{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:M6QYA5OODYFOEA32OXFWVIC22W","short_pith_number":"pith:M6QYA5OO","canonical_record":{"source":{"id":"1610.01132","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-10-04T19:22:44Z","cross_cats_sorted":["cs.DS","stat.ML"],"title_canon_sha256":"74f6c767354d0f86a7fa3df481cab957937e80a6fcbff01838da05d38f6d7574","abstract_canon_sha256":"d01157fabe6228c8e3fff4b2f21100508375aae31bd7e20423f3f333a7aca1ec"},"schema_version":"1.0"},"canonical_sha256":"67a18075ce1e0ae2037a75cb6aa05ad5a5ec111ada93b9c74ebaf69e5f99e7cd","source":{"kind":"arxiv","id":"1610.01132","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.01132","created_at":"2026-05-18T00:53:58Z"},{"alias_kind":"arxiv_version","alias_value":"1610.01132v3","created_at":"2026-05-18T00:53:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01132","created_at":"2026-05-18T00:53:58Z"},{"alias_kind":"pith_short_12","alias_value":"M6QYA5OODYFO","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"M6QYA5OODYFOEA32","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"M6QYA5OO","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:M6QYA5OODYFOEA32OXFWVIC22W","target":"record","payload":{"canonical_record":{"source":{"id":"1610.01132","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-10-04T19:22:44Z","cross_cats_sorted":["cs.DS","stat.ML"],"title_canon_sha256":"74f6c767354d0f86a7fa3df481cab957937e80a6fcbff01838da05d38f6d7574","abstract_canon_sha256":"d01157fabe6228c8e3fff4b2f21100508375aae31bd7e20423f3f333a7aca1ec"},"schema_version":"1.0"},"canonical_sha256":"67a18075ce1e0ae2037a75cb6aa05ad5a5ec111ada93b9c74ebaf69e5f99e7cd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:58.488305Z","signature_b64":"LptYtYBg9i4TNNpIhZX0Hb931jfMy+TYMWaonymDQPnuUU5mvrwTSjpRFubz9NvIcHJbEu4cougwLq7Pr5rODA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67a18075ce1e0ae2037a75cb6aa05ad5a5ec111ada93b9c74ebaf69e5f99e7cd","last_reissued_at":"2026-05-18T00:53:58.487807Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:58.487807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.01132","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3G6Up2zAxcaNSg3/fHhb8fF8knNRMwc9Mre6FGV5aGrgJVEBsO2noGAqP52KxBOH/6Pnn+pGBpal+UftV9p7Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:51:13.778982Z"},"content_sha256":"3f998d9b1e9c686b9482b4db2f3e7598c7ec8ca70d1fbf62f7d98a41a77fb721","schema_version":"1.0","event_id":"sha256:3f998d9b1e9c686b9482b4db2f3e7598c7ec8ca70d1fbf62f7d98a41a77fb721"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:M6QYA5OODYFOEA32OXFWVIC22W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Non-generative Framework and Convex Relaxations for Unsupervised Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","stat.ML"],"primary_cat":"cs.LG","authors_text":"Elad Hazan, Tengyu Ma","submitted_at":"2016-10-04T19:22:44Z","abstract_excerpt":"We give a novel formal theoretical framework for unsupervised learning with two distinctive characteristics. First, it does not assume any generative model and based on a worst-case performance metric. Second, it is comparative, namely performance is measured with respect to a given hypothesis class. This allows to avoid known computational hardness results and improper algorithms based on convex relaxations. We show how several families of unsupervised learning models, which were previously only analyzed under probabilistic assumptions and are otherwise provably intractable, can be efficientl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01132","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J7SJFX+e8YL/vgnIn09oROT53v8PTeuqImXv50Tp7YXm4KzyySKH7rTyd/n5/5R7g4xQbmBU/loBzdjaNyAXAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:51:13.779336Z"},"content_sha256":"420e3f320096c3123e3b37af772f5fd656082db395a8a6eab5d5e1ae7067ea5b","schema_version":"1.0","event_id":"sha256:420e3f320096c3123e3b37af772f5fd656082db395a8a6eab5d5e1ae7067ea5b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M6QYA5OODYFOEA32OXFWVIC22W/bundle.json","state_url":"https://pith.science/pith/M6QYA5OODYFOEA32OXFWVIC22W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M6QYA5OODYFOEA32OXFWVIC22W/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T16:51:13Z","links":{"resolver":"https://pith.science/pith/M6QYA5OODYFOEA32OXFWVIC22W","bundle":"https://pith.science/pith/M6QYA5OODYFOEA32OXFWVIC22W/bundle.json","state":"https://pith.science/pith/M6QYA5OODYFOEA32OXFWVIC22W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M6QYA5OODYFOEA32OXFWVIC22W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:M6QYA5OODYFOEA32OXFWVIC22W","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":"d01157fabe6228c8e3fff4b2f21100508375aae31bd7e20423f3f333a7aca1ec","cross_cats_sorted":["cs.DS","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-10-04T19:22:44Z","title_canon_sha256":"74f6c767354d0f86a7fa3df481cab957937e80a6fcbff01838da05d38f6d7574"},"schema_version":"1.0","source":{"id":"1610.01132","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.01132","created_at":"2026-05-18T00:53:58Z"},{"alias_kind":"arxiv_version","alias_value":"1610.01132v3","created_at":"2026-05-18T00:53:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01132","created_at":"2026-05-18T00:53:58Z"},{"alias_kind":"pith_short_12","alias_value":"M6QYA5OODYFO","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"M6QYA5OODYFOEA32","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"M6QYA5OO","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:420e3f320096c3123e3b37af772f5fd656082db395a8a6eab5d5e1ae7067ea5b","target":"graph","created_at":"2026-05-18T00:53:58Z","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"},"paper":{"abstract_excerpt":"We give a novel formal theoretical framework for unsupervised learning with two distinctive characteristics. First, it does not assume any generative model and based on a worst-case performance metric. Second, it is comparative, namely performance is measured with respect to a given hypothesis class. This allows to avoid known computational hardness results and improper algorithms based on convex relaxations. We show how several families of unsupervised learning models, which were previously only analyzed under probabilistic assumptions and are otherwise provably intractable, can be efficientl","authors_text":"Elad Hazan, Tengyu Ma","cross_cats":["cs.DS","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-10-04T19:22:44Z","title":"A Non-generative Framework and Convex Relaxations for Unsupervised Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01132","kind":"arxiv","version":3},"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":"sha256:3f998d9b1e9c686b9482b4db2f3e7598c7ec8ca70d1fbf62f7d98a41a77fb721","target":"record","created_at":"2026-05-18T00:53:58Z","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":"d01157fabe6228c8e3fff4b2f21100508375aae31bd7e20423f3f333a7aca1ec","cross_cats_sorted":["cs.DS","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-10-04T19:22:44Z","title_canon_sha256":"74f6c767354d0f86a7fa3df481cab957937e80a6fcbff01838da05d38f6d7574"},"schema_version":"1.0","source":{"id":"1610.01132","kind":"arxiv","version":3}},"canonical_sha256":"67a18075ce1e0ae2037a75cb6aa05ad5a5ec111ada93b9c74ebaf69e5f99e7cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67a18075ce1e0ae2037a75cb6aa05ad5a5ec111ada93b9c74ebaf69e5f99e7cd","first_computed_at":"2026-05-18T00:53:58.487807Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:58.487807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LptYtYBg9i4TNNpIhZX0Hb931jfMy+TYMWaonymDQPnuUU5mvrwTSjpRFubz9NvIcHJbEu4cougwLq7Pr5rODA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:58.488305Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.01132","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f998d9b1e9c686b9482b4db2f3e7598c7ec8ca70d1fbf62f7d98a41a77fb721","sha256:420e3f320096c3123e3b37af772f5fd656082db395a8a6eab5d5e1ae7067ea5b"],"state_sha256":"71bd5ed04e11b9f5ee9b1c9978d358462a3c685318a99ad7afacfbbbb19424c0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zi37FNcqMxMhz4ZiEcubA7+VPK3UtaA73puMM2ojB38W1I/Pd6bV9Uke3uS9M+Fy4xCR8M8/jgcEN/jUjPX5Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T16:51:13.781223Z","bundle_sha256":"ee98ea625cef9f5f0c1cab782b1e0d377b99705b3c980d632d89863c9302b11a"}}