokking via embedding transfer from a weaker model","venue":null,"work_id":"2b028250-f3b4-4d45-bc2a-93d7f0690772","year":2025},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:39.461362Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:e2ff6b8ac2823c575823b4dfa82110631e70a88a0daa7776e2f6b1011d6e5cd7","observation_id":"68d2ef77-6cb4-4ae1-9692-15533032f792","resolution":{"observed_at":"2026-08-07T01:00:41.395452Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:41.183573Z","title":"Learning multiple layers of features from tiny images","venue":null,"work_id":"632f344a-7907-4366-b746-a5c20b2fda0b","year":2009},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:39.529923Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:b532b36a03182964ce64ac67f94228b8fc10fe8529f3f0c43e7f6d3bf4c8e00d","observation_id":"311ca792-b959-497d-9030-6ba42517b0a4","resolution":{"observed_at":"2026-08-07T01:00:41.253784Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:41.053333Z","title":"Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks","venue":null,"work_id":"d9a3780c-ae03-4774-bd1f-3c45cfbb1397","year":2020},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:39.596447Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:9cf2eda51cf42eaf977876357cc48ffcd0b7dc22b5595313aa6f4226f2e2026a","observation_id":"39bc73e4-8267-4b19-8343-2344c2dd1b91","resolution":{"observed_at":"2026-08-07T01:00:41.100233Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2311.06597","last_updated":"2024-02-02T14:03:32Z","snapshot_observed_at":"2026-08-02T19:33:20.317724Z","submitted_at":"2023-11-11T15:45:44Z","title":"Understanding Grokking Through A Robustness Viewpoint","version":2},"cited_work":{"arxiv_id":"2311.06597","doi":null,"metadata_source":"pith","pith_arxiv_id":"2311.06597","snapshot_observed_at":"2026-08-07T01:00:40.081605Z","title":"Understanding Grokking Through A Robustness Viewpoint","venue":"cs.LG","work_id":"c8a330cd-1464-4218-8c68-8920f5fc2390","year":2023},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:39.665801Z"},"links":{"cited_paper":"/paper/2311.06597","citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:c5c3df38c1301856b53dc7df303fb692d32f6d2498c806333553d7c5baab87b7","observation_id":"215bb04b-da33-4bf8-b375-93741a3f6be8","resolution":{"observed_at":"2026-08-07T01:00:40.143032Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:40.922482Z","title":"Attention is All you Need","venue":null,"work_id":"9e7c232b-04f6-4874-89eb-9084c7216f9f","year":2017},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:39.698286Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:7fa96145c7901fe38a075acb7fbd82ea4deb744312bf4ed888f4d29186080f46","observation_id":"7569540f-b536-4e9f-afef-b4a6f9cf14ae","resolution":{"observed_at":"2026-08-07T01:00:40.971487Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:40.771041Z","title":"Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent","venue":null,"work_id":"13a193a0-5c2b-41f5-95ee-e3179b837dd2","year":2019},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:39.763502Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:f416807a339a8185c218b5532b757522317555d096dacfe9ccf3a51b379714ee","observation_id":"d6d8a535-2826-47bd-bece-3c0d22b09606","resolution":{"observed_at":"2026-08-07T01:00:40.834039Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:40.630195Z","title":"Disentangling feature and lazy training in deep neural networks","venue":null,"work_id":"a7e47cab-2541-4d16-b883-7e32730e545d","year":2020},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:39.839604Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:f6ccb44149896e404dee3582b451e2475289827f149b0866a61677af7de957e5","observation_id":"1e3450e1-eca7-4ddd-9b53-d50d8548a0d3","resolution":{"observed_at":"2026-08-07T01:00:40.691885Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:40.494891Z","title":"Under the assumptions, the output of the neural network at xp is Aωxp xp","venue":null,"work_id":"46a0f321-018d-476d-b518-71e808c1ac4e","year":null},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:39.902451Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:3fe41706c38a72bb211ed2172c2dda244aa3bd3dc5de2b0c91c607b3e51cf114","observation_id":"c7787172-5fc7-4859-a95e-db65f454e073","resolution":{"observed_at":"2026-08-07T01:00:40.575702Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-07T01:00:40.367163Z","title":"Under the assumptions, the output of the deep network at xp is Aωxp xp","venue":null,"work_id":"0105cc9f-f24b-47da-bbeb-dca238b41151","year":null},"citing_paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-07T01:00:39.989192Z"},"links":{"citing_paper":"/paper/2506.12284"},"observation_digest":"sha256:bca40936cd8e8e8a92c22eec6855606fef3e1ca56502a09ba5b97e36db7b256b","observation_id":"69e23375-60a2-4d81-a0e5-a0a5ab99de57","resolution":{"observed_at":"2026-08-07T01:00:40.435375Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.12284","last_updated":"2025-07-31T05:15:21Z","latest_version":2,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-08T17:16:27.271130Z","submitted_at":"2025-06-14T00:16:11Z","title":"GrokAlign: Geometric Characterisation and Acceleration of Grokking"},"reference_resolution":{"displayed":44,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":6,"verified_exact":2,"verified_fuzzy":36},"total_outbound_references":44},"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":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 44 of 44 outbound references and 1 inbound Pith citation observation for arXiv:2506.12284."}