{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:XHLQWELIB64D4RUPPZLKZEFPYU","short_pith_number":"pith:XHLQWELI","canonical_record":{"source":{"id":"1806.00952","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-06-04T04:53:00Z","cross_cats_sorted":["cs.AI","math.OC","stat.ML"],"title_canon_sha256":"32c6736b7d1ec3d2b86566364d351d7a38d0661fe12aff5f2e0644f7d0dcf2c1","abstract_canon_sha256":"8eb42fd7e7ad80499903f2453c94663f52b7d8a252a5fba6f9fdc488ef2d39ef"},"schema_version":"1.0"},"canonical_sha256":"b9d70b11680fb83e468f7e56ac90afc51874840406518cc0d825939d56089af5","source":{"kind":"arxiv","id":"1806.00952","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.00952","created_at":"2026-05-17T23:56:05Z"},{"alias_kind":"arxiv_version","alias_value":"1806.00952v4","created_at":"2026-05-17T23:56:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.00952","created_at":"2026-05-17T23:56:05Z"},{"alias_kind":"pith_short_12","alias_value":"XHLQWELIB64D","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XHLQWELIB64D4RUP","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XHLQWELI","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:XHLQWELIB64D4RUPPZLKZEFPYU","target":"record","payload":{"canonical_record":{"source":{"id":"1806.00952","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-06-04T04:53:00Z","cross_cats_sorted":["cs.AI","math.OC","stat.ML"],"title_canon_sha256":"32c6736b7d1ec3d2b86566364d351d7a38d0661fe12aff5f2e0644f7d0dcf2c1","abstract_canon_sha256":"8eb42fd7e7ad80499903f2453c94663f52b7d8a252a5fba6f9fdc488ef2d39ef"},"schema_version":"1.0"},"canonical_sha256":"b9d70b11680fb83e468f7e56ac90afc51874840406518cc0d825939d56089af5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:05.308412Z","signature_b64":"gWdDJ1GbM9rGdpwNOXaSR3hQzzz/Psmr+cEEYImyvEejjhPAv3sbLFbXhTc7OmWqVo/FPzm9csnkX2qYtJqgCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9d70b11680fb83e468f7e56ac90afc51874840406518cc0d825939d56089af5","last_reissued_at":"2026-05-17T23:56:05.307754Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:05.307754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.00952","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:56:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o2GvLlaiaisjaMMNAhZ1FHXo8IYmOBK+1bHs26ew6sWrPntnuAoPPBlr9GKijzRKieAlBKIT+3FE6bEUl52GAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:14:58.198907Z"},"content_sha256":"a900bd18842b23ed4fa137bbab1f9f0d04d8688dc70458880d65ab1c4e23556d","schema_version":"1.0","event_id":"sha256:a900bd18842b23ed4fa137bbab1f9f0d04d8688dc70458880d65ab1c4e23556d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:XHLQWELIB64D4RUPPZLKZEFPYU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic Gradient/Mirror Descent: Minimax Optimality and Implicit Regularization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Babak Hassibi, Navid Azizan","submitted_at":"2018-06-04T04:53:00Z","abstract_excerpt":"Stochastic descent methods (of the gradient and mirror varieties) have become increasingly popular in optimization. In fact, it is now widely recognized that the success of deep learning is not only due to the special deep architecture of the models, but also due to the behavior of the stochastic descent methods used, which play a key role in reaching \"good\" solutions that generalize well to unseen data. In an attempt to shed some light on why this is the case, we revisit some minimax properties of stochastic gradient descent (SGD) for the square loss of linear models---originally developed in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00952","kind":"arxiv","version":4},"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":"2026-05-17T23:56:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3pioCgYSYvFPIFO2TwcsPLP6SHqJc9pgkj1wRYIQPWXz1FiAc9Z21OQJBhc8ml3UyKxLPFa1NjUyAgweoD5rAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:14:58.199635Z"},"content_sha256":"6fd148c41661ce7bf199c5c5fd2f814b23f2ab343bad8c30acb117a55540fc12","schema_version":"1.0","event_id":"sha256:6fd148c41661ce7bf199c5c5fd2f814b23f2ab343bad8c30acb117a55540fc12"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XHLQWELIB64D4RUPPZLKZEFPYU/bundle.json","state_url":"https://pith.science/pith/XHLQWELIB64D4RUPPZLKZEFPYU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XHLQWELIB64D4RUPPZLKZEFPYU/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":"2026-05-25T23:14:58Z","links":{"resolver":"https://pith.science/pith/XHLQWELIB64D4RUPPZLKZEFPYU","bundle":"https://pith.science/pith/XHLQWELIB64D4RUPPZLKZEFPYU/bundle.json","state":"https://pith.science/pith/XHLQWELIB64D4RUPPZLKZEFPYU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XHLQWELIB64D4RUPPZLKZEFPYU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XHLQWELIB64D4RUPPZLKZEFPYU","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":"8eb42fd7e7ad80499903f2453c94663f52b7d8a252a5fba6f9fdc488ef2d39ef","cross_cats_sorted":["cs.AI","math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-06-04T04:53:00Z","title_canon_sha256":"32c6736b7d1ec3d2b86566364d351d7a38d0661fe12aff5f2e0644f7d0dcf2c1"},"schema_version":"1.0","source":{"id":"1806.00952","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.00952","created_at":"2026-05-17T23:56:05Z"},{"alias_kind":"arxiv_version","alias_value":"1806.00952v4","created_at":"2026-05-17T23:56:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.00952","created_at":"2026-05-17T23:56:05Z"},{"alias_kind":"pith_short_12","alias_value":"XHLQWELIB64D","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XHLQWELIB64D4RUP","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XHLQWELI","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:6fd148c41661ce7bf199c5c5fd2f814b23f2ab343bad8c30acb117a55540fc12","target":"graph","created_at":"2026-05-17T23:56:05Z","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":"Stochastic descent methods (of the gradient and mirror varieties) have become increasingly popular in optimization. In fact, it is now widely recognized that the success of deep learning is not only due to the special deep architecture of the models, but also due to the behavior of the stochastic descent methods used, which play a key role in reaching \"good\" solutions that generalize well to unseen data. In an attempt to shed some light on why this is the case, we revisit some minimax properties of stochastic gradient descent (SGD) for the square loss of linear models---originally developed in","authors_text":"Babak Hassibi, Navid Azizan","cross_cats":["cs.AI","math.OC","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-06-04T04:53:00Z","title":"Stochastic Gradient/Mirror Descent: Minimax Optimality and Implicit Regularization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00952","kind":"arxiv","version":4},"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:a900bd18842b23ed4fa137bbab1f9f0d04d8688dc70458880d65ab1c4e23556d","target":"record","created_at":"2026-05-17T23:56:05Z","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":"8eb42fd7e7ad80499903f2453c94663f52b7d8a252a5fba6f9fdc488ef2d39ef","cross_cats_sorted":["cs.AI","math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-06-04T04:53:00Z","title_canon_sha256":"32c6736b7d1ec3d2b86566364d351d7a38d0661fe12aff5f2e0644f7d0dcf2c1"},"schema_version":"1.0","source":{"id":"1806.00952","kind":"arxiv","version":4}},"canonical_sha256":"b9d70b11680fb83e468f7e56ac90afc51874840406518cc0d825939d56089af5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9d70b11680fb83e468f7e56ac90afc51874840406518cc0d825939d56089af5","first_computed_at":"2026-05-17T23:56:05.307754Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:05.307754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gWdDJ1GbM9rGdpwNOXaSR3hQzzz/Psmr+cEEYImyvEejjhPAv3sbLFbXhTc7OmWqVo/FPzm9csnkX2qYtJqgCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:05.308412Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.00952","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a900bd18842b23ed4fa137bbab1f9f0d04d8688dc70458880d65ab1c4e23556d","sha256:6fd148c41661ce7bf199c5c5fd2f814b23f2ab343bad8c30acb117a55540fc12"],"state_sha256":"23859a319b09dd468fa99205031228fc65e5e970ac8b47a1411c2ce6d83ed1de"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yORdMWrlfuZ6nZTcTQgBs8VOmHXLCGi0HoIer0ONPIXD9x3qPakRDA7pDx3pelTgNG/Rlr8YQG4wUHm2L4EVCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T23:14:58.203774Z","bundle_sha256":"056948f31a4ee191d3ad5c8b4f5a43bc30ad9afcf4bfd6cdce1e160917734fa3"}}