{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ZKPHDTSP6BZXWTRN6YOXACCUJV","short_pith_number":"pith:ZKPHDTSP","schema_version":"1.0","canonical_sha256":"ca9e71ce4ff0737b4e2df61d7008544d7b92d0c6e71f9ad406524f393f2d7fad","source":{"kind":"arxiv","id":"1711.01596","version":1},"attestation_state":"computed","paper":{"title":"Is Input Sparsity Time Possible for Kernel Low-Rank Approximation?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"Cameron Musco, David P. Woodruff","submitted_at":"2017-11-05T14:36:25Z","abstract_excerpt":"Low-rank approximation is a common tool used to accelerate kernel methods: the $n \\times n$ kernel matrix $K$ is approximated via a rank-$k$ matrix $\\tilde K$ which can be stored in much less space and processed more quickly. In this work we study the limits of computationally efficient low-rank kernel approximation. We show that for a broad class of kernels, including the popular Gaussian and polynomial kernels, computing a relative error $k$-rank approximation to $K$ is at least as difficult as multiplying the input data matrix $A \\in \\mathbb{R}^{n \\times d}$ by an arbitrary matrix $C \\in \\m"},"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":"1711.01596","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-11-05T14:36:25Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"f31951d0571800248161fffa26ea2247581c2e016a71163bad1549b2d6b76dcf","abstract_canon_sha256":"8fb00af4aba2319b1401b2becaacb310308b5f5ba5bd90d743e0b0536ca10731"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:17.346424Z","signature_b64":"06k5qGz3RZj4NbPIc2K4AXoFgFhnCurkYN987F3nCvzXfbXIll1NHrlTD3ogahUzAHc7TiFBw19ZAPDyr28DCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca9e71ce4ff0737b4e2df61d7008544d7b92d0c6e71f9ad406524f393f2d7fad","last_reissued_at":"2026-05-18T00:31:17.345618Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:17.345618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Is Input Sparsity Time Possible for Kernel Low-Rank Approximation?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"Cameron Musco, David P. Woodruff","submitted_at":"2017-11-05T14:36:25Z","abstract_excerpt":"Low-rank approximation is a common tool used to accelerate kernel methods: the $n \\times n$ kernel matrix $K$ is approximated via a rank-$k$ matrix $\\tilde K$ which can be stored in much less space and processed more quickly. In this work we study the limits of computationally efficient low-rank kernel approximation. We show that for a broad class of kernels, including the popular Gaussian and polynomial kernels, computing a relative error $k$-rank approximation to $K$ is at least as difficult as multiplying the input data matrix $A \\in \\mathbb{R}^{n \\times d}$ by an arbitrary matrix $C \\in \\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01596","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":"1711.01596","created_at":"2026-05-18T00:31:17.345767+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.01596v1","created_at":"2026-05-18T00:31:17.345767+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.01596","created_at":"2026-05-18T00:31:17.345767+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZKPHDTSP6BZX","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZKPHDTSP6BZXWTRN","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZKPHDTSP","created_at":"2026-05-18T12:31:59.375834+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/ZKPHDTSP6BZXWTRN6YOXACCUJV","json":"https://pith.science/pith/ZKPHDTSP6BZXWTRN6YOXACCUJV.json","graph_json":"https://pith.science/api/pith-number/ZKPHDTSP6BZXWTRN6YOXACCUJV/graph.json","events_json":"https://pith.science/api/pith-number/ZKPHDTSP6BZXWTRN6YOXACCUJV/events.json","paper":"https://pith.science/paper/ZKPHDTSP"},"agent_actions":{"view_html":"https://pith.science/pith/ZKPHDTSP6BZXWTRN6YOXACCUJV","download_json":"https://pith.science/pith/ZKPHDTSP6BZXWTRN6YOXACCUJV.json","view_paper":"https://pith.science/paper/ZKPHDTSP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.01596&json=true","fetch_graph":"https://pith.science/api/pith-number/ZKPHDTSP6BZXWTRN6YOXACCUJV/graph.json","fetch_events":"https://pith.science/api/pith-number/ZKPHDTSP6BZXWTRN6YOXACCUJV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZKPHDTSP6BZXWTRN6YOXACCUJV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZKPHDTSP6BZXWTRN6YOXACCUJV/action/storage_attestation","attest_author":"https://pith.science/pith/ZKPHDTSP6BZXWTRN6YOXACCUJV/action/author_attestation","sign_citation":"https://pith.science/pith/ZKPHDTSP6BZXWTRN6YOXACCUJV/action/citation_signature","submit_replication":"https://pith.science/pith/ZKPHDTSP6BZXWTRN6YOXACCUJV/action/replication_record"}},"created_at":"2026-05-18T00:31:17.345767+00:00","updated_at":"2026-05-18T00:31:17.345767+00:00"}