{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:JRJGODKCCJFUUXCRGGK4QJJQI2","short_pith_number":"pith:JRJGODKC","canonical_record":{"source":{"id":"2105.00507","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-05-02T16:46:38Z","cross_cats_sorted":["cs.NE","math.OC","stat.ML"],"title_canon_sha256":"70e45f76e664d8877f3ff7df8846a96c08bb1a43645872d839bca1d74df9b70e","abstract_canon_sha256":"e18bc6009d03842dc710261fb6bd5b6f0a52b76d405a0d948b013a4b624e0a7c"},"schema_version":"1.0"},"canonical_sha256":"4c52670d42124b4a5c513195c825304696a4b29b75c4010a356c2ef49a825835","source":{"kind":"arxiv","id":"2105.00507","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.00507","created_at":"2026-07-05T02:36:55Z"},{"alias_kind":"arxiv_version","alias_value":"2105.00507v1","created_at":"2026-07-05T02:36:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.00507","created_at":"2026-07-05T02:36:55Z"},{"alias_kind":"pith_short_12","alias_value":"JRJGODKCCJFU","created_at":"2026-07-05T02:36:55Z"},{"alias_kind":"pith_short_16","alias_value":"JRJGODKCCJFUUXCR","created_at":"2026-07-05T02:36:55Z"},{"alias_kind":"pith_short_8","alias_value":"JRJGODKC","created_at":"2026-07-05T02:36:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:JRJGODKCCJFUUXCRGGK4QJJQI2","target":"record","payload":{"canonical_record":{"source":{"id":"2105.00507","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-05-02T16:46:38Z","cross_cats_sorted":["cs.NE","math.OC","stat.ML"],"title_canon_sha256":"70e45f76e664d8877f3ff7df8846a96c08bb1a43645872d839bca1d74df9b70e","abstract_canon_sha256":"e18bc6009d03842dc710261fb6bd5b6f0a52b76d405a0d948b013a4b624e0a7c"},"schema_version":"1.0"},"canonical_sha256":"4c52670d42124b4a5c513195c825304696a4b29b75c4010a356c2ef49a825835","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:36:55.122866Z","signature_b64":"3nJGpdf97ycLBOJMMOAc4U0Xn81suAQZ1Xbc16++8cy2fxBN/0zai2+bB5s6mO9Ui7YEnCE+lF7UGmnIt4YfDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c52670d42124b4a5c513195c825304696a4b29b75c4010a356c2ef49a825835","last_reissued_at":"2026-07-05T02:36:55.122462Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:36:55.122462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2105.00507","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":"2026-07-05T02:36:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/GkXtSn9OTrWJSq4dJU9cl7zhWZp8BP2Z7IZpdwEuExaThCr0zs31luYcEaNGstEOMeJpKaJdkR40GTdTTTTAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T14:38:43.408086Z"},"content_sha256":"8896dec277529cdea16e766b4525849552aa7bf32b43ff307b13d173387b94b7","schema_version":"1.0","event_id":"sha256:8896dec277529cdea16e766b4525849552aa7bf32b43ff307b13d173387b94b7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:JRJGODKCCJFUUXCRGGK4QJJQI2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Universal scaling laws in the gradient descent training of neural networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NE","math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Dmitry Yarotsky, Maksim Velikanov","submitted_at":"2021-05-02T16:46:38Z","abstract_excerpt":"Current theoretical results on optimization trajectories of neural networks trained by gradient descent typically have the form of rigorous but potentially loose bounds on the loss values. In the present work we take a different approach and show that the learning trajectory can be characterized by an explicit asymptotic at large training times. Specifically, the leading term in the asymptotic expansion of the loss behaves as a power law $L(t) \\sim t^{-\\xi}$ with exponent $\\xi$ expressed only through the data dimension, the smoothness of the activation function, and the class of function being"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.00507","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/2105.00507/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":"2026-07-05T02:36:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2DClWFJM4PEZ9gy7uI2stTc0s8FjYeZadLj8Mq6PzOQnSc6+Bh4SllZWL0kAF1gVjeU4Cug9hRj53XatTyt5CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T14:38:43.408439Z"},"content_sha256":"4df5d12b1e7872b53c6bc8b2df839f0fe765440baa95cebad95b4299ec1a62c7","schema_version":"1.0","event_id":"sha256:4df5d12b1e7872b53c6bc8b2df839f0fe765440baa95cebad95b4299ec1a62c7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JRJGODKCCJFUUXCRGGK4QJJQI2/bundle.json","state_url":"https://pith.science/pith/JRJGODKCCJFUUXCRGGK4QJJQI2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JRJGODKCCJFUUXCRGGK4QJJQI2/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":"2026-08-14T14:38:43Z","links":{"resolver":"https://pith.science/pith/JRJGODKCCJFUUXCRGGK4QJJQI2","bundle":"https://pith.science/pith/JRJGODKCCJFUUXCRGGK4QJJQI2/bundle.json","state":"https://pith.science/pith/JRJGODKCCJFUUXCRGGK4QJJQI2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JRJGODKCCJFUUXCRGGK4QJJQI2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:JRJGODKCCJFUUXCRGGK4QJJQI2","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":"e18bc6009d03842dc710261fb6bd5b6f0a52b76d405a0d948b013a4b624e0a7c","cross_cats_sorted":["cs.NE","math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-05-02T16:46:38Z","title_canon_sha256":"70e45f76e664d8877f3ff7df8846a96c08bb1a43645872d839bca1d74df9b70e"},"schema_version":"1.0","source":{"id":"2105.00507","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.00507","created_at":"2026-07-05T02:36:55Z"},{"alias_kind":"arxiv_version","alias_value":"2105.00507v1","created_at":"2026-07-05T02:36:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.00507","created_at":"2026-07-05T02:36:55Z"},{"alias_kind":"pith_short_12","alias_value":"JRJGODKCCJFU","created_at":"2026-07-05T02:36:55Z"},{"alias_kind":"pith_short_16","alias_value":"JRJGODKCCJFUUXCR","created_at":"2026-07-05T02:36:55Z"},{"alias_kind":"pith_short_8","alias_value":"JRJGODKC","created_at":"2026-07-05T02:36:55Z"}],"graph_snapshots":[{"event_id":"sha256:4df5d12b1e7872b53c6bc8b2df839f0fe765440baa95cebad95b4299ec1a62c7","target":"graph","created_at":"2026-07-05T02:36:55Z","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/2105.00507/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Current theoretical results on optimization trajectories of neural networks trained by gradient descent typically have the form of rigorous but potentially loose bounds on the loss values. In the present work we take a different approach and show that the learning trajectory can be characterized by an explicit asymptotic at large training times. Specifically, the leading term in the asymptotic expansion of the loss behaves as a power law $L(t) \\sim t^{-\\xi}$ with exponent $\\xi$ expressed only through the data dimension, the smoothness of the activation function, and the class of function being","authors_text":"Dmitry Yarotsky, Maksim Velikanov","cross_cats":["cs.NE","math.OC","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-05-02T16:46:38Z","title":"Universal scaling laws in the gradient descent training of neural networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.00507","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":"sha256:8896dec277529cdea16e766b4525849552aa7bf32b43ff307b13d173387b94b7","target":"record","created_at":"2026-07-05T02:36:55Z","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":"e18bc6009d03842dc710261fb6bd5b6f0a52b76d405a0d948b013a4b624e0a7c","cross_cats_sorted":["cs.NE","math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-05-02T16:46:38Z","title_canon_sha256":"70e45f76e664d8877f3ff7df8846a96c08bb1a43645872d839bca1d74df9b70e"},"schema_version":"1.0","source":{"id":"2105.00507","kind":"arxiv","version":1}},"canonical_sha256":"4c52670d42124b4a5c513195c825304696a4b29b75c4010a356c2ef49a825835","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c52670d42124b4a5c513195c825304696a4b29b75c4010a356c2ef49a825835","first_computed_at":"2026-07-05T02:36:55.122462Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:36:55.122462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3nJGpdf97ycLBOJMMOAc4U0Xn81suAQZ1Xbc16++8cy2fxBN/0zai2+bB5s6mO9Ui7YEnCE+lF7UGmnIt4YfDw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:36:55.122866Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.00507","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8896dec277529cdea16e766b4525849552aa7bf32b43ff307b13d173387b94b7","sha256:4df5d12b1e7872b53c6bc8b2df839f0fe765440baa95cebad95b4299ec1a62c7"],"state_sha256":"e90dbb716719d31e88548f26403115c32557617aa430c34dffdba2dfd7ed58c8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CWz5jKOVqs82FfYBx1WdO9LXYesn/2WvrRwRE8oAV2Kf24aPwMCmEL7DmLzrwxoGOWsB6fYlxRzHMNoI+SWTDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T14:38:43.411756Z","bundle_sha256":"4198b278a7d9cf793c63b81ff5d4f073e035c71102e9db64d1280b4b03405bcc"}}