{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:XMSHAI22X6MHIBX7SYX6PTVIN7","short_pith_number":"pith:XMSHAI22","canonical_record":{"source":{"id":"2201.04545","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2022-01-12T16:41:34Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"5f98860df8f625f76e5f06d5ce7fc3d2e44241130db5d0e408314b75a31276b9","abstract_canon_sha256":"de8686947e8d74b693d6a150e57055c9e8e16d85ce0b571582387bd30408a2a0"},"schema_version":"1.0"},"canonical_sha256":"bb2470235abf987406ff962fe7cea86fcecd5e5ae856985d64e1c96cbde71d32","source":{"kind":"arxiv","id":"2201.04545","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.04545","created_at":"2026-07-05T05:06:54Z"},{"alias_kind":"arxiv_version","alias_value":"2201.04545v3","created_at":"2026-07-05T05:06:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.04545","created_at":"2026-07-05T05:06:54Z"},{"alias_kind":"pith_short_12","alias_value":"XMSHAI22X6MH","created_at":"2026-07-05T05:06:54Z"},{"alias_kind":"pith_short_16","alias_value":"XMSHAI22X6MHIBX7","created_at":"2026-07-05T05:06:54Z"},{"alias_kind":"pith_short_8","alias_value":"XMSHAI22","created_at":"2026-07-05T05:06:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:XMSHAI22X6MHIBX7SYX6PTVIN7","target":"record","payload":{"canonical_record":{"source":{"id":"2201.04545","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2022-01-12T16:41:34Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"5f98860df8f625f76e5f06d5ce7fc3d2e44241130db5d0e408314b75a31276b9","abstract_canon_sha256":"de8686947e8d74b693d6a150e57055c9e8e16d85ce0b571582387bd30408a2a0"},"schema_version":"1.0"},"canonical_sha256":"bb2470235abf987406ff962fe7cea86fcecd5e5ae856985d64e1c96cbde71d32","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:06:54.247187Z","signature_b64":"hNXSpoOkEQmBsUxEDBEp1oFsSo7YOlTkzcdrBMlPEJo710cWzTgJu9mYUxKBcsN3QC2RVn+GnFsRiA7cr8CfAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb2470235abf987406ff962fe7cea86fcecd5e5ae856985d64e1c96cbde71d32","last_reissued_at":"2026-07-05T05:06:54.246721Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:06:54.246721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2201.04545","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":"2026-07-05T05:06:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mG1cX/r8g23pAx5bVYSVmOXQM+eYxVaxCiRHTA2tfmhW3YnnfH0xsPzRMmaMF4TUJzMo4hiDnCXMzUiZ8oYxBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T14:50:10.244960Z"},"content_sha256":"e599ec16455de152075bb6ecaab3eb1963b959f9cf106af9d4bd9873655864a8","schema_version":"1.0","event_id":"sha256:e599ec16455de152075bb6ecaab3eb1963b959f9cf106af9d4bd9873655864a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:XMSHAI22X6MHIBX7SYX6PTVIN7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On generalization bounds for deep networks based on loss surface implicit regularization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Johannes Schmidt-Hieber, Masaaki Imaizumi","submitted_at":"2022-01-12T16:41:34Z","abstract_excerpt":"The classical statistical learning theory implies that fitting too many parameters leads to overfitting and poor performance. That modern deep neural networks generalize well despite a large number of parameters contradicts this finding and constitutes a major unsolved problem towards explaining the success of deep learning. While previous work focuses on the implicit regularization induced by stochastic gradient descent (SGD), we study here how the local geometry of the energy landscape around local minima affects the statistical properties of SGD with Gaussian gradient noise. We argue that u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.04545","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/2201.04545/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":"2026-07-05T05:06:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hk1LPhHh7t7H3MPiwjJ658vHH6AQLFQZUS/O/11SAhB8/QGZdHHMkyrVx9mKW2wzVPTSsiYn/CmcaAoVs5SOAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T14:50:10.245341Z"},"content_sha256":"3ebd2f2faaef85a40de680340cf5686276c6619744fb369a0e91eed52819e85c","schema_version":"1.0","event_id":"sha256:3ebd2f2faaef85a40de680340cf5686276c6619744fb369a0e91eed52819e85c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XMSHAI22X6MHIBX7SYX6PTVIN7/bundle.json","state_url":"https://pith.science/pith/XMSHAI22X6MHIBX7SYX6PTVIN7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XMSHAI22X6MHIBX7SYX6PTVIN7/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":"2026-07-06T14:50:10Z","links":{"resolver":"https://pith.science/pith/XMSHAI22X6MHIBX7SYX6PTVIN7","bundle":"https://pith.science/pith/XMSHAI22X6MHIBX7SYX6PTVIN7/bundle.json","state":"https://pith.science/pith/XMSHAI22X6MHIBX7SYX6PTVIN7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XMSHAI22X6MHIBX7SYX6PTVIN7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:XMSHAI22X6MHIBX7SYX6PTVIN7","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":"de8686947e8d74b693d6a150e57055c9e8e16d85ce0b571582387bd30408a2a0","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2022-01-12T16:41:34Z","title_canon_sha256":"5f98860df8f625f76e5f06d5ce7fc3d2e44241130db5d0e408314b75a31276b9"},"schema_version":"1.0","source":{"id":"2201.04545","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.04545","created_at":"2026-07-05T05:06:54Z"},{"alias_kind":"arxiv_version","alias_value":"2201.04545v3","created_at":"2026-07-05T05:06:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.04545","created_at":"2026-07-05T05:06:54Z"},{"alias_kind":"pith_short_12","alias_value":"XMSHAI22X6MH","created_at":"2026-07-05T05:06:54Z"},{"alias_kind":"pith_short_16","alias_value":"XMSHAI22X6MHIBX7","created_at":"2026-07-05T05:06:54Z"},{"alias_kind":"pith_short_8","alias_value":"XMSHAI22","created_at":"2026-07-05T05:06:54Z"}],"graph_snapshots":[{"event_id":"sha256:3ebd2f2faaef85a40de680340cf5686276c6619744fb369a0e91eed52819e85c","target":"graph","created_at":"2026-07-05T05:06:54Z","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/2201.04545/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The classical statistical learning theory implies that fitting too many parameters leads to overfitting and poor performance. That modern deep neural networks generalize well despite a large number of parameters contradicts this finding and constitutes a major unsolved problem towards explaining the success of deep learning. While previous work focuses on the implicit regularization induced by stochastic gradient descent (SGD), we study here how the local geometry of the energy landscape around local minima affects the statistical properties of SGD with Gaussian gradient noise. We argue that u","authors_text":"Johannes Schmidt-Hieber, Masaaki Imaizumi","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2022-01-12T16:41:34Z","title":"On generalization bounds for deep networks based on loss surface implicit regularization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.04545","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:e599ec16455de152075bb6ecaab3eb1963b959f9cf106af9d4bd9873655864a8","target":"record","created_at":"2026-07-05T05:06:54Z","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":"de8686947e8d74b693d6a150e57055c9e8e16d85ce0b571582387bd30408a2a0","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2022-01-12T16:41:34Z","title_canon_sha256":"5f98860df8f625f76e5f06d5ce7fc3d2e44241130db5d0e408314b75a31276b9"},"schema_version":"1.0","source":{"id":"2201.04545","kind":"arxiv","version":3}},"canonical_sha256":"bb2470235abf987406ff962fe7cea86fcecd5e5ae856985d64e1c96cbde71d32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb2470235abf987406ff962fe7cea86fcecd5e5ae856985d64e1c96cbde71d32","first_computed_at":"2026-07-05T05:06:54.246721Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:06:54.246721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hNXSpoOkEQmBsUxEDBEp1oFsSo7YOlTkzcdrBMlPEJo710cWzTgJu9mYUxKBcsN3QC2RVn+GnFsRiA7cr8CfAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:06:54.247187Z","signed_message":"canonical_sha256_bytes"},"source_id":"2201.04545","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e599ec16455de152075bb6ecaab3eb1963b959f9cf106af9d4bd9873655864a8","sha256:3ebd2f2faaef85a40de680340cf5686276c6619744fb369a0e91eed52819e85c"],"state_sha256":"388a9daf96aba3fa9efc02de6fc40cf8749e0047270e3275759bb15dea0f04ec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hHS2jVebU2eCh9+JVrhZerHyvVpVBESdA7wAgA9mEam8DkGnAvXi5VIi2ZJFZVcBShQRuSYPXxcy9eyqZFjdDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T14:50:10.247427Z","bundle_sha256":"39d115d1c84ccf7f094a02790ea1bc29c97c98ec7b4bca9e2952492ef48d3510"}}