{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:W3CGHZ5NFJP2BYZQQ4VZP6W5T3","short_pith_number":"pith:W3CGHZ5N","canonical_record":{"source":{"id":"2403.14917","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-03-22T02:41:57Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"50a3d0a5d11638aa9844fb6e39072ceb4a9c7c6508ab834fa6e29308e31d9f02","abstract_canon_sha256":"2971b1a471579e1c74ddb402da3b9b5072b7636a736a0bde44c67fa8a6df91ab"},"schema_version":"1.0"},"canonical_sha256":"b6c463e7ad2a5fa0e330872b97fadd9eea30b4e1e544f8cbc3dd19f479dc4187","source":{"kind":"arxiv","id":"2403.14917","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.14917","created_at":"2026-07-05T08:05:12Z"},{"alias_kind":"arxiv_version","alias_value":"2403.14917v2","created_at":"2026-07-05T08:05:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.14917","created_at":"2026-07-05T08:05:12Z"},{"alias_kind":"pith_short_12","alias_value":"W3CGHZ5NFJP2","created_at":"2026-07-05T08:05:12Z"},{"alias_kind":"pith_short_16","alias_value":"W3CGHZ5NFJP2BYZQ","created_at":"2026-07-05T08:05:12Z"},{"alias_kind":"pith_short_8","alias_value":"W3CGHZ5N","created_at":"2026-07-05T08:05:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:W3CGHZ5NFJP2BYZQQ4VZP6W5T3","target":"record","payload":{"canonical_record":{"source":{"id":"2403.14917","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-03-22T02:41:57Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"50a3d0a5d11638aa9844fb6e39072ceb4a9c7c6508ab834fa6e29308e31d9f02","abstract_canon_sha256":"2971b1a471579e1c74ddb402da3b9b5072b7636a736a0bde44c67fa8a6df91ab"},"schema_version":"1.0"},"canonical_sha256":"b6c463e7ad2a5fa0e330872b97fadd9eea30b4e1e544f8cbc3dd19f479dc4187","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:05:12.340849Z","signature_b64":"yZewKpEiu3LKhPBGikF9FmWTLVNHWp/mRKQK6Qm3SWLirPUWZBTewEkm+me8W5xgiYit1vJ/k6QbwlDjI48lDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6c463e7ad2a5fa0e330872b97fadd9eea30b4e1e544f8cbc3dd19f479dc4187","last_reissued_at":"2026-07-05T08:05:12.340389Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:05:12.340389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2403.14917","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":"2026-07-05T08:05:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JLaE3IIAq3wBBdo4mkgxcessSctDvRUtzoFTzpeP+yPiSrN73o1qCZVyvii4IakRj4gS956quYVY1J8fc4wcCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T16:24:48.375368Z"},"content_sha256":"50494a2fa2b5dc08bb2029a1463cdbcbd5906406c671f14caeb771b17bfe16a4","schema_version":"1.0","event_id":"sha256:50494a2fa2b5dc08bb2029a1463cdbcbd5906406c671f14caeb771b17bfe16a4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:W3CGHZ5NFJP2BYZQQ4VZP6W5T3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mean-field Analysis on Two-layer Neural Networks from a Kernel Perspective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Shokichi Takakura, Taiji Suzuki","submitted_at":"2024-03-22T02:41:57Z","abstract_excerpt":"In this paper, we study the feature learning ability of two-layer neural networks in the mean-field regime through the lens of kernel methods. To focus on the dynamics of the kernel induced by the first layer, we utilize a two-timescale limit, where the second layer moves much faster than the first layer. In this limit, the learning problem is reduced to the minimization problem over the intrinsic kernel. Then, we show the global convergence of the mean-field Langevin dynamics and derive time and particle discretization error. We also demonstrate that two-layer neural networks can learn a unio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.14917","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/2403.14917/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":"2026-07-05T08:05:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RoJoa/9TueLDq+OzZqs3NnshSgIbjyeao8BUqmTHi6xiWjsP19KlR6QjP5+6phCTsoOMHC6luChWbniR1ZGwBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T16:24:48.375990Z"},"content_sha256":"1f96cb7661ffad8bd8bb8287d88de6d86519ebd0162a8a467add93928addb6db","schema_version":"1.0","event_id":"sha256:1f96cb7661ffad8bd8bb8287d88de6d86519ebd0162a8a467add93928addb6db"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W3CGHZ5NFJP2BYZQQ4VZP6W5T3/bundle.json","state_url":"https://pith.science/pith/W3CGHZ5NFJP2BYZQQ4VZP6W5T3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W3CGHZ5NFJP2BYZQQ4VZP6W5T3/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":"2026-08-16T16:24:48Z","links":{"resolver":"https://pith.science/pith/W3CGHZ5NFJP2BYZQQ4VZP6W5T3","bundle":"https://pith.science/pith/W3CGHZ5NFJP2BYZQQ4VZP6W5T3/bundle.json","state":"https://pith.science/pith/W3CGHZ5NFJP2BYZQQ4VZP6W5T3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W3CGHZ5NFJP2BYZQQ4VZP6W5T3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:W3CGHZ5NFJP2BYZQQ4VZP6W5T3","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":"2971b1a471579e1c74ddb402da3b9b5072b7636a736a0bde44c67fa8a6df91ab","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-03-22T02:41:57Z","title_canon_sha256":"50a3d0a5d11638aa9844fb6e39072ceb4a9c7c6508ab834fa6e29308e31d9f02"},"schema_version":"1.0","source":{"id":"2403.14917","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.14917","created_at":"2026-07-05T08:05:12Z"},{"alias_kind":"arxiv_version","alias_value":"2403.14917v2","created_at":"2026-07-05T08:05:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.14917","created_at":"2026-07-05T08:05:12Z"},{"alias_kind":"pith_short_12","alias_value":"W3CGHZ5NFJP2","created_at":"2026-07-05T08:05:12Z"},{"alias_kind":"pith_short_16","alias_value":"W3CGHZ5NFJP2BYZQ","created_at":"2026-07-05T08:05:12Z"},{"alias_kind":"pith_short_8","alias_value":"W3CGHZ5N","created_at":"2026-07-05T08:05:12Z"}],"graph_snapshots":[{"event_id":"sha256:1f96cb7661ffad8bd8bb8287d88de6d86519ebd0162a8a467add93928addb6db","target":"graph","created_at":"2026-07-05T08:05:12Z","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/2403.14917/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the feature learning ability of two-layer neural networks in the mean-field regime through the lens of kernel methods. To focus on the dynamics of the kernel induced by the first layer, we utilize a two-timescale limit, where the second layer moves much faster than the first layer. In this limit, the learning problem is reduced to the minimization problem over the intrinsic kernel. Then, we show the global convergence of the mean-field Langevin dynamics and derive time and particle discretization error. We also demonstrate that two-layer neural networks can learn a unio","authors_text":"Shokichi Takakura, Taiji Suzuki","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-03-22T02:41:57Z","title":"Mean-field Analysis on Two-layer Neural Networks from a Kernel Perspective"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.14917","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":"sha256:50494a2fa2b5dc08bb2029a1463cdbcbd5906406c671f14caeb771b17bfe16a4","target":"record","created_at":"2026-07-05T08:05:12Z","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":"2971b1a471579e1c74ddb402da3b9b5072b7636a736a0bde44c67fa8a6df91ab","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-03-22T02:41:57Z","title_canon_sha256":"50a3d0a5d11638aa9844fb6e39072ceb4a9c7c6508ab834fa6e29308e31d9f02"},"schema_version":"1.0","source":{"id":"2403.14917","kind":"arxiv","version":2}},"canonical_sha256":"b6c463e7ad2a5fa0e330872b97fadd9eea30b4e1e544f8cbc3dd19f479dc4187","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6c463e7ad2a5fa0e330872b97fadd9eea30b4e1e544f8cbc3dd19f479dc4187","first_computed_at":"2026-07-05T08:05:12.340389Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:05:12.340389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yZewKpEiu3LKhPBGikF9FmWTLVNHWp/mRKQK6Qm3SWLirPUWZBTewEkm+me8W5xgiYit1vJ/k6QbwlDjI48lDg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:05:12.340849Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.14917","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50494a2fa2b5dc08bb2029a1463cdbcbd5906406c671f14caeb771b17bfe16a4","sha256:1f96cb7661ffad8bd8bb8287d88de6d86519ebd0162a8a467add93928addb6db"],"state_sha256":"fdb445fb58ec13f2d3120d3113036738513b0427b494dc3c137673d8ee3b7531"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hc9qw5+ZvLQVdv94yjIODh+b1UFd26fIAUxm87cgRMrbXqD5X3cRqwlISOHvulq8aEW9NEMLrLUYZ4FOzPSoAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T16:24:48.381096Z","bundle_sha256":"6c86ad7afe1c3068b1e04af23ca404a14b34bfed09551dba30994b61353dbbb9"}}