{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:SWA6TQEKKRZZJ35HIFZC3NNBXG","short_pith_number":"pith:SWA6TQEK","schema_version":"1.0","canonical_sha256":"9581e9c08a547394efa741722db5a1b99d7ed35e6cedbe2f3fa5880bf58744b4","source":{"kind":"arxiv","id":"1902.03498","version":3},"attestation_state":"computed","paper":{"title":"Space lower bounds for linear prediction in the streaming model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Gil Kur, Ohad Shamir, Yuval Dagan","submitted_at":"2019-02-09T21:44:40Z","abstract_excerpt":"We show that fundamental learning tasks, such as finding an approximate linear separator or linear regression, require memory at least \\emph{quadratic} in the dimension, in a natural streaming setting. This implies that such problems cannot be solved (at least in this setting) by scalable memory-efficient streaming algorithms. Our results build on a memory lower bound for a simple linear-algebraic problem -- finding orthogonal vectors -- and utilize the estimates on the packing of the Grassmannian, the manifold of all linear subspaces of fixed dimension."},"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":"1902.03498","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-02-09T21:44:40Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"ded1a3cbe83b560b492079332225665fe9763efc19d2ea76f94c014811d7ba09","abstract_canon_sha256":"d1063a9de7dcb75e487b10f4af59da321fa2d3c21d64cce952a2910f168cff22"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:32.845107Z","signature_b64":"YqWHwbLf2gcjAjfKLztLY7tDs5hOsFf/HBCs1v1SudSEZi0Aay1fps3uEkHShvbH5V1JEb2302Pq3HKpEaoFCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9581e9c08a547394efa741722db5a1b99d7ed35e6cedbe2f3fa5880bf58744b4","last_reissued_at":"2026-05-17T23:43:32.844688Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:32.844688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Space lower bounds for linear prediction in the streaming model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Gil Kur, Ohad Shamir, Yuval Dagan","submitted_at":"2019-02-09T21:44:40Z","abstract_excerpt":"We show that fundamental learning tasks, such as finding an approximate linear separator or linear regression, require memory at least \\emph{quadratic} in the dimension, in a natural streaming setting. This implies that such problems cannot be solved (at least in this setting) by scalable memory-efficient streaming algorithms. Our results build on a memory lower bound for a simple linear-algebraic problem -- finding orthogonal vectors -- and utilize the estimates on the packing of the Grassmannian, the manifold of all linear subspaces of fixed dimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03498","kind":"arxiv","version":3},"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":"1902.03498","created_at":"2026-05-17T23:43:32.844758+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.03498v3","created_at":"2026-05-17T23:43:32.844758+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03498","created_at":"2026-05-17T23:43:32.844758+00:00"},{"alias_kind":"pith_short_12","alias_value":"SWA6TQEKKRZZ","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_16","alias_value":"SWA6TQEKKRZZJ35H","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_8","alias_value":"SWA6TQEK","created_at":"2026-05-18T12:33:27.125529+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/SWA6TQEKKRZZJ35HIFZC3NNBXG","json":"https://pith.science/pith/SWA6TQEKKRZZJ35HIFZC3NNBXG.json","graph_json":"https://pith.science/api/pith-number/SWA6TQEKKRZZJ35HIFZC3NNBXG/graph.json","events_json":"https://pith.science/api/pith-number/SWA6TQEKKRZZJ35HIFZC3NNBXG/events.json","paper":"https://pith.science/paper/SWA6TQEK"},"agent_actions":{"view_html":"https://pith.science/pith/SWA6TQEKKRZZJ35HIFZC3NNBXG","download_json":"https://pith.science/pith/SWA6TQEKKRZZJ35HIFZC3NNBXG.json","view_paper":"https://pith.science/paper/SWA6TQEK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.03498&json=true","fetch_graph":"https://pith.science/api/pith-number/SWA6TQEKKRZZJ35HIFZC3NNBXG/graph.json","fetch_events":"https://pith.science/api/pith-number/SWA6TQEKKRZZJ35HIFZC3NNBXG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SWA6TQEKKRZZJ35HIFZC3NNBXG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SWA6TQEKKRZZJ35HIFZC3NNBXG/action/storage_attestation","attest_author":"https://pith.science/pith/SWA6TQEKKRZZJ35HIFZC3NNBXG/action/author_attestation","sign_citation":"https://pith.science/pith/SWA6TQEKKRZZJ35HIFZC3NNBXG/action/citation_signature","submit_replication":"https://pith.science/pith/SWA6TQEKKRZZJ35HIFZC3NNBXG/action/replication_record"}},"created_at":"2026-05-17T23:43:32.844758+00:00","updated_at":"2026-05-17T23:43:32.844758+00:00"}