{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:DSH7ZZ2E2KBHAFPXU3YHC3WE6T","short_pith_number":"pith:DSH7ZZ2E","schema_version":"1.0","canonical_sha256":"1c8ffce744d2827015f7a6f0716ec4f4e9c256d0ed206a3972406fb12e4c0d84","source":{"kind":"arxiv","id":"1707.02757","version":2},"attestation_state":"computed","paper":{"title":"Subdeterminant Maximization via Nonconvex Relaxations and Anti-concentration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.OC","math.PR","stat.ML"],"primary_cat":"cs.DS","authors_text":"Damian Straszak, Javad B. Ebrahimi, Nisheeth K. Vishnoi","submitted_at":"2017-07-10T09:04:51Z","abstract_excerpt":"Several fundamental problems that arise in optimization and computer science can be cast as follows: Given vectors $v_1,\\ldots,v_m \\in \\mathbb{R}^d$ and a constraint family ${\\cal B}\\subseteq 2^{[m]}$, find a set $S \\in \\cal{B}$ that maximizes the squared volume of the simplex spanned by the vectors in $S$. A motivating example is the data-summarization problem in machine learning where one is given a collection of vectors that represent data such as documents or images. The volume of a set of vectors is used as a measure of their diversity, and partition or matroid constraints over $[m]$ are "},"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":"1707.02757","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-07-10T09:04:51Z","cross_cats_sorted":["cs.LG","math.OC","math.PR","stat.ML"],"title_canon_sha256":"0bc54941a4e41d4749aac7db68dfa03823b8a3c1dc90028dbde866d12206abc8","abstract_canon_sha256":"5f7edb30f6ac770145132c09ab3003881eb05718c80868c810fbc3720364c373"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:13.589616Z","signature_b64":"HHR4FmqKU8BJNiqXZZi/gLkoOARUuI/O9HglNlYaeBw+BNYgRGr3vX4PSu80Ku2dq0FBiPd8xe2G0dznUJkhAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c8ffce744d2827015f7a6f0716ec4f4e9c256d0ed206a3972406fb12e4c0d84","last_reissued_at":"2026-05-18T00:10:13.588950Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:13.588950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Subdeterminant Maximization via Nonconvex Relaxations and Anti-concentration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.OC","math.PR","stat.ML"],"primary_cat":"cs.DS","authors_text":"Damian Straszak, Javad B. Ebrahimi, Nisheeth K. Vishnoi","submitted_at":"2017-07-10T09:04:51Z","abstract_excerpt":"Several fundamental problems that arise in optimization and computer science can be cast as follows: Given vectors $v_1,\\ldots,v_m \\in \\mathbb{R}^d$ and a constraint family ${\\cal B}\\subseteq 2^{[m]}$, find a set $S \\in \\cal{B}$ that maximizes the squared volume of the simplex spanned by the vectors in $S$. A motivating example is the data-summarization problem in machine learning where one is given a collection of vectors that represent data such as documents or images. The volume of a set of vectors is used as a measure of their diversity, and partition or matroid constraints over $[m]$ are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02757","kind":"arxiv","version":2},"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":"1707.02757","created_at":"2026-05-18T00:10:13.589040+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.02757v2","created_at":"2026-05-18T00:10:13.589040+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.02757","created_at":"2026-05-18T00:10:13.589040+00:00"},{"alias_kind":"pith_short_12","alias_value":"DSH7ZZ2E2KBH","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"DSH7ZZ2E2KBHAFPX","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"DSH7ZZ2E","created_at":"2026-05-18T12:31:12.930513+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/DSH7ZZ2E2KBHAFPXU3YHC3WE6T","json":"https://pith.science/pith/DSH7ZZ2E2KBHAFPXU3YHC3WE6T.json","graph_json":"https://pith.science/api/pith-number/DSH7ZZ2E2KBHAFPXU3YHC3WE6T/graph.json","events_json":"https://pith.science/api/pith-number/DSH7ZZ2E2KBHAFPXU3YHC3WE6T/events.json","paper":"https://pith.science/paper/DSH7ZZ2E"},"agent_actions":{"view_html":"https://pith.science/pith/DSH7ZZ2E2KBHAFPXU3YHC3WE6T","download_json":"https://pith.science/pith/DSH7ZZ2E2KBHAFPXU3YHC3WE6T.json","view_paper":"https://pith.science/paper/DSH7ZZ2E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.02757&json=true","fetch_graph":"https://pith.science/api/pith-number/DSH7ZZ2E2KBHAFPXU3YHC3WE6T/graph.json","fetch_events":"https://pith.science/api/pith-number/DSH7ZZ2E2KBHAFPXU3YHC3WE6T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DSH7ZZ2E2KBHAFPXU3YHC3WE6T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DSH7ZZ2E2KBHAFPXU3YHC3WE6T/action/storage_attestation","attest_author":"https://pith.science/pith/DSH7ZZ2E2KBHAFPXU3YHC3WE6T/action/author_attestation","sign_citation":"https://pith.science/pith/DSH7ZZ2E2KBHAFPXU3YHC3WE6T/action/citation_signature","submit_replication":"https://pith.science/pith/DSH7ZZ2E2KBHAFPXU3YHC3WE6T/action/replication_record"}},"created_at":"2026-05-18T00:10:13.589040+00:00","updated_at":"2026-05-18T00:10:13.589040+00:00"}