{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:7ZB2QCKM5IOVOH35PQ66UOZXZN","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":"b8df31147dc4eee49c98fd1f80e6580846fa5942f400d043af0b8f27aac75e64","cross_cats_sorted":["cond-mat.stat-mech","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-06-08T05:20:00Z","title_canon_sha256":"e310fe6c4d0b0ea34bdcd1b8d0504dd1379cd24333dc1fe6880aa070224b6538"},"schema_version":"1.0","source":{"id":"2106.04110","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.04110","created_at":"2026-07-05T02:47:12Z"},{"alias_kind":"arxiv_version","alias_value":"2106.04110v1","created_at":"2026-07-05T02:47:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.04110","created_at":"2026-07-05T02:47:12Z"},{"alias_kind":"pith_short_12","alias_value":"7ZB2QCKM5IOV","created_at":"2026-07-05T02:47:12Z"},{"alias_kind":"pith_short_16","alias_value":"7ZB2QCKM5IOVOH35","created_at":"2026-07-05T02:47:12Z"},{"alias_kind":"pith_short_8","alias_value":"7ZB2QCKM","created_at":"2026-07-05T02:47:12Z"}],"graph_snapshots":[{"event_id":"sha256:d610181e3f3b12a122255339b72305e201a9dc47099e2bc2f1cf79e70446090a","target":"graph","created_at":"2026-07-05T02:47:12Z","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/2106.04110/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Deep neural networks (DNNs) in the infinite width/channel limit have received much attention recently, as they provide a clear analytical window to deep learning via mappings to Gaussian Processes (GPs). Despite its theoretical appeal, this viewpoint lacks a crucial ingredient of deep learning in finite DNNs, laying at the heart of their success -- feature learning. Here we consider DNNs trained with noisy gradient descent on a large training set and derive a self consistent Gaussian Process theory accounting for strong finite-DNN and feature learning effects. Applying this to a toy model of a","authors_text":"Gadi Naveh, Zohar Ringel","cross_cats":["cond-mat.stat-mech","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-06-08T05:20:00Z","title":"A self consistent theory of Gaussian Processes captures feature learning effects in finite CNNs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.04110","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":"sha256:6713c987198ffd906775401879d39f6015571094a3e592fdea5eb42910f89a21","target":"record","created_at":"2026-07-05T02:47:12Z","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":"b8df31147dc4eee49c98fd1f80e6580846fa5942f400d043af0b8f27aac75e64","cross_cats_sorted":["cond-mat.stat-mech","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-06-08T05:20:00Z","title_canon_sha256":"e310fe6c4d0b0ea34bdcd1b8d0504dd1379cd24333dc1fe6880aa070224b6538"},"schema_version":"1.0","source":{"id":"2106.04110","kind":"arxiv","version":1}},"canonical_sha256":"fe43a8094cea1d571f7d7c3dea3b37cb526a734e01412ca6d710333ee713271e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe43a8094cea1d571f7d7c3dea3b37cb526a734e01412ca6d710333ee713271e","first_computed_at":"2026-07-05T02:47:12.137587Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:47:12.137587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vbDFvN+j1yDaLmltBbeHnWLoG+NAvWOPoKN+UjcVXSD9E4iuqO9ImSqJRHWVbzdOV/YdqwP+rVWzFU+i8S+oCA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:47:12.138004Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.04110","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6713c987198ffd906775401879d39f6015571094a3e592fdea5eb42910f89a21","sha256:d610181e3f3b12a122255339b72305e201a9dc47099e2bc2f1cf79e70446090a"],"state_sha256":"a139ca0f9a1d5763aac7ff533d2e6f407ec794d75d9d4444b103a301e9da1481"}