{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:NLTMMNO4SH5C4W4WOB2VIJHT42","short_pith_number":"pith:NLTMMNO4","canonical_record":{"source":{"id":"2412.08424","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-12-11T14:43:39Z","cross_cats_sorted":[],"title_canon_sha256":"7849bc1f55dbaa08cca6bea70e5c92e4e758a784b573a49c11240b3b0355ebde","abstract_canon_sha256":"4ababc36e6a1d376a7487002f3d8ab38376703ae5617bd46d2160c5cd5a0784f"},"schema_version":"1.0"},"canonical_sha256":"6ae6c635dc91fa2e5b9670755424f3e6a4466382552a8586b706110152a6babf","source":{"kind":"arxiv","id":"2412.08424","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.08424","created_at":"2026-07-05T09:47:49Z"},{"alias_kind":"arxiv_version","alias_value":"2412.08424v1","created_at":"2026-07-05T09:47:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.08424","created_at":"2026-07-05T09:47:49Z"},{"alias_kind":"pith_short_12","alias_value":"NLTMMNO4SH5C","created_at":"2026-07-05T09:47:49Z"},{"alias_kind":"pith_short_16","alias_value":"NLTMMNO4SH5C4W4W","created_at":"2026-07-05T09:47:49Z"},{"alias_kind":"pith_short_8","alias_value":"NLTMMNO4","created_at":"2026-07-05T09:47:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:NLTMMNO4SH5C4W4WOB2VIJHT42","target":"record","payload":{"canonical_record":{"source":{"id":"2412.08424","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-12-11T14:43:39Z","cross_cats_sorted":[],"title_canon_sha256":"7849bc1f55dbaa08cca6bea70e5c92e4e758a784b573a49c11240b3b0355ebde","abstract_canon_sha256":"4ababc36e6a1d376a7487002f3d8ab38376703ae5617bd46d2160c5cd5a0784f"},"schema_version":"1.0"},"canonical_sha256":"6ae6c635dc91fa2e5b9670755424f3e6a4466382552a8586b706110152a6babf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:47:49.950566Z","signature_b64":"qGDbOFjIsw+qz6koRFQ8Y6Mbk8AoKv6YyBSik+bHGh9Nj9Qs/i8wK2WKcC+aQKKTsH3AFbYqaCKZZvkJnLH2CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ae6c635dc91fa2e5b9670755424f3e6a4466382552a8586b706110152a6babf","last_reissued_at":"2026-07-05T09:47:49.950134Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:47:49.950134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.08424","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:47:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xIeZsq3ArWqpxmnDDJYX03cN0Zz9MIX2hmeaBsQAc8YwIr21agervbXw4OUG+MYFWZPmuuuPl9OvvR+DQ9l1Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T19:35:51.998632Z"},"content_sha256":"5162b77b1e10af4edeb13ec70f8592f824ebf2c1c2dd3af34f15d0b279c554f8","schema_version":"1.0","event_id":"sha256:5162b77b1e10af4edeb13ec70f8592f824ebf2c1c2dd3af34f15d0b279c554f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:NLTMMNO4SH5C4W4WOB2VIJHT42","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"From Logistic Regression to the Perceptron Algorithm: Exploring Gradient Descent with Large Step Sizes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Alexander Tyurin","submitted_at":"2024-12-11T14:43:39Z","abstract_excerpt":"We focus on the classification problem with a separable dataset, one of the most important and classical problems from machine learning. The standard approach to this task is logistic regression with gradient descent (LR+GD). Recent studies have observed that LR+GD can find a solution with arbitrarily large step sizes, defying conventional optimization theory. Our work investigates this phenomenon and makes three interconnected key observations about LR+GD with large step sizes. First, we find a remarkably simple explanation of why LR+GD with large step sizes solves the classification problem:"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.08424","kind":"arxiv","version":1},"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/2412.08424/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":"2026-07-05T09:47:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JGAWoFanAOy1+WfIiSw7p/61fZiE0VdMisiIGgJrH3iPhxHWJDbhkpSn8oleLEcVd3HzJiSOtgrCD46dcTi1Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T19:35:51.999920Z"},"content_sha256":"84102f56db8b5aff70ad0a7537d2e0e79e21a861aacd67e2c1139e0efa15ef30","schema_version":"1.0","event_id":"sha256:84102f56db8b5aff70ad0a7537d2e0e79e21a861aacd67e2c1139e0efa15ef30"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NLTMMNO4SH5C4W4WOB2VIJHT42/bundle.json","state_url":"https://pith.science/pith/NLTMMNO4SH5C4W4WOB2VIJHT42/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NLTMMNO4SH5C4W4WOB2VIJHT42/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":"2026-08-13T19:35:52Z","links":{"resolver":"https://pith.science/pith/NLTMMNO4SH5C4W4WOB2VIJHT42","bundle":"https://pith.science/pith/NLTMMNO4SH5C4W4WOB2VIJHT42/bundle.json","state":"https://pith.science/pith/NLTMMNO4SH5C4W4WOB2VIJHT42/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NLTMMNO4SH5C4W4WOB2VIJHT42/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:NLTMMNO4SH5C4W4WOB2VIJHT42","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":"4ababc36e6a1d376a7487002f3d8ab38376703ae5617bd46d2160c5cd5a0784f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-12-11T14:43:39Z","title_canon_sha256":"7849bc1f55dbaa08cca6bea70e5c92e4e758a784b573a49c11240b3b0355ebde"},"schema_version":"1.0","source":{"id":"2412.08424","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.08424","created_at":"2026-07-05T09:47:49Z"},{"alias_kind":"arxiv_version","alias_value":"2412.08424v1","created_at":"2026-07-05T09:47:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.08424","created_at":"2026-07-05T09:47:49Z"},{"alias_kind":"pith_short_12","alias_value":"NLTMMNO4SH5C","created_at":"2026-07-05T09:47:49Z"},{"alias_kind":"pith_short_16","alias_value":"NLTMMNO4SH5C4W4W","created_at":"2026-07-05T09:47:49Z"},{"alias_kind":"pith_short_8","alias_value":"NLTMMNO4","created_at":"2026-07-05T09:47:49Z"}],"graph_snapshots":[{"event_id":"sha256:84102f56db8b5aff70ad0a7537d2e0e79e21a861aacd67e2c1139e0efa15ef30","target":"graph","created_at":"2026-07-05T09:47:49Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2412.08424/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We focus on the classification problem with a separable dataset, one of the most important and classical problems from machine learning. The standard approach to this task is logistic regression with gradient descent (LR+GD). Recent studies have observed that LR+GD can find a solution with arbitrarily large step sizes, defying conventional optimization theory. Our work investigates this phenomenon and makes three interconnected key observations about LR+GD with large step sizes. First, we find a remarkably simple explanation of why LR+GD with large step sizes solves the classification problem:","authors_text":"Alexander Tyurin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-12-11T14:43:39Z","title":"From Logistic Regression to the Perceptron Algorithm: Exploring Gradient Descent with Large Step Sizes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.08424","kind":"arxiv","version":1},"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":"sha256:5162b77b1e10af4edeb13ec70f8592f824ebf2c1c2dd3af34f15d0b279c554f8","target":"record","created_at":"2026-07-05T09:47:49Z","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":"4ababc36e6a1d376a7487002f3d8ab38376703ae5617bd46d2160c5cd5a0784f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-12-11T14:43:39Z","title_canon_sha256":"7849bc1f55dbaa08cca6bea70e5c92e4e758a784b573a49c11240b3b0355ebde"},"schema_version":"1.0","source":{"id":"2412.08424","kind":"arxiv","version":1}},"canonical_sha256":"6ae6c635dc91fa2e5b9670755424f3e6a4466382552a8586b706110152a6babf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ae6c635dc91fa2e5b9670755424f3e6a4466382552a8586b706110152a6babf","first_computed_at":"2026-07-05T09:47:49.950134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:47:49.950134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qGDbOFjIsw+qz6koRFQ8Y6Mbk8AoKv6YyBSik+bHGh9Nj9Qs/i8wK2WKcC+aQKKTsH3AFbYqaCKZZvkJnLH2CA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:47:49.950566Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.08424","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5162b77b1e10af4edeb13ec70f8592f824ebf2c1c2dd3af34f15d0b279c554f8","sha256:84102f56db8b5aff70ad0a7537d2e0e79e21a861aacd67e2c1139e0efa15ef30"],"state_sha256":"4ae39e8738ab6c0a268fda8939090cb68060027f89645774997838f493faf6f9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CMYj02l+v5yvnw6Ad5abvM47Jk7yTF5Lf7iJU2QSvm61iJTgUOxoFEbYDTeK1fr8Q70/zVXzfLYO3z3sSJTxDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T19:35:52.005905Z","bundle_sha256":"f5aba673d540eb13155920e94365fcc720707b8f144cc7584c05a6d3c9a4045c"}}