{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:YPLBHM247DRAHNP7A6H7DJ6E3W","short_pith_number":"pith:YPLBHM24","canonical_record":{"source":{"id":"1903.09139","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-03-21T17:51:12Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"b5fad5032639fe39310c383c88ed15f49af9860a1e19b6501c98b4511d83ddcb","abstract_canon_sha256":"6163397d0f657fd2a9af0d0b5238902400a037165bc7795f8737b4815a704ed0"},"schema_version":"1.0"},"canonical_sha256":"c3d613b35cf8e203b5ff078ff1a7c4ddbc043030012e9b01d79336abbb2526e6","source":{"kind":"arxiv","id":"1903.09139","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.09139","created_at":"2026-07-05T00:02:57Z"},{"alias_kind":"arxiv_version","alias_value":"1903.09139v2","created_at":"2026-07-05T00:02:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.09139","created_at":"2026-07-05T00:02:57Z"},{"alias_kind":"pith_short_12","alias_value":"YPLBHM247DRA","created_at":"2026-07-05T00:02:57Z"},{"alias_kind":"pith_short_16","alias_value":"YPLBHM247DRAHNP7","created_at":"2026-07-05T00:02:57Z"},{"alias_kind":"pith_short_8","alias_value":"YPLBHM24","created_at":"2026-07-05T00:02:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:YPLBHM247DRAHNP7A6H7DJ6E3W","target":"record","payload":{"canonical_record":{"source":{"id":"1903.09139","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-03-21T17:51:12Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"b5fad5032639fe39310c383c88ed15f49af9860a1e19b6501c98b4511d83ddcb","abstract_canon_sha256":"6163397d0f657fd2a9af0d0b5238902400a037165bc7795f8737b4815a704ed0"},"schema_version":"1.0"},"canonical_sha256":"c3d613b35cf8e203b5ff078ff1a7c4ddbc043030012e9b01d79336abbb2526e6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:02:57.613130Z","signature_b64":"y7Piy9FWOM+kUBYbS+n3um8TnfZLQcCl32GClvLDrsAQ9zM7ITanFuVQua7D5AEv6/jSuG/IgN+Wnt44Boe9AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3d613b35cf8e203b5ff078ff1a7c4ddbc043030012e9b01d79336abbb2526e6","last_reissued_at":"2026-07-05T00:02:57.612635Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:02:57.612635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.09139","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:02:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vZ+5s1HWRJHYYxYyxw1Y/9io8axmNqF+o+GIQwsnC8oeMHXe/HuK+g2w/xoguQm6fueEWW56Rz7Vms1/QDvyBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T13:08:39.800603Z"},"content_sha256":"3982e466489ec78ad9f9ed619e726f3d1cc22e1ead972766d25e5d364cfa416e","schema_version":"1.0","event_id":"sha256:3982e466489ec78ad9f9ed619e726f3d1cc22e1ead972766d25e5d364cfa416e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:YPLBHM247DRAHNP7A6H7DJ6E3W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Harmless interpolation of noisy data in regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Anant Sahai, Kailas Vodrahalli, Vidya Muthukumar, Vignesh Subramanian","submitted_at":"2019-03-21T17:51:12Z","abstract_excerpt":"A continuing mystery in understanding the empirical success of deep neural networks is their ability to achieve zero training error and generalize well, even when the training data is noisy and there are more parameters than data points. We investigate this overparameterized regime in linear regression, where all solutions that minimize training error interpolate the data, including noise. We characterize the fundamental generalization (mean-squared) error of any interpolating solution in the presence of noise, and show that this error decays to zero with the number of features. Thus, overpara"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.09139","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1903.09139/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:02:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bD6pCJw4tPxIwezt/DeM7c4+s3H7obTij6RWbWTaH+SJytj79YE8LpaKPkYLm4hHq5sz/kHgtBs/hkn01agUCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T13:08:39.801617Z"},"content_sha256":"f5342a14672afa0acb377d6119f066d7fda57f62e37e39c348363490721bac3f","schema_version":"1.0","event_id":"sha256:f5342a14672afa0acb377d6119f066d7fda57f62e37e39c348363490721bac3f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YPLBHM247DRAHNP7A6H7DJ6E3W/bundle.json","state_url":"https://pith.science/pith/YPLBHM247DRAHNP7A6H7DJ6E3W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YPLBHM247DRAHNP7A6H7DJ6E3W/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":"2026-08-09T13:08:39Z","links":{"resolver":"https://pith.science/pith/YPLBHM247DRAHNP7A6H7DJ6E3W","bundle":"https://pith.science/pith/YPLBHM247DRAHNP7A6H7DJ6E3W/bundle.json","state":"https://pith.science/pith/YPLBHM247DRAHNP7A6H7DJ6E3W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YPLBHM247DRAHNP7A6H7DJ6E3W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:YPLBHM247DRAHNP7A6H7DJ6E3W","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":"6163397d0f657fd2a9af0d0b5238902400a037165bc7795f8737b4815a704ed0","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-03-21T17:51:12Z","title_canon_sha256":"b5fad5032639fe39310c383c88ed15f49af9860a1e19b6501c98b4511d83ddcb"},"schema_version":"1.0","source":{"id":"1903.09139","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.09139","created_at":"2026-07-05T00:02:57Z"},{"alias_kind":"arxiv_version","alias_value":"1903.09139v2","created_at":"2026-07-05T00:02:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.09139","created_at":"2026-07-05T00:02:57Z"},{"alias_kind":"pith_short_12","alias_value":"YPLBHM247DRA","created_at":"2026-07-05T00:02:57Z"},{"alias_kind":"pith_short_16","alias_value":"YPLBHM247DRAHNP7","created_at":"2026-07-05T00:02:57Z"},{"alias_kind":"pith_short_8","alias_value":"YPLBHM24","created_at":"2026-07-05T00:02:57Z"}],"graph_snapshots":[{"event_id":"sha256:f5342a14672afa0acb377d6119f066d7fda57f62e37e39c348363490721bac3f","target":"graph","created_at":"2026-07-05T00:02:57Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1903.09139/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A continuing mystery in understanding the empirical success of deep neural networks is their ability to achieve zero training error and generalize well, even when the training data is noisy and there are more parameters than data points. We investigate this overparameterized regime in linear regression, where all solutions that minimize training error interpolate the data, including noise. We characterize the fundamental generalization (mean-squared) error of any interpolating solution in the presence of noise, and show that this error decays to zero with the number of features. Thus, overpara","authors_text":"Anant Sahai, Kailas Vodrahalli, Vidya Muthukumar, Vignesh Subramanian","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-03-21T17:51:12Z","title":"Harmless interpolation of noisy data in regression"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.09139","kind":"arxiv","version":2},"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":"sha256:3982e466489ec78ad9f9ed619e726f3d1cc22e1ead972766d25e5d364cfa416e","target":"record","created_at":"2026-07-05T00:02:57Z","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":"6163397d0f657fd2a9af0d0b5238902400a037165bc7795f8737b4815a704ed0","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-03-21T17:51:12Z","title_canon_sha256":"b5fad5032639fe39310c383c88ed15f49af9860a1e19b6501c98b4511d83ddcb"},"schema_version":"1.0","source":{"id":"1903.09139","kind":"arxiv","version":2}},"canonical_sha256":"c3d613b35cf8e203b5ff078ff1a7c4ddbc043030012e9b01d79336abbb2526e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3d613b35cf8e203b5ff078ff1a7c4ddbc043030012e9b01d79336abbb2526e6","first_computed_at":"2026-07-05T00:02:57.612635Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:02:57.612635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y7Piy9FWOM+kUBYbS+n3um8TnfZLQcCl32GClvLDrsAQ9zM7ITanFuVQua7D5AEv6/jSuG/IgN+Wnt44Boe9AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:02:57.613130Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.09139","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3982e466489ec78ad9f9ed619e726f3d1cc22e1ead972766d25e5d364cfa416e","sha256:f5342a14672afa0acb377d6119f066d7fda57f62e37e39c348363490721bac3f"],"state_sha256":"c111e29b5d3b9b8b312f046836de71fbee20ff7ccf28e255812b0b7d37f8d883"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lyJ/ch7vgfMGDza1IlNw5LyBp5zUaU3DXJdCV4Pc8FT2Kj0dTRSSpDOSr30+VCqOOobVLLr22slEM5UKcz02Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T13:08:39.809035Z","bundle_sha256":"20ab6698f45194139e84ccc22df8913a00e90b794faf305aa3921c94a8661970"}}