{"as_of":"2026-08-09T06:12:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:82da92725e67614a39f26b509485e2bdf8b6be4cb137fef4abf8b9fbc7254dce","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":14,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":14,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+00:00","state":"measured"},{"denominator":14,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":14,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-08T14:37:23.815685Z","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":"2026-07-08T22:25:39.550471Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2412.05270","last_updated":"2025-02-17T08:27:58Z","snapshot_observed_at":"2026-08-06T09:09:00.082930Z","submitted_at":"2024-12-06T18:55:34Z","title":"APOLLO: SGD-like Memory, AdamW-level Performance","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.05270","snapshot_observed_at":"2026-08-08T14:37:23.815685Z","title":"Z., Wang, Z., and Lee, J","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2502.06742","last_updated":"2025-02-10T18:09:53Z","snapshot_observed_at":"2026-08-09T03:57:33.421199Z","submitted_at":"2025-02-10T18:09:53Z","title":"Gradient Multi-Normalization for Stateless and Scalable LLM Training","version":1},"reference_index":52,"source":"arxiv_source","source_observed_at":"2026-08-08T14:37:23.815685Z"},"links":{"cited_paper":"/paper/2412.05270","citing_paper":"/paper/2502.06742"},"observation_digest":"sha256:a10a80b1ea06de2dd1497c6977225faf4d03247632af179b74a430c681eb4cb5","observation_id":"a6b8083a-4cd7-47bb-ad53-6e19cd7f3df8","resolution":{"observed_at":"2026-08-08T14:37:23.815685Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.05270","last_updated":"2025-02-17T08:27:58Z","snapshot_observed_at":"2026-08-06T09:09:00.082930Z","submitted_at":"2024-12-06T18:55:34Z","title":"APOLLO: SGD-like Memory, AdamW-level Performance","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.05270","snapshot_observed_at":"2026-08-07T13:06:27.700501Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.22922","last_updated":"2025-05-28T22:51:43Z","snapshot_observed_at":"2026-08-07T23:35:02.219408Z","submitted_at":"2025-05-28T22:51:43Z","title":"Scalable Parameter and Memory Efficient Pretraining for LLM: Recent Algorithmic Advances and Benchmarking","version":1},"reference_index":60,"source":"arxiv_source","source_observed_at":"2026-08-07T13:06:27.700501Z"},"links":{"cited_paper":"/paper/2412.05270","citing_paper":"/paper/2505.22922"},"observation_digest":"sha256:01c955fb4893572bf26eb30b0fb8717815d792a3656dff707e042d66991c6427","observation_id":"655bdb2d-85e9-4505-b312-13a44980bbd8","resolution":{"observed_at":"2026-08-07T13:06:27.700501Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.05270","last_updated":"2025-02-17T08:27:58Z","snapshot_observed_at":"2026-08-06T09:09:00.082930Z","submitted_at":"2024-12-06T18:55:34Z","title":"APOLLO: SGD-like Memory, AdamW-level Performance","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.05270","snapshot_observed_at":"2026-08-07T11:57:29.271257Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.01049","last_updated":"2025-06-01T15:30:37Z","snapshot_observed_at":"2026-08-07T22:23:46.839915Z","submitted_at":"2025-06-01T15:30:37Z","title":"Taming LLMs by Scaling Learning Rates with Gradient Grouping","version":1},"reference_index":90,"source":"arxiv_source","source_observed_at":"2026-08-07T11:57:29.271257Z"},"links":{"cited_paper":"/paper/2412.05270","citing_paper":"/paper/2506.01049"},"observation_digest":"sha256:a957f77dd4dd71d389284cc85608fae2278cc0a11247612874883289dd2aa330","observation_id":"4ec620a7-60ca-46d6-8a67-437c76a0961b","resolution":{"observed_at":"2026-08-07T11:57:29.271257Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.05270","last_updated":"2025-02-17T08:27:58Z","snapshot_observed_at":"2026-08-06T09:09:00.082930Z","submitted_at":"2024-12-06T18:55:34Z","title":"APOLLO: SGD-like Memory, AdamW-level Performance","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.05270","snapshot_observed_at":"2026-08-07T11:36:07.981342Z","title":"Apollo: Sgd-like memory, adamw-level performance","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.01933","last_updated":"2025-07-10T17:55:35Z","snapshot_observed_at":"2026-08-09T04:18:07.584928Z","submitted_at":"2025-06-02T17:53:09Z","title":"E3D-Bench: A Benchmark for End-to-End 3D Geometric Foundation Models","version":3},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-07T11:36:07.981342Z"},"links":{"cited_paper":"/paper/2412.05270","citing_paper":"/paper/2506.01933"},"observation_digest":"sha256:1b13726ab25acbb12db947234acdd45b5ceb465d894092dc8551779bf82da74b","observation_id":"cc89ca25-c48d-4b56-a5f7-8ed01bc56d6d","resolution":{"observed_at":"2026-08-07T11:36:07.981342Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.05270","last_updated":"2025-02-17T08:27:58Z","snapshot_observed_at":"2026-08-06T09:09:00.082930Z","submitted_at":"2024-12-06T18:55:34Z","title":"APOLLO: SGD-like Memory, AdamW-level Performance","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.05270","snapshot_observed_at":"2026-08-06T18:35:40.249822Z","title":"Apollo: Sgd-like memory, adamw-level performance","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.08091","last_updated":"2025-07-10T18:04:52Z","snapshot_observed_at":"2026-08-08T23:54:01.601611Z","submitted_at":"2025-07-10T18:04:52Z","title":"Low-rank Momentum Factorization for Memory Efficient Training","version":1},"reference_index":66,"source":"arxiv_source","source_observed_at":"2026-08-06T18:35:40.249822Z"},"links":{"cited_paper":"/paper/2412.05270","citing_paper":"/paper/2507.08091"},"observation_digest":"sha256:39fff4fecf8c5ed9f55aba5bc7f11b3784581445ffddbf3ce1d35722dc7892c5","observation_id":"008ee817-5a97-436a-97d1-a07d2e8019f7","resolution":{"observed_at":"2026-08-06T18:35:40.249822Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.05270","last_updated":"2025-02-17T08:27:58Z","snapshot_observed_at":"2026-08-06T09:09:00.082930Z","submitted_at":"2024-12-06T18:55:34Z","title":"APOLLO: SGD-like Memory, AdamW-level Performance","version":4},"cited_work":{"arxiv_id":"2412.05270","doi":null,"metadata_source":"pith","pith_arxiv_id":"2412.05270","snapshot_observed_at":"2026-07-08T22:25:39.550471Z","title":"DAtts L ⊙ 1√ h softmax′ gAtt s L√ h !# Y K L , DY K L =","venue":"cs.LG","work_id":"fe712d95-0ed1-4d1a-94aa-b36a44a56919","year":2024},"citing_paper":{"arxiv_id":"2509.18993","last_updated":"2026-05-13T13:30:21Z","snapshot_observed_at":"2026-08-02T18:52:22.902766Z","submitted_at":"2025-09-23T13:43:02Z","title":"CR-Net: Scaling Parameter-Efficient Training with Cross-Layer Low-Rank Structure","version":3},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-05-18T14:51:30.312509Z"},"links":{"cited_paper":"/paper/2412.05270","citing_paper":"/paper/2509.18993"},"observation_digest":"sha256:08b177ed4601a4b6403e633de243a0c879a233fa4046a18603e80546b05ee57f","observation_id":"e821d31e-544f-4a05-9313-2182433925af","resolution":{"observed_at":"2026-05-18T14:52:41.115843Z","resolver_source":"arxiv_id","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.05270","last_updated":"2025-02-17T08:27:58Z","snapshot_observed_at":"2026-08-06T09:09:00.082930Z","submitted_at":"2024-12-06T18:55:34Z","title":"APOLLO: SGD-like Memory, AdamW-level Performance","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.05270","snapshot_observed_at":"2026-08-04T12:51:27.373729Z","title":"Pan, Zhangyang Wang, and Jinwon Lee","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2510.01878","last_updated":"2026-06-26T18:31:10Z","snapshot_observed_at":"2026-08-07T11:40:04.374398Z","submitted_at":"2025-10-02T10:35:38Z","title":"Geometrically Principled Randomized Optimization for Efficient LLM Training","version":2},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-04T12:51:27.373729Z"},"links":{"cited_paper":"/paper/2412.05270","citing_paper":"/paper/2510.01878"},"observation_digest":"sha256:6174d74499b7d3a4ac65ac459e352601d0b50745461c9e9327bcab25247bd461","observation_id":"17c8cba1-b950-42e7-87c1-9f2477ed13d0","resolution":{"observed_at":"2026-08-04T12:51:27.373729Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.05270","last_updated":"2025-02-17T08:27:58Z","snapshot_observed_at":"2026-08-06T09:09:00.082930Z","submitted_at":"2024-12-06T18:55:34Z","title":"APOLLO: SGD-like Memory, AdamW-level Performance","version":4},"cited_work":{"arxiv_id":"2412.05270","doi":null,"metadata_source":"pith","pith_arxiv_id":"2412.05270","snapshot_observed_at":"2026-07-08T22:25:39.550471Z","title":"DAtts L ⊙ 1√ h softmax′ gAtt s L√ h !# Y K L , DY K L =","venue":"cs.LG","work_id":"fe712d95-0ed1-4d1a-94aa-b36a44a56919","year":2024},"citing_paper":{"arxiv_id":"2512.12131","last_updated":"2026-05-11T19:05:27Z","snapshot_observed_at":"2026-08-02T10:02:28.902022Z","submitted_at":"2025-12-13T01:50:18Z","title":"BOOST: BOttleneck-Optimized Scalable Training Framework for Low-Rank Large Language Models","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-05-16T23:19:02.358348Z"},"links":{"cited_paper":"/paper/2412.05270","citing_paper":"/paper/2512.12131"},"observation_digest":"sha256:a1695ef2fdca473d5f98c49fe62cab5fee7691b17aa6ab3f45c13b001a943d05","observation_id":"8f25b09b-a1c8-4319-a8dd-7557c3b9e99c","resolution":{"observed_at":"2026-05-16T23:21:21.529366Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.05270","last_updated":"2025-02-17T08:27:58Z","snapshot_observed_at":"2026-08-06T09:09:00.082930Z","submitted_at":"2024-12-06T18:55:34Z","title":"APOLLO: SGD-like Memory, AdamW-level Performance","version":4},"cited_work":{"arxiv_id":"2412.05270","doi":null,"metadata_source":"pith","pith_arxiv_id":"2412.05270","snapshot_observed_at":"2026-07-08T22:25:39.550471Z","title":"DAtts L ⊙ 1√ h softmax′ gAtt s L√ h !# Y K L , DY K L =","venue":"cs.LG","work_id":"fe712d95-0ed1-4d1a-94aa-b36a44a56919","year":2024},"citing_paper":{"arxiv_id":"2604.07663","last_updated":"2026-04-15T21:35:18Z","snapshot_observed_at":"2026-07-06T22:55:50.808914Z","submitted_at":"2026-04-09T00:07:38Z","title":"SAGE: Sign-Adaptive Gradient for Memory-Efficient LLM Optimization","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-10T18:37:16.046496Z"},"links":{"cited_paper":"/paper/2412.05270","citing_paper":"/paper/2604.07663"},"observation_digest":"sha256:d7ab2d8c660c410cb4050a5904bf3efc5b18361c9c8003a7223f472d330debad","observation_id":"0bd458b2-0d94-4159-9439-f18c11a1393f","resolution":{"observed_at":"2026-05-11T00:15:54.526152Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.05270","last_updated":"2025-02-17T08:27:58Z","snapshot_observed_at":"2026-08-06T09:09:00.082930Z","submitted_at":"2024-12-06T18:55:34Z","title":"APOLLO: SGD-like Memory, AdamW-level Performance","version":4},"cited_work":{"arxiv_id":"2412.05270","doi":null,"metadata_source":"pith","pith_arxiv_id":"2412.05270","snapshot_observed_at":"2026-07-08T22:25:39.550471Z","title":"DAtts L ⊙ 1√ h softmax′ gAtt s L√ h !# Y K L , DY K L =","venue":"cs.LG","work_id":"fe712d95-0ed1-4d1a-94aa-b36a44a56919","year":2024},"citing_paper":{"arxiv_id":"2604.11867","last_updated":"2026-04-13T17:40:31Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-13T17:40:31Z","title":"Disposition Distillation at Small Scale: A Three-Arc Negative Result","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-05-10T16:09:21.845152Z"},"links":{"cited_paper":"/paper/2412.05270","citing_paper":"/paper/2604.11867"},"observation_digest":"sha256:8133b95c03d0bb538054019f3acf74e62191dce6fba36828e1b9a655c945a32f","observation_id":"7ca6f309-152d-4b9e-aac2-f30151b65e20","resolution":{"observed_at":"2026-05-11T09:16:00.993265Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.05270","last_updated":"2025-02-17T08:27:58Z","snapshot_observed_at":"2026-08-06T09:09:00.082930Z","submitted_at":"2024-12-06T18:55:34Z","title":"APOLLO: SGD-like Memory, AdamW-level Performance","version":4},"cited_work":{"arxiv_id":"2412.05270","doi":null,"metadata_source":"pith","pith_arxiv_id":"2412.05270","snapshot_observed_at":"2026-07-08T22:25:39.550471Z","title":"DAtts L ⊙ 1√ h softmax′ gAtt s L√ h !# Y K L , DY K L =","venue":"cs.LG","work_id":"fe712d95-0ed1-4d1a-94aa-b36a44a56919","year":2024},"citing_paper":{"arxiv_id":"2605.09176","last_updated":"2026-05-09T21:34:28Z","snapshot_observed_at":"2026-08-09T01:35:49.848565Z","submitted_at":"2026-05-09T21:34:28Z","title":"Navigating LLM Valley: From AdamW to Memory-Efficient and Matrix-Based Optimizers","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-05-12T04:01:32.057022Z"},"links":{"cited_paper":"/paper/2412.05270","citing_paper":"/paper/2605.09176"},"observation_digest":"sha256:1d4a18801dc860c7cf50d953b0874bb3a95a1e87919e3339029196ed8dcf1a41","observation_id":"ddb8d743-3783-47a7-adc1-b84d8c41579d","resolution":{"observed_at":"2026-05-12T06:41:45.424865Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.05270","last_updated":"2025-02-17T08:27:58Z","snapshot_observed_at":"2026-08-06T09:09:00.082930Z","submitted_at":"2024-12-06T18:55:34Z","title":"APOLLO: SGD-like Memory, AdamW-level Performance","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.05270","snapshot_observed_at":"2026-07-14T18:00:57.430970Z","title":"Pan, Zhangyang Wang, and Jinwon Lee","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.13894","last_updated":"2026-07-12T13:45:38Z","snapshot_observed_at":"2026-08-06T19:19:15.546228Z","submitted_at":"2026-06-11T20:38:09Z","title":"Gefen: Optimized Stochastic Optimizer","version":2},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-07-14T18:00:57.430970Z"},"links":{"cited_paper":"/paper/2412.05270","citing_paper":"/paper/2606.13894"},"observation_digest":"sha256:a8d5c2355b345b73955bd07947e16756646460affe79dd05e8a82db55faed1b7","observation_id":"fc6b2427-7f56-471d-a466-d846900c002f","resolution":{"observed_at":"2026-07-14T18:00:57.430970Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.05270","last_updated":"2025-02-17T08:27:58Z","snapshot_observed_at":"2026-08-06T09:09:00.082930Z","submitted_at":"2024-12-06T18:55:34Z","title":"APOLLO: SGD-like Memory, AdamW-level Performance","version":4},"cited_work":{"arxiv_id":"2412.05270","doi":null,"metadata_source":"pith","pith_arxiv_id":"2412.05270","snapshot_observed_at":"2026-07-08T22:25:39.550471Z","title":"DAtts L ⊙ 1√ h softmax′ gAtt s L√ h !# Y K L , DY K L =","venue":"cs.LG","work_id":"fe712d95-0ed1-4d1a-94aa-b36a44a56919","year":2024},"citing_paper":{"arxiv_id":"2607.05872","last_updated":"2026-07-19T20:06:25Z","snapshot_observed_at":"2026-08-02T08:27:39.275378Z","submitted_at":"2026-07-07T06:06:04Z","title":"No Subspace to Track: Non-Identifiability and Optimizer State in Low-Rank Training","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-07-08T22:16:44.668076Z"},"links":{"cited_paper":"/paper/2412.05270","citing_paper":"/paper/2607.05872"},"observation_digest":"sha256:c303d08a1f6862f7f6c07f8016fbb57eb2e2876973bff5323eb61ba63f4dd307","observation_id":"a8699242-10a0-4e8a-8ba6-3ddd1afd4b28","resolution":{"observed_at":"2026-07-08T22:25:39.551975Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.05270","last_updated":"2025-02-17T08:27:58Z","snapshot_observed_at":"2026-08-06T09:09:00.082930Z","submitted_at":"2024-12-06T18:55:34Z","title":"APOLLO: SGD-like Memory, AdamW-level Performance","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.05270","snapshot_observed_at":"2026-08-02T08:27:40.404285Z","title":"APOLLO: SGD-like memory, AdamW-level performance.arXiv:2412.05270,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.05872","last_updated":"2026-07-19T20:06:25Z","snapshot_observed_at":"2026-08-02T08:27:39.275378Z","submitted_at":"2026-07-07T06:06:04Z","title":"No Subspace to Track: Non-Identifiability and Optimizer State in Low-Rank Training","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-02T08:27:40.404285Z"},"links":{"cited_paper":"/paper/2412.05270","citing_paper":"/paper/2607.05872"},"observation_digest":"sha256:0bb49374d215ecb6680c3684f0e0c4df2bfd6c3c7b14dc63c01fb8a47837b3d8","observation_id":"d2e2757c-9340-43b9-8b47-67ebdd72bca5","resolution":{"observed_at":"2026-08-02T08:27:40.404285Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2412.05270/citation-record","integrity":"/paper/2412.05270/integrity","json":"/paper/2412.05270/citation-record.json","paper":"/paper/2412.05270"},"outbound":[],"paper":{"arxiv_id":"2412.05270","last_updated":"2025-02-17T08:27:58Z","latest_version":4,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-06T09:09:00.082930Z","submitted_at":"2024-12-06T18:55:34Z","title":"APOLLO: SGD-like Memory, AdamW-level Performance"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 14 inbound Pith citation observations for arXiv:2412.05270."}