{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ULOV2HQUHPWLHNOSFXZCHMEXFJ","short_pith_number":"pith:ULOV2HQU","schema_version":"1.0","canonical_sha256":"a2dd5d1e143becb3b5d22df223b0972a7450b9641f4e6cbfad936198b04c899c","source":{"kind":"arxiv","id":"1506.04838","version":1},"attestation_state":"computed","paper":{"title":"Spectral Sparsification and Regret Minimization Beyond Matrix Multiplicative Updates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Lorenzo Orecchia, Zeyuan Allen-Zhu, Zhenyu Liao","submitted_at":"2015-06-16T05:31:57Z","abstract_excerpt":"In this paper, we provide a novel construction of the linear-sized spectral sparsifiers of Batson, Spielman and Srivastava [BSS14]. While previous constructions required $\\Omega(n^4)$ running time [BSS14, Zou12], our sparsification routine can be implemented in almost-quadratic running time $O(n^{2+\\varepsilon})$.\n  The fundamental conceptual novelty of our work is the leveraging of a strong connection between sparsification and a regret minimization problem over density matrices. This connection was known to provide an interpretation of the randomized sparsifiers of Spielman and Srivastava [S"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1506.04838","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-06-16T05:31:57Z","cross_cats_sorted":["cs.DS","math.OC","stat.ML"],"title_canon_sha256":"85a2983f302b4fa0d6dfc6184896a244d9782734c5c870327812281381b68fb4","abstract_canon_sha256":"8c5a45ca9b65016bd0624e821a0977aa0ffdf4f35407f36f6f79ff73f765cec1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:48:05.784004Z","signature_b64":"INbM4m2A6Sl5U1XqJUkMCx3Y7YfnkVLgsr0z90Q9ids2yN+qhf7vsy+c1XRZjIsBEyLwDAubWFi4qiChn88LDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2dd5d1e143becb3b5d22df223b0972a7450b9641f4e6cbfad936198b04c899c","last_reissued_at":"2026-05-18T01:48:05.783363Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:48:05.783363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral Sparsification and Regret Minimization Beyond Matrix Multiplicative Updates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Lorenzo Orecchia, Zeyuan Allen-Zhu, Zhenyu Liao","submitted_at":"2015-06-16T05:31:57Z","abstract_excerpt":"In this paper, we provide a novel construction of the linear-sized spectral sparsifiers of Batson, Spielman and Srivastava [BSS14]. While previous constructions required $\\Omega(n^4)$ running time [BSS14, Zou12], our sparsification routine can be implemented in almost-quadratic running time $O(n^{2+\\varepsilon})$.\n  The fundamental conceptual novelty of our work is the leveraging of a strong connection between sparsification and a regret minimization problem over density matrices. This connection was known to provide an interpretation of the randomized sparsifiers of Spielman and Srivastava [S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04838","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1506.04838","created_at":"2026-05-18T01:48:05.783456+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.04838v1","created_at":"2026-05-18T01:48:05.783456+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.04838","created_at":"2026-05-18T01:48:05.783456+00:00"},{"alias_kind":"pith_short_12","alias_value":"ULOV2HQUHPWL","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"ULOV2HQUHPWLHNOS","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"ULOV2HQU","created_at":"2026-05-18T12:29:44.643036+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ULOV2HQUHPWLHNOSFXZCHMEXFJ","json":"https://pith.science/pith/ULOV2HQUHPWLHNOSFXZCHMEXFJ.json","graph_json":"https://pith.science/api/pith-number/ULOV2HQUHPWLHNOSFXZCHMEXFJ/graph.json","events_json":"https://pith.science/api/pith-number/ULOV2HQUHPWLHNOSFXZCHMEXFJ/events.json","paper":"https://pith.science/paper/ULOV2HQU"},"agent_actions":{"view_html":"https://pith.science/pith/ULOV2HQUHPWLHNOSFXZCHMEXFJ","download_json":"https://pith.science/pith/ULOV2HQUHPWLHNOSFXZCHMEXFJ.json","view_paper":"https://pith.science/paper/ULOV2HQU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.04838&json=true","fetch_graph":"https://pith.science/api/pith-number/ULOV2HQUHPWLHNOSFXZCHMEXFJ/graph.json","fetch_events":"https://pith.science/api/pith-number/ULOV2HQUHPWLHNOSFXZCHMEXFJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ULOV2HQUHPWLHNOSFXZCHMEXFJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ULOV2HQUHPWLHNOSFXZCHMEXFJ/action/storage_attestation","attest_author":"https://pith.science/pith/ULOV2HQUHPWLHNOSFXZCHMEXFJ/action/author_attestation","sign_citation":"https://pith.science/pith/ULOV2HQUHPWLHNOSFXZCHMEXFJ/action/citation_signature","submit_replication":"https://pith.science/pith/ULOV2HQUHPWLHNOSFXZCHMEXFJ/action/replication_record"}},"created_at":"2026-05-18T01:48:05.783456+00:00","updated_at":"2026-05-18T01:48:05.783456+00:00"}