{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:XFNC4AWYWIB6LJOZFEMT5K6WVE","short_pith_number":"pith:XFNC4AWY","canonical_record":{"source":{"id":"2605.26327","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-25T21:03:03Z","cross_cats_sorted":[],"title_canon_sha256":"a6312293b7eb2bf713f6ced816f6cfaa6e4cb0c92b3e4a9fd71f0aef81152b55","abstract_canon_sha256":"9d68586a0ea2c07197b3c61ed4a29ae62980eb5a346a0cb97382f4bd7b124719"},"schema_version":"1.0"},"canonical_sha256":"b95a2e02d8b203e5a5d929193eabd6a9364cad032ed8eb0cd5f29893a366775e","source":{"kind":"arxiv","id":"2605.26327","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.26327","created_at":"2026-05-27T01:05:12Z"},{"alias_kind":"arxiv_version","alias_value":"2605.26327v1","created_at":"2026-05-27T01:05:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.26327","created_at":"2026-05-27T01:05:12Z"},{"alias_kind":"pith_short_12","alias_value":"XFNC4AWYWIB6","created_at":"2026-05-27T01:05:12Z"},{"alias_kind":"pith_short_16","alias_value":"XFNC4AWYWIB6LJOZ","created_at":"2026-05-27T01:05:12Z"},{"alias_kind":"pith_short_8","alias_value":"XFNC4AWY","created_at":"2026-05-27T01:05:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:XFNC4AWYWIB6LJOZFEMT5K6WVE","target":"record","payload":{"canonical_record":{"source":{"id":"2605.26327","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-25T21:03:03Z","cross_cats_sorted":[],"title_canon_sha256":"a6312293b7eb2bf713f6ced816f6cfaa6e4cb0c92b3e4a9fd71f0aef81152b55","abstract_canon_sha256":"9d68586a0ea2c07197b3c61ed4a29ae62980eb5a346a0cb97382f4bd7b124719"},"schema_version":"1.0"},"canonical_sha256":"b95a2e02d8b203e5a5d929193eabd6a9364cad032ed8eb0cd5f29893a366775e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-27T01:05:12.179200Z","signature_b64":"zueH6z7aGSRwAjDeEtsgiUTthHRB4nIf2WIoM8xMGZ0m/rWcwM8ZlnKjyD8uPLHyrz/Umvv/uXvTbfluKJqnBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b95a2e02d8b203e5a5d929193eabd6a9364cad032ed8eb0cd5f29893a366775e","last_reissued_at":"2026-05-27T01:05:12.178426Z","signature_status":"signed_v1","first_computed_at":"2026-05-27T01:05:12.178426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.26327","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-27T01:05:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wJQnBdDLIVRCkIYFIBLfCPfwyVj09CdShRx0cXs3zv35geUBMwq66v+AufgnL5js5mD0qfLfOVAq457R8QiABg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T18:15:47.891435Z"},"content_sha256":"b56559cfc1fd6ad5ac9801b04a8c36e1aaf21a32337b7e26f06eef029b50d75a","schema_version":"1.0","event_id":"sha256:b56559cfc1fd6ad5ac9801b04a8c36e1aaf21a32337b7e26f06eef029b50d75a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:XFNC4AWYWIB6LJOZFEMT5K6WVE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reparametrizing Shampoo and SOAP for Subspace Basis Updates and BFloat16 Storage","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Alan Milligan, Felix Dangel, Simon Lacoste-Julien, Wu Lin, Zikun Xu","submitted_at":"2026-05-25T21:03:03Z","abstract_excerpt":"Shampoo-based methods, such as KL-Shampoo and SOAP, have demonstrated strong performance in training neural networks and rely on QR decomposition. Because existing QR implementations require single-precision (FP32) arithmetic and remain computationally expensive, these methods become time- and memory-intensive when their preconditioning matrices are large. Moreover, using BFloat16 (BFP16) storage to reduce memory usage can degrade the performance of Shampoo-based methods. We propose a reparametrization of the preconditioner that supports BFP16 storage and forms a complete basis by combining up"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26327","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.26327/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-27T01:05:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O3u8ft2fbCrbT49NTjFuUtL4pF9DX6BWzkN2okL6Qzldyc4nD3rRsHaxA53i9ST5tMTPLBwFQzSEyhXGrW43Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T18:15:47.891821Z"},"content_sha256":"94682132779ffa9c69d45fc9cdd7a9b13ab46a9bb71910db21181493f88a2bb2","schema_version":"1.0","event_id":"sha256:94682132779ffa9c69d45fc9cdd7a9b13ab46a9bb71910db21181493f88a2bb2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XFNC4AWYWIB6LJOZFEMT5K6WVE/bundle.json","state_url":"https://pith.science/pith/XFNC4AWYWIB6LJOZFEMT5K6WVE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XFNC4AWYWIB6LJOZFEMT5K6WVE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T18:15:47Z","links":{"resolver":"https://pith.science/pith/XFNC4AWYWIB6LJOZFEMT5K6WVE","bundle":"https://pith.science/pith/XFNC4AWYWIB6LJOZFEMT5K6WVE/bundle.json","state":"https://pith.science/pith/XFNC4AWYWIB6LJOZFEMT5K6WVE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XFNC4AWYWIB6LJOZFEMT5K6WVE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:XFNC4AWYWIB6LJOZFEMT5K6WVE","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9d68586a0ea2c07197b3c61ed4a29ae62980eb5a346a0cb97382f4bd7b124719","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-25T21:03:03Z","title_canon_sha256":"a6312293b7eb2bf713f6ced816f6cfaa6e4cb0c92b3e4a9fd71f0aef81152b55"},"schema_version":"1.0","source":{"id":"2605.26327","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.26327","created_at":"2026-05-27T01:05:12Z"},{"alias_kind":"arxiv_version","alias_value":"2605.26327v1","created_at":"2026-05-27T01:05:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.26327","created_at":"2026-05-27T01:05:12Z"},{"alias_kind":"pith_short_12","alias_value":"XFNC4AWYWIB6","created_at":"2026-05-27T01:05:12Z"},{"alias_kind":"pith_short_16","alias_value":"XFNC4AWYWIB6LJOZ","created_at":"2026-05-27T01:05:12Z"},{"alias_kind":"pith_short_8","alias_value":"XFNC4AWY","created_at":"2026-05-27T01:05:12Z"}],"graph_snapshots":[{"event_id":"sha256:94682132779ffa9c69d45fc9cdd7a9b13ab46a9bb71910db21181493f88a2bb2","target":"graph","created_at":"2026-05-27T01:05:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.26327/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Shampoo-based methods, such as KL-Shampoo and SOAP, have demonstrated strong performance in training neural networks and rely on QR decomposition. Because existing QR implementations require single-precision (FP32) arithmetic and remain computationally expensive, these methods become time- and memory-intensive when their preconditioning matrices are large. Moreover, using BFloat16 (BFP16) storage to reduce memory usage can degrade the performance of Shampoo-based methods. We propose a reparametrization of the preconditioner that supports BFP16 storage and forms a complete basis by combining up","authors_text":"Alan Milligan, Felix Dangel, Simon Lacoste-Julien, Wu Lin, Zikun Xu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-25T21:03:03Z","title":"Reparametrizing Shampoo and SOAP for Subspace Basis Updates and BFloat16 Storage"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26327","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b56559cfc1fd6ad5ac9801b04a8c36e1aaf21a32337b7e26f06eef029b50d75a","target":"record","created_at":"2026-05-27T01:05:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9d68586a0ea2c07197b3c61ed4a29ae62980eb5a346a0cb97382f4bd7b124719","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-25T21:03:03Z","title_canon_sha256":"a6312293b7eb2bf713f6ced816f6cfaa6e4cb0c92b3e4a9fd71f0aef81152b55"},"schema_version":"1.0","source":{"id":"2605.26327","kind":"arxiv","version":1}},"canonical_sha256":"b95a2e02d8b203e5a5d929193eabd6a9364cad032ed8eb0cd5f29893a366775e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b95a2e02d8b203e5a5d929193eabd6a9364cad032ed8eb0cd5f29893a366775e","first_computed_at":"2026-05-27T01:05:12.178426Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-27T01:05:12.178426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zueH6z7aGSRwAjDeEtsgiUTthHRB4nIf2WIoM8xMGZ0m/rWcwM8ZlnKjyD8uPLHyrz/Umvv/uXvTbfluKJqnBw==","signature_status":"signed_v1","signed_at":"2026-05-27T01:05:12.179200Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.26327","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b56559cfc1fd6ad5ac9801b04a8c36e1aaf21a32337b7e26f06eef029b50d75a","sha256:94682132779ffa9c69d45fc9cdd7a9b13ab46a9bb71910db21181493f88a2bb2"],"state_sha256":"dbfd6f576a4e11a7d58011f93f0a092c22f3152fabd3ca122ecc234a65bc499b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wkbcoiUegHGa10gK3NbE8uTaSwcMmqkS1zMdd6huL53EPL/QM68tcIAvTifmo7fceUhTmHWOQkZdhesiJboXCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T18:15:47.893875Z","bundle_sha256":"39c68e1df43239eededd2af4ea3a22e5ce8d6dba2703caee4115f625b8e5b685"}}