{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:X54CEM5BUBFPSMUZ5UVO62O6TP","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":"b35915a6de358ad76f0e7f4827ee8e7a645eabd1195d6943f87e43df0af40e9b","cross_cats_sorted":["cs.AI","cs.DS","quant-ph","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-09-10T18:15:41Z","title_canon_sha256":"06999add61dec2bcc10d62e4ab325830801fcb0212a41ca8809e65cb3972dd32"},"schema_version":"1.0","source":{"id":"2509.08911","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.08911","created_at":"2026-07-05T12:08:39Z"},{"alias_kind":"arxiv_version","alias_value":"2509.08911v1","created_at":"2026-07-05T12:08:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.08911","created_at":"2026-07-05T12:08:39Z"},{"alias_kind":"pith_short_12","alias_value":"X54CEM5BUBFP","created_at":"2026-07-05T12:08:39Z"},{"alias_kind":"pith_short_16","alias_value":"X54CEM5BUBFPSMUZ","created_at":"2026-07-05T12:08:39Z"},{"alias_kind":"pith_short_8","alias_value":"X54CEM5B","created_at":"2026-07-05T12:08:39Z"}],"graph_snapshots":[{"event_id":"sha256:c312e9bbab0aa42b1144afc6bb27474351ab7a284331daf69d2e147d1530c1bd","target":"graph","created_at":"2026-07-05T12:08:39Z","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/2509.08911/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Matrix Multiplicative Weight Update (MMWU) is a seminal online learning algorithm with numerous applications. Applied to the matrix version of the Learning from Expert Advice (LEA) problem on the $d$-dimensional spectraplex, it is well known that MMWU achieves the minimax-optimal regret bound of $O(\\sqrt{T\\log d})$, where $T$ is the time horizon. In this paper, we present an improved algorithm achieving the instance-optimal regret bound of $O(\\sqrt{T\\cdot S(X||d^{-1}I_d)})$, where $X$ is the comparator in the regret, $I_d$ is the identity matrix, and $S(\\cdot||\\cdot)$ denotes the quantum r","authors_text":"Tongyang Li, Weiyuan Gong, Xinzhao Wang, Zhiyu Zhang","cross_cats":["cs.AI","cs.DS","quant-ph","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-09-10T18:15:41Z","title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.08911","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":"sha256:444e35cc014f20e84b0c9a619b68fbae644e905e051e44edc5c81c2ea632d9e1","target":"record","created_at":"2026-07-05T12:08:39Z","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":"b35915a6de358ad76f0e7f4827ee8e7a645eabd1195d6943f87e43df0af40e9b","cross_cats_sorted":["cs.AI","cs.DS","quant-ph","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-09-10T18:15:41Z","title_canon_sha256":"06999add61dec2bcc10d62e4ab325830801fcb0212a41ca8809e65cb3972dd32"},"schema_version":"1.0","source":{"id":"2509.08911","kind":"arxiv","version":1}},"canonical_sha256":"bf782233a1a04af93299ed2aef69de9bd0d42771e2f2365cfab08dc1bcb6214e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf782233a1a04af93299ed2aef69de9bd0d42771e2f2365cfab08dc1bcb6214e","first_computed_at":"2026-07-05T12:08:39.183712Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:08:39.183712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KMTybwq/hf7VhVgzCpt8dQfZljcAhF7c/OcRIj0tg58cqEao+Dj82HgiXeXmoZqu+hN7JGCYu3YuWQB6s7E6DA==","signature_status":"signed_v1","signed_at":"2026-07-05T12:08:39.184200Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.08911","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:444e35cc014f20e84b0c9a619b68fbae644e905e051e44edc5c81c2ea632d9e1","sha256:c312e9bbab0aa42b1144afc6bb27474351ab7a284331daf69d2e147d1530c1bd"],"state_sha256":"301e6e755409ea3aef8d5f3adbb732ce6a3823bce88b01ee360b0c9566aebb6d"}