{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:2FWF64424FDIOVCBL4PCI63E72","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":"9257a3f5fbfa23c9945edc97acb3606dc27ae1c9ae4b22131bbec54561eb3f72","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-01T15:13:28Z","title_canon_sha256":"6b7cdfc010ed3c72d5f3c71c395cb6677e577d4b8e3193a95f1b99deedbcb128"},"schema_version":"1.0","source":{"id":"2606.02365","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.02365","created_at":"2026-06-02T03:04:57Z"},{"alias_kind":"arxiv_version","alias_value":"2606.02365v1","created_at":"2026-06-02T03:04:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.02365","created_at":"2026-06-02T03:04:57Z"},{"alias_kind":"pith_short_12","alias_value":"2FWF64424FDI","created_at":"2026-06-02T03:04:57Z"},{"alias_kind":"pith_short_16","alias_value":"2FWF64424FDIOVCB","created_at":"2026-06-02T03:04:57Z"},{"alias_kind":"pith_short_8","alias_value":"2FWF6442","created_at":"2026-06-02T03:04:57Z"}],"graph_snapshots":[{"event_id":"sha256:d3329ba99a3a5a578387f61f0a2bcc13a7911ffb2661504e1d11e353c8899c33","target":"graph","created_at":"2026-06-02T03:04:57Z","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/2606.02365/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Shampoo is attracting considerable attention for its superior performance on large-scale optimization benchmarks; yet it faces a significant practical bottleneck: the prohibitive computational overhead of matrix inversion. To mitigate this, practitioners typically rely on stale preconditioner updates, creating a fundamental trade-off between computational efficiency and optimization fidelity. In this work, we provide a theoretical study of staleness through the complementary lenses of convergence and stability. While staleness improves computational efficiency, it inherently degrades performan","authors_text":"Kyunghun Nam, Sumyeong Ahn","cross_cats":["cs.AI"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-01T15:13:28Z","title":"FOAM: Frequency and Operator Error-Based Adaptive Damping Method for Reducing Staleness-Oriented Error for Shampoo"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02365","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:fde744f3477bd21c8d04413c798016bfded8e68accf4d01ee49d859747c6d374","target":"record","created_at":"2026-06-02T03:04:57Z","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":"9257a3f5fbfa23c9945edc97acb3606dc27ae1c9ae4b22131bbec54561eb3f72","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-01T15:13:28Z","title_canon_sha256":"6b7cdfc010ed3c72d5f3c71c395cb6677e577d4b8e3193a95f1b99deedbcb128"},"schema_version":"1.0","source":{"id":"2606.02365","kind":"arxiv","version":1}},"canonical_sha256":"d16c5f739ae1468754415f1e247b64feaf6f71c11cb12cf0cf369c400c6f1aa4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d16c5f739ae1468754415f1e247b64feaf6f71c11cb12cf0cf369c400c6f1aa4","first_computed_at":"2026-06-02T03:04:57.196384Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T03:04:57.196384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AOe6jgEB7FRMRuvwL1Gq8wK4qWu3xfmFqaMinTsjpAXlPCI3v9At2hI7l56fD/n2uxTTkQKwnHyfHpfXuHF/Cw==","signature_status":"signed_v1","signed_at":"2026-06-02T03:04:57.196777Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.02365","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fde744f3477bd21c8d04413c798016bfded8e68accf4d01ee49d859747c6d374","sha256:d3329ba99a3a5a578387f61f0a2bcc13a7911ffb2661504e1d11e353c8899c33"],"state_sha256":"c88e6171831c299315a2fecf5ca42f90725dc84144411af721a3b23a9293c084"}