{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:2ISEK7MSL5YKEBZUPXSAH7ZZNY","short_pith_number":"pith:2ISEK7MS","canonical_record":{"source":{"id":"2411.07724","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-11-12T11:30:53Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"151a45ec617174e44fe95d85d46d121032ed19ba348cb9359c2573547af00865","abstract_canon_sha256":"a80864a6353bd7bd2f5a66822d34e4afb512605f35628926780e5e1ff5012e3e"},"schema_version":"1.0"},"canonical_sha256":"d224457d925f70a207347de403ff396e36848c9029324d97e664496d31b4d3bd","source":{"kind":"arxiv","id":"2411.07724","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.07724","created_at":"2026-06-23T03:13:43Z"},{"alias_kind":"arxiv_version","alias_value":"2411.07724v2","created_at":"2026-06-23T03:13:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.07724","created_at":"2026-06-23T03:13:43Z"},{"alias_kind":"pith_short_12","alias_value":"2ISEK7MSL5YK","created_at":"2026-06-23T03:13:43Z"},{"alias_kind":"pith_short_16","alias_value":"2ISEK7MSL5YKEBZU","created_at":"2026-06-23T03:13:43Z"},{"alias_kind":"pith_short_8","alias_value":"2ISEK7MS","created_at":"2026-06-23T03:13:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:2ISEK7MSL5YKEBZUPXSAH7ZZNY","target":"record","payload":{"canonical_record":{"source":{"id":"2411.07724","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-11-12T11:30:53Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"151a45ec617174e44fe95d85d46d121032ed19ba348cb9359c2573547af00865","abstract_canon_sha256":"a80864a6353bd7bd2f5a66822d34e4afb512605f35628926780e5e1ff5012e3e"},"schema_version":"1.0"},"canonical_sha256":"d224457d925f70a207347de403ff396e36848c9029324d97e664496d31b4d3bd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T03:13:43.921948Z","signature_b64":"96S/bYP6OK5EAlSRBZTtQ76X6QR9ky6TS9mjpt875o09FaMLbZT78V4Uc2G9To/dVkBgdEcXFa7A78QEGPY4DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d224457d925f70a207347de403ff396e36848c9029324d97e664496d31b4d3bd","last_reissued_at":"2026-06-23T03:13:43.921464Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T03:13:43.921464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.07724","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":"2026-06-23T03:13:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"unwxVCmv4Uk5bjZwdqU1DMQ6vHyGWU0GSvCPvvqmMp+AIjfvVmyat9A+jFu1tJ3XA7ygVZ5nORdEH0+jwuF0Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T02:13:59.748625Z"},"content_sha256":"64675d723f063278930b337ef47462231ef2128a9c2642ba532be0bc499395b4","schema_version":"1.0","event_id":"sha256:64675d723f063278930b337ef47462231ef2128a9c2642ba532be0bc499395b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:2ISEK7MSL5YKEBZUPXSAH7ZZNY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence Rate Analysis of LION","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Huan Li, Yiming Dong, Zhouchen Lin","submitted_at":"2024-11-12T11:30:53Z","abstract_excerpt":"The LION (evoLved sIgn mOmeNtum) optimizer for deep neural network training was found by Google via program search, with the simple sign update yet showing impressive performance in training large scale networks. Although previous studies have investigated its convergence properties, a comprehensive analysis, especially the convergence rate, is still desirable. Recognizing that LION can be regarded as solving a specific constrained problem, this paper focuses on demonstrating its convergence to the Karush-Kuhn-Tucker (KKT) point at the rate of $\\cal O(\\sqrt{d}K^{-1/4})$ measured by gradient $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.07724","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/2411.07724/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":"2026-06-23T03:13:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1DJnoFGO04dEZ2SpeT283c4SLvjhEfofQKPr6CUdneplZsuL/ZBZ0L0sDR4ONUfv374isX96yntrcaVJW4xWAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T02:13:59.749007Z"},"content_sha256":"5cb4d4d9f533321873acdd848ca7ec6c2f8702637b6edb0f95759babb6e70ef6","schema_version":"1.0","event_id":"sha256:5cb4d4d9f533321873acdd848ca7ec6c2f8702637b6edb0f95759babb6e70ef6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2ISEK7MSL5YKEBZUPXSAH7ZZNY/bundle.json","state_url":"https://pith.science/pith/2ISEK7MSL5YKEBZUPXSAH7ZZNY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2ISEK7MSL5YKEBZUPXSAH7ZZNY/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":"2026-07-01T02:13:59Z","links":{"resolver":"https://pith.science/pith/2ISEK7MSL5YKEBZUPXSAH7ZZNY","bundle":"https://pith.science/pith/2ISEK7MSL5YKEBZUPXSAH7ZZNY/bundle.json","state":"https://pith.science/pith/2ISEK7MSL5YKEBZUPXSAH7ZZNY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2ISEK7MSL5YKEBZUPXSAH7ZZNY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:2ISEK7MSL5YKEBZUPXSAH7ZZNY","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":"a80864a6353bd7bd2f5a66822d34e4afb512605f35628926780e5e1ff5012e3e","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-11-12T11:30:53Z","title_canon_sha256":"151a45ec617174e44fe95d85d46d121032ed19ba348cb9359c2573547af00865"},"schema_version":"1.0","source":{"id":"2411.07724","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.07724","created_at":"2026-06-23T03:13:43Z"},{"alias_kind":"arxiv_version","alias_value":"2411.07724v2","created_at":"2026-06-23T03:13:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.07724","created_at":"2026-06-23T03:13:43Z"},{"alias_kind":"pith_short_12","alias_value":"2ISEK7MSL5YK","created_at":"2026-06-23T03:13:43Z"},{"alias_kind":"pith_short_16","alias_value":"2ISEK7MSL5YKEBZU","created_at":"2026-06-23T03:13:43Z"},{"alias_kind":"pith_short_8","alias_value":"2ISEK7MS","created_at":"2026-06-23T03:13:43Z"}],"graph_snapshots":[{"event_id":"sha256:5cb4d4d9f533321873acdd848ca7ec6c2f8702637b6edb0f95759babb6e70ef6","target":"graph","created_at":"2026-06-23T03:13:43Z","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/2411.07724/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The LION (evoLved sIgn mOmeNtum) optimizer for deep neural network training was found by Google via program search, with the simple sign update yet showing impressive performance in training large scale networks. Although previous studies have investigated its convergence properties, a comprehensive analysis, especially the convergence rate, is still desirable. Recognizing that LION can be regarded as solving a specific constrained problem, this paper focuses on demonstrating its convergence to the Karush-Kuhn-Tucker (KKT) point at the rate of $\\cal O(\\sqrt{d}K^{-1/4})$ measured by gradient $\\","authors_text":"Huan Li, Yiming Dong, Zhouchen Lin","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-11-12T11:30:53Z","title":"Convergence Rate Analysis of LION"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.07724","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":"sha256:64675d723f063278930b337ef47462231ef2128a9c2642ba532be0bc499395b4","target":"record","created_at":"2026-06-23T03:13:43Z","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":"a80864a6353bd7bd2f5a66822d34e4afb512605f35628926780e5e1ff5012e3e","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-11-12T11:30:53Z","title_canon_sha256":"151a45ec617174e44fe95d85d46d121032ed19ba348cb9359c2573547af00865"},"schema_version":"1.0","source":{"id":"2411.07724","kind":"arxiv","version":2}},"canonical_sha256":"d224457d925f70a207347de403ff396e36848c9029324d97e664496d31b4d3bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d224457d925f70a207347de403ff396e36848c9029324d97e664496d31b4d3bd","first_computed_at":"2026-06-23T03:13:43.921464Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T03:13:43.921464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"96S/bYP6OK5EAlSRBZTtQ76X6QR9ky6TS9mjpt875o09FaMLbZT78V4Uc2G9To/dVkBgdEcXFa7A78QEGPY4DQ==","signature_status":"signed_v1","signed_at":"2026-06-23T03:13:43.921948Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.07724","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64675d723f063278930b337ef47462231ef2128a9c2642ba532be0bc499395b4","sha256:5cb4d4d9f533321873acdd848ca7ec6c2f8702637b6edb0f95759babb6e70ef6"],"state_sha256":"f0c2d2322defdbe46021b59812a289fa58b961b784ba22467081e15f0348cefa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YlvfnbaiznjnUvVdOttw+ACK7kAYb4+varfDngg0uy83aedvspJPhBtzd2UCCt9SlaiHj6BvlGwFXNCtrpeaBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T02:13:59.751007Z","bundle_sha256":"8daf0b5576d3b49a59fdfe3bb9772e79a56ec372819b7eef3d84ff2242acbfcb"}}