{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:AC4FRKG4N7KGK5AYZP6GG4RD2U","short_pith_number":"pith:AC4FRKG4","canonical_record":{"source":{"id":"2512.11587","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-12-12T14:16:35Z","cross_cats_sorted":["cs.NA","math.NA","math.OC"],"title_canon_sha256":"c0ff70bc7d128aab7f49e611ec5c2ef95ff926ad5952f9ebb0fa9e5c21eaafe3","abstract_canon_sha256":"45588a8731113b1431860e66437af001b435100852be188c8315b31069870a2b"},"schema_version":"1.0"},"canonical_sha256":"00b858a8dc6fd4657418cbfc637223d52e30f6cc2a1a8efa83744bfd577b1919","source":{"kind":"arxiv","id":"2512.11587","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.11587","created_at":"2026-05-22T01:03:52Z"},{"alias_kind":"arxiv_version","alias_value":"2512.11587v2","created_at":"2026-05-22T01:03:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.11587","created_at":"2026-05-22T01:03:52Z"},{"alias_kind":"pith_short_12","alias_value":"AC4FRKG4N7KG","created_at":"2026-05-22T01:03:52Z"},{"alias_kind":"pith_short_16","alias_value":"AC4FRKG4N7KGK5AY","created_at":"2026-05-22T01:03:52Z"},{"alias_kind":"pith_short_8","alias_value":"AC4FRKG4","created_at":"2026-05-22T01:03:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:AC4FRKG4N7KGK5AYZP6GG4RD2U","target":"record","payload":{"canonical_record":{"source":{"id":"2512.11587","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-12-12T14:16:35Z","cross_cats_sorted":["cs.NA","math.NA","math.OC"],"title_canon_sha256":"c0ff70bc7d128aab7f49e611ec5c2ef95ff926ad5952f9ebb0fa9e5c21eaafe3","abstract_canon_sha256":"45588a8731113b1431860e66437af001b435100852be188c8315b31069870a2b"},"schema_version":"1.0"},"canonical_sha256":"00b858a8dc6fd4657418cbfc637223d52e30f6cc2a1a8efa83744bfd577b1919","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T01:03:52.125640Z","signature_b64":"YlBU8wv00xCmpxyvM/dAB3BYTv0mqKfdL0NPcu8To9MZThTaQctvl5cl7GIGZMJ3IGpT7DOeMUb4+EZZOicQCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00b858a8dc6fd4657418cbfc637223d52e30f6cc2a1a8efa83744bfd577b1919","last_reissued_at":"2026-05-22T01:03:52.124528Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T01:03:52.124528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2512.11587","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":"2026-05-22T01:03:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UATnbwlK0MtLzqBtKb62DcAGQjAjpvMwrbnlg0rCxXbEuYXky3dtVbeKePkDL2etSgqpA9JZ8pOhpmwM8qwoDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T05:02:27.223543Z"},"content_sha256":"c85cf1259ae9656da5f29c6c68d7712e3bf64efcbf602174086a9df93e63bb85","schema_version":"1.0","event_id":"sha256:c85cf1259ae9656da5f29c6c68d7712e3bf64efcbf602174086a9df93e63bb85"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:AC4FRKG4N7KGK5AYZP6GG4RD2U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gradient Descent as a Perceptron Algorithm: Understanding Dynamics and Implicit Acceleration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","math.OC"],"primary_cat":"cs.LG","authors_text":"Alexander Tyurin","submitted_at":"2025-12-12T14:16:35Z","abstract_excerpt":"Even for the gradient descent (GD) method applied to neural network training, understanding its optimization dynamics, including convergence rate, iterate trajectories, function value oscillations, and especially its implicit acceleration, remains a challenging problem. We analyze nonlinear models with the logistic loss and show that the steps of GD reduce to those of generalized perceptron algorithms (Rosenblatt, 1958), providing a new perspective on the dynamics. This reduction yields significantly simpler algorithmic steps, which we analyze using classical linear algebra tools. Using these "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.11587","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/2512.11587/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":"2026-05-22T01:03:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ewqg1g0bC6og9KqU+XeQVZe0Jl5iGMfNfToOccO7Pkw8otLRu6r6CEvihGO2Ja1a/9sLcWBIKQ8AaD/VdI8xDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T05:02:27.223985Z"},"content_sha256":"9b48a3d5b86034ac1b5d02eb76de052bf37d22ff492a9b778e34a627ab32e506","schema_version":"1.0","event_id":"sha256:9b48a3d5b86034ac1b5d02eb76de052bf37d22ff492a9b778e34a627ab32e506"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AC4FRKG4N7KGK5AYZP6GG4RD2U/bundle.json","state_url":"https://pith.science/pith/AC4FRKG4N7KGK5AYZP6GG4RD2U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AC4FRKG4N7KGK5AYZP6GG4RD2U/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":"2026-05-26T05:02:27Z","links":{"resolver":"https://pith.science/pith/AC4FRKG4N7KGK5AYZP6GG4RD2U","bundle":"https://pith.science/pith/AC4FRKG4N7KGK5AYZP6GG4RD2U/bundle.json","state":"https://pith.science/pith/AC4FRKG4N7KGK5AYZP6GG4RD2U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AC4FRKG4N7KGK5AYZP6GG4RD2U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:AC4FRKG4N7KGK5AYZP6GG4RD2U","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":"45588a8731113b1431860e66437af001b435100852be188c8315b31069870a2b","cross_cats_sorted":["cs.NA","math.NA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-12-12T14:16:35Z","title_canon_sha256":"c0ff70bc7d128aab7f49e611ec5c2ef95ff926ad5952f9ebb0fa9e5c21eaafe3"},"schema_version":"1.0","source":{"id":"2512.11587","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.11587","created_at":"2026-05-22T01:03:52Z"},{"alias_kind":"arxiv_version","alias_value":"2512.11587v2","created_at":"2026-05-22T01:03:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.11587","created_at":"2026-05-22T01:03:52Z"},{"alias_kind":"pith_short_12","alias_value":"AC4FRKG4N7KG","created_at":"2026-05-22T01:03:52Z"},{"alias_kind":"pith_short_16","alias_value":"AC4FRKG4N7KGK5AY","created_at":"2026-05-22T01:03:52Z"},{"alias_kind":"pith_short_8","alias_value":"AC4FRKG4","created_at":"2026-05-22T01:03:52Z"}],"graph_snapshots":[{"event_id":"sha256:9b48a3d5b86034ac1b5d02eb76de052bf37d22ff492a9b778e34a627ab32e506","target":"graph","created_at":"2026-05-22T01:03:52Z","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/2512.11587/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Even for the gradient descent (GD) method applied to neural network training, understanding its optimization dynamics, including convergence rate, iterate trajectories, function value oscillations, and especially its implicit acceleration, remains a challenging problem. We analyze nonlinear models with the logistic loss and show that the steps of GD reduce to those of generalized perceptron algorithms (Rosenblatt, 1958), providing a new perspective on the dynamics. This reduction yields significantly simpler algorithmic steps, which we analyze using classical linear algebra tools. Using these ","authors_text":"Alexander Tyurin","cross_cats":["cs.NA","math.NA","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-12-12T14:16:35Z","title":"Gradient Descent as a Perceptron Algorithm: Understanding Dynamics and Implicit Acceleration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.11587","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:c85cf1259ae9656da5f29c6c68d7712e3bf64efcbf602174086a9df93e63bb85","target":"record","created_at":"2026-05-22T01:03:52Z","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":"45588a8731113b1431860e66437af001b435100852be188c8315b31069870a2b","cross_cats_sorted":["cs.NA","math.NA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-12-12T14:16:35Z","title_canon_sha256":"c0ff70bc7d128aab7f49e611ec5c2ef95ff926ad5952f9ebb0fa9e5c21eaafe3"},"schema_version":"1.0","source":{"id":"2512.11587","kind":"arxiv","version":2}},"canonical_sha256":"00b858a8dc6fd4657418cbfc637223d52e30f6cc2a1a8efa83744bfd577b1919","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00b858a8dc6fd4657418cbfc637223d52e30f6cc2a1a8efa83744bfd577b1919","first_computed_at":"2026-05-22T01:03:52.124528Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T01:03:52.124528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YlBU8wv00xCmpxyvM/dAB3BYTv0mqKfdL0NPcu8To9MZThTaQctvl5cl7GIGZMJ3IGpT7DOeMUb4+EZZOicQCw==","signature_status":"signed_v1","signed_at":"2026-05-22T01:03:52.125640Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.11587","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c85cf1259ae9656da5f29c6c68d7712e3bf64efcbf602174086a9df93e63bb85","sha256:9b48a3d5b86034ac1b5d02eb76de052bf37d22ff492a9b778e34a627ab32e506"],"state_sha256":"ae242b1b2d8a590d29a37abb79e132cc9754917fa3d75ad19ff33f121803666a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rT+mv2Zt6WuPMC0mRDEN9zsLZWLjQEavd/KoXKErHJpCJEzzDtdvV42vCBuynBxSJPhhghUTl6v4Fh9cE819BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T05:02:27.226837Z","bundle_sha256":"dccb7eb6e2e0aff744909d985a6cc69afba434402b13c9a1279e1e116475b9cf"}}