{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:KGFI4NE22R2UW6NTGF4INHSC7L","short_pith_number":"pith:KGFI4NE2","canonical_record":{"source":{"id":"1607.06534","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-07-22T01:37:30Z","cross_cats_sorted":[],"title_canon_sha256":"f767264767560332cf671a68be911ae747759d8a3ccf3457f98695c1de584b70","abstract_canon_sha256":"a527e79944cf24913c7b9252c6fc607ec3b03fdfb7bb857b881b64ef2e233b4c"},"schema_version":"1.0"},"canonical_sha256":"518a8e349ad4754b79b33178869e42fafbcf1fb98c9a130bb6604c109a4b9bf5","source":{"kind":"arxiv","id":"1607.06534","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.06534","created_at":"2026-05-18T00:52:49Z"},{"alias_kind":"arxiv_version","alias_value":"1607.06534v3","created_at":"2026-05-18T00:52:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06534","created_at":"2026-05-18T00:52:49Z"},{"alias_kind":"pith_short_12","alias_value":"KGFI4NE22R2U","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KGFI4NE22R2UW6NT","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KGFI4NE2","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:KGFI4NE22R2UW6NTGF4INHSC7L","target":"record","payload":{"canonical_record":{"source":{"id":"1607.06534","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-07-22T01:37:30Z","cross_cats_sorted":[],"title_canon_sha256":"f767264767560332cf671a68be911ae747759d8a3ccf3457f98695c1de584b70","abstract_canon_sha256":"a527e79944cf24913c7b9252c6fc607ec3b03fdfb7bb857b881b64ef2e233b4c"},"schema_version":"1.0"},"canonical_sha256":"518a8e349ad4754b79b33178869e42fafbcf1fb98c9a130bb6604c109a4b9bf5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:49.914573Z","signature_b64":"T10+B9txxGDI0b0a30nH4PrsYKrevarLUAzlrDaTmzEG88AOsfQUngEJGXS8r+mEjAsKqsUjhNhu7m+Xt9KQAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"518a8e349ad4754b79b33178869e42fafbcf1fb98c9a130bb6604c109a4b9bf5","last_reissued_at":"2026-05-18T00:52:49.913877Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:49.913877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.06534","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":"2026-05-18T00:52:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dLqIplK93gv/laftei/Izllb9cgGvpNOMvLHWGVIsal1py1sdebSeL/UqH0zR4HJV9ajp55jTShajOnkbAsECA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:26:42.960940Z"},"content_sha256":"6586515a826eb803b1827b3c8b83dab7cbd31ae107dbdf801b2c554e83c2ff26","schema_version":"1.0","event_id":"sha256:6586515a826eb803b1827b3c8b83dab7cbd31ae107dbdf801b2c554e83c2ff26"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:KGFI4NE22R2UW6NTGF4INHSC7L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Landscape of Empirical Risk for Non-convex Losses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Andrea Montanari, Song Mei, Yu Bai","submitted_at":"2016-07-22T01:37:30Z","abstract_excerpt":"Most high-dimensional estimation and prediction methods propose to minimize a cost function (empirical risk) that is written as a sum of losses associated to each data point. In this paper we focus on the case of non-convex losses, which is practically important but still poorly understood. Classical empirical process theory implies uniform convergence of the empirical risk to the population risk. While uniform convergence implies consistency of the resulting M-estimator, it does not ensure that the latter can be computed efficiently.\n  In order to capture the complexity of computing M-estimat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06534","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":"2026-05-18T00:52:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eKd1r02LD3kXElJbFqYEb9GDOWt+697ZYzj9akRtW1CJhl6VaGgeZfWEgiJ5abgTnBKoHzbXfIMfzf7wfB8ZBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:26:42.961639Z"},"content_sha256":"f565acea5899b7d618c55d240cfb645508470be01603d8fa37b51c909119b9c1","schema_version":"1.0","event_id":"sha256:f565acea5899b7d618c55d240cfb645508470be01603d8fa37b51c909119b9c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KGFI4NE22R2UW6NTGF4INHSC7L/bundle.json","state_url":"https://pith.science/pith/KGFI4NE22R2UW6NTGF4INHSC7L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KGFI4NE22R2UW6NTGF4INHSC7L/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":"2026-05-25T16:26:42Z","links":{"resolver":"https://pith.science/pith/KGFI4NE22R2UW6NTGF4INHSC7L","bundle":"https://pith.science/pith/KGFI4NE22R2UW6NTGF4INHSC7L/bundle.json","state":"https://pith.science/pith/KGFI4NE22R2UW6NTGF4INHSC7L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KGFI4NE22R2UW6NTGF4INHSC7L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KGFI4NE22R2UW6NTGF4INHSC7L","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":"a527e79944cf24913c7b9252c6fc607ec3b03fdfb7bb857b881b64ef2e233b4c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-07-22T01:37:30Z","title_canon_sha256":"f767264767560332cf671a68be911ae747759d8a3ccf3457f98695c1de584b70"},"schema_version":"1.0","source":{"id":"1607.06534","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.06534","created_at":"2026-05-18T00:52:49Z"},{"alias_kind":"arxiv_version","alias_value":"1607.06534v3","created_at":"2026-05-18T00:52:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06534","created_at":"2026-05-18T00:52:49Z"},{"alias_kind":"pith_short_12","alias_value":"KGFI4NE22R2U","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KGFI4NE22R2UW6NT","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KGFI4NE2","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:f565acea5899b7d618c55d240cfb645508470be01603d8fa37b51c909119b9c1","target":"graph","created_at":"2026-05-18T00:52:49Z","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":"Most high-dimensional estimation and prediction methods propose to minimize a cost function (empirical risk) that is written as a sum of losses associated to each data point. In this paper we focus on the case of non-convex losses, which is practically important but still poorly understood. Classical empirical process theory implies uniform convergence of the empirical risk to the population risk. While uniform convergence implies consistency of the resulting M-estimator, it does not ensure that the latter can be computed efficiently.\n  In order to capture the complexity of computing M-estimat","authors_text":"Andrea Montanari, Song Mei, Yu Bai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-07-22T01:37:30Z","title":"The Landscape of Empirical Risk for Non-convex Losses"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06534","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":"sha256:6586515a826eb803b1827b3c8b83dab7cbd31ae107dbdf801b2c554e83c2ff26","target":"record","created_at":"2026-05-18T00:52:49Z","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":"a527e79944cf24913c7b9252c6fc607ec3b03fdfb7bb857b881b64ef2e233b4c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-07-22T01:37:30Z","title_canon_sha256":"f767264767560332cf671a68be911ae747759d8a3ccf3457f98695c1de584b70"},"schema_version":"1.0","source":{"id":"1607.06534","kind":"arxiv","version":3}},"canonical_sha256":"518a8e349ad4754b79b33178869e42fafbcf1fb98c9a130bb6604c109a4b9bf5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"518a8e349ad4754b79b33178869e42fafbcf1fb98c9a130bb6604c109a4b9bf5","first_computed_at":"2026-05-18T00:52:49.913877Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:49.913877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T10+B9txxGDI0b0a30nH4PrsYKrevarLUAzlrDaTmzEG88AOsfQUngEJGXS8r+mEjAsKqsUjhNhu7m+Xt9KQAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:49.914573Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.06534","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6586515a826eb803b1827b3c8b83dab7cbd31ae107dbdf801b2c554e83c2ff26","sha256:f565acea5899b7d618c55d240cfb645508470be01603d8fa37b51c909119b9c1"],"state_sha256":"2ef7d8bac90fbdc960e113f74a39fb3b4ed3f23310ea0ed423ef93bc96557e7d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M0O1oTVYm5Lsb1UgzcSFS1/brdS7LXOkh4LH3yKaxKTNYLm7TT/4+tuhNZ1v8itZck9E6eOsn/0QNFu48z+HCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T16:26:42.965689Z","bundle_sha256":"bcc0512fdee8cbb9b8ed674f990d5638b3596b5979686a0e46f4444c59e8a764"}}