{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:XJBBNVVWSTMB7YGKQTDODPM6RE","short_pith_number":"pith:XJBBNVVW","canonical_record":{"source":{"id":"2012.09816","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-12-17T18:34:45Z","cross_cats_sorted":["cs.NE","math.OC","stat.ML"],"title_canon_sha256":"8f013ec81032165aff59e014868038faac29556c38f381019e701efe4ff61980","abstract_canon_sha256":"4fc92c7c77c321d2e375bd6f083267cc522e96ccbb4e05f3b2bd2596f4b965c7"},"schema_version":"1.0"},"canonical_sha256":"ba4216d6b694d81fe0ca84c6e1bd9e8918183a7f396241be09177fb220e78ffa","source":{"kind":"arxiv","id":"2012.09816","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.09816","created_at":"2026-07-05T05:41:59Z"},{"alias_kind":"arxiv_version","alias_value":"2012.09816v3","created_at":"2026-07-05T05:41:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.09816","created_at":"2026-07-05T05:41:59Z"},{"alias_kind":"pith_short_12","alias_value":"XJBBNVVWSTMB","created_at":"2026-07-05T05:41:59Z"},{"alias_kind":"pith_short_16","alias_value":"XJBBNVVWSTMB7YGK","created_at":"2026-07-05T05:41:59Z"},{"alias_kind":"pith_short_8","alias_value":"XJBBNVVW","created_at":"2026-07-05T05:41:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:XJBBNVVWSTMB7YGKQTDODPM6RE","target":"record","payload":{"canonical_record":{"source":{"id":"2012.09816","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-12-17T18:34:45Z","cross_cats_sorted":["cs.NE","math.OC","stat.ML"],"title_canon_sha256":"8f013ec81032165aff59e014868038faac29556c38f381019e701efe4ff61980","abstract_canon_sha256":"4fc92c7c77c321d2e375bd6f083267cc522e96ccbb4e05f3b2bd2596f4b965c7"},"schema_version":"1.0"},"canonical_sha256":"ba4216d6b694d81fe0ca84c6e1bd9e8918183a7f396241be09177fb220e78ffa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:41:59.930546Z","signature_b64":"xM1UlP0b4PPpNxX7G+Nafg+reZd2grPs2pmR8Z+K2qgyZYv8mZeW4R5i3vzeJBdFPmR66Wm35bSs0451ESosBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba4216d6b694d81fe0ca84c6e1bd9e8918183a7f396241be09177fb220e78ffa","last_reissued_at":"2026-07-05T05:41:59.930124Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:41:59.930124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2012.09816","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":"2026-07-05T05:41:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"te9XrMFMzhxpSrlxUuRC1mr5dY789ovfZr3je6J+LCYnQQxqWMPR8qji9nhjH++w9nn4IvlVOaFKzkUv0ayCBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T20:58:15.897293Z"},"content_sha256":"ffc78d7b1813134c76f700f0589b470ac2c04c62e8a19b87e5522e0cb74b851d","schema_version":"1.0","event_id":"sha256:ffc78d7b1813134c76f700f0589b470ac2c04c62e8a19b87e5522e0cb74b851d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:XJBBNVVWSTMB7YGKQTDODPM6RE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Towards Understanding Ensemble, Knowledge Distillation and Self-Distillation in Deep Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NE","math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Yuanzhi Li, Zeyuan Allen-Zhu","submitted_at":"2020-12-17T18:34:45Z","abstract_excerpt":"We formally study how ensemble of deep learning models can improve test accuracy, and how the superior performance of ensemble can be distilled into a single model using knowledge distillation. We consider the challenging case where the ensemble is simply an average of the outputs of a few independently trained neural networks with the SAME architecture, trained using the SAME algorithm on the SAME data set, and they only differ by the random seeds used in the initialization.\n  We show that ensemble/knowledge distillation in Deep Learning works very differently from traditional learning theory"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.09816","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2012.09816/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":"2026-07-05T05:41:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AaVPiTDhCTSYW8LBc75H4o14m9G+cukq0EiwhordJY8nmEWHOMgbNsgb8XcAI1wBcjEmc5eS64mx9SS8fjV/Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T20:58:15.897590Z"},"content_sha256":"31e672ce991cbad595c6fed6646a49f3582d439316341c93ea99f80e6129c865","schema_version":"1.0","event_id":"sha256:31e672ce991cbad595c6fed6646a49f3582d439316341c93ea99f80e6129c865"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XJBBNVVWSTMB7YGKQTDODPM6RE/bundle.json","state_url":"https://pith.science/pith/XJBBNVVWSTMB7YGKQTDODPM6RE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XJBBNVVWSTMB7YGKQTDODPM6RE/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":"2026-08-14T20:58:15Z","links":{"resolver":"https://pith.science/pith/XJBBNVVWSTMB7YGKQTDODPM6RE","bundle":"https://pith.science/pith/XJBBNVVWSTMB7YGKQTDODPM6RE/bundle.json","state":"https://pith.science/pith/XJBBNVVWSTMB7YGKQTDODPM6RE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XJBBNVVWSTMB7YGKQTDODPM6RE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:XJBBNVVWSTMB7YGKQTDODPM6RE","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":"4fc92c7c77c321d2e375bd6f083267cc522e96ccbb4e05f3b2bd2596f4b965c7","cross_cats_sorted":["cs.NE","math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-12-17T18:34:45Z","title_canon_sha256":"8f013ec81032165aff59e014868038faac29556c38f381019e701efe4ff61980"},"schema_version":"1.0","source":{"id":"2012.09816","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.09816","created_at":"2026-07-05T05:41:59Z"},{"alias_kind":"arxiv_version","alias_value":"2012.09816v3","created_at":"2026-07-05T05:41:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.09816","created_at":"2026-07-05T05:41:59Z"},{"alias_kind":"pith_short_12","alias_value":"XJBBNVVWSTMB","created_at":"2026-07-05T05:41:59Z"},{"alias_kind":"pith_short_16","alias_value":"XJBBNVVWSTMB7YGK","created_at":"2026-07-05T05:41:59Z"},{"alias_kind":"pith_short_8","alias_value":"XJBBNVVW","created_at":"2026-07-05T05:41:59Z"}],"graph_snapshots":[{"event_id":"sha256:31e672ce991cbad595c6fed6646a49f3582d439316341c93ea99f80e6129c865","target":"graph","created_at":"2026-07-05T05:41:59Z","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/2012.09816/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We formally study how ensemble of deep learning models can improve test accuracy, and how the superior performance of ensemble can be distilled into a single model using knowledge distillation. We consider the challenging case where the ensemble is simply an average of the outputs of a few independently trained neural networks with the SAME architecture, trained using the SAME algorithm on the SAME data set, and they only differ by the random seeds used in the initialization.\n  We show that ensemble/knowledge distillation in Deep Learning works very differently from traditional learning theory","authors_text":"Yuanzhi Li, Zeyuan Allen-Zhu","cross_cats":["cs.NE","math.OC","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-12-17T18:34:45Z","title":"Towards Understanding Ensemble, Knowledge Distillation and Self-Distillation in Deep Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.09816","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:ffc78d7b1813134c76f700f0589b470ac2c04c62e8a19b87e5522e0cb74b851d","target":"record","created_at":"2026-07-05T05:41:59Z","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":"4fc92c7c77c321d2e375bd6f083267cc522e96ccbb4e05f3b2bd2596f4b965c7","cross_cats_sorted":["cs.NE","math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-12-17T18:34:45Z","title_canon_sha256":"8f013ec81032165aff59e014868038faac29556c38f381019e701efe4ff61980"},"schema_version":"1.0","source":{"id":"2012.09816","kind":"arxiv","version":3}},"canonical_sha256":"ba4216d6b694d81fe0ca84c6e1bd9e8918183a7f396241be09177fb220e78ffa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba4216d6b694d81fe0ca84c6e1bd9e8918183a7f396241be09177fb220e78ffa","first_computed_at":"2026-07-05T05:41:59.930124Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:41:59.930124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xM1UlP0b4PPpNxX7G+Nafg+reZd2grPs2pmR8Z+K2qgyZYv8mZeW4R5i3vzeJBdFPmR66Wm35bSs0451ESosBA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:41:59.930546Z","signed_message":"canonical_sha256_bytes"},"source_id":"2012.09816","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ffc78d7b1813134c76f700f0589b470ac2c04c62e8a19b87e5522e0cb74b851d","sha256:31e672ce991cbad595c6fed6646a49f3582d439316341c93ea99f80e6129c865"],"state_sha256":"1aba5cd350f15b9e295ae9af8984c15244a436bc9e29574c89b8e770fd8e7f15"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hPQA5n6jndp507kTLjBDGmyq5bBSH8HA3qdbprExYlUh9Q4CPLTBUijhakCxR0sJdkch1b0/F7EZu9uhZrGgAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T20:58:15.901408Z","bundle_sha256":"c56effb473b3c3b7a493b8791a36fd3dc1542ca7d71867b268f902ca2e05568f"}}