{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:6KA3GEFYTO5SIOHI2MSKV4QI6G","short_pith_number":"pith:6KA3GEFY","schema_version":"1.0","canonical_sha256":"f281b310b89bbb2438e8d324aaf208f18c20569878b6f13d3984554cf37cf415","source":{"kind":"arxiv","id":"2108.12862","version":3},"attestation_state":"computed","paper":{"title":"Neural Network Gaussian Processes by Increasing Depth","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Fei Wang, Feng-lei Fan, Shao-Qun Zhang","submitted_at":"2021-08-29T15:37:26Z","abstract_excerpt":"Recent years have witnessed an increasing interest in the correspondence between infinitely wide networks and Gaussian processes. Despite the effectiveness and elegance of the current neural network Gaussian process theory, to the best of our knowledge, all the neural network Gaussian processes are essentially induced by increasing width. However, in the era of deep learning, what concerns us more regarding a neural network is its depth as well as how depth impacts the behaviors of a network. Inspired by a width-depth symmetry consideration, we use a shortcut network to show that increasing th"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2108.12862","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-08-29T15:37:26Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"f574d0b844efbd9978480b938569890fbda53e900ae8b6acac9d24d51135a4f0","abstract_canon_sha256":"d102cec79724c053a8230b6b08f732728e480376e43c5d2c1b6283110874757b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:37:18.076523Z","signature_b64":"s/GLy9gzk8UZNmGO8N/lLnt8iUML7/R4l/mHOcNK8Ajk5pfLMnTEPto9S6eHkXU9cDw3qljoP9vmiyNBK7hYDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f281b310b89bbb2438e8d324aaf208f18c20569878b6f13d3984554cf37cf415","last_reissued_at":"2026-07-05T04:37:18.076042Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:37:18.076042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Neural Network Gaussian Processes by Increasing Depth","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Fei Wang, Feng-lei Fan, Shao-Qun Zhang","submitted_at":"2021-08-29T15:37:26Z","abstract_excerpt":"Recent years have witnessed an increasing interest in the correspondence between infinitely wide networks and Gaussian processes. Despite the effectiveness and elegance of the current neural network Gaussian process theory, to the best of our knowledge, all the neural network Gaussian processes are essentially induced by increasing width. However, in the era of deep learning, what concerns us more regarding a neural network is its depth as well as how depth impacts the behaviors of a network. Inspired by a width-depth symmetry consideration, we use a shortcut network to show that increasing th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.12862","kind":"arxiv","version":3},"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/2108.12862/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2108.12862","created_at":"2026-07-05T04:37:18.076103+00:00"},{"alias_kind":"arxiv_version","alias_value":"2108.12862v3","created_at":"2026-07-05T04:37:18.076103+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.12862","created_at":"2026-07-05T04:37:18.076103+00:00"},{"alias_kind":"pith_short_12","alias_value":"6KA3GEFYTO5S","created_at":"2026-07-05T04:37:18.076103+00:00"},{"alias_kind":"pith_short_16","alias_value":"6KA3GEFYTO5SIOHI","created_at":"2026-07-05T04:37:18.076103+00:00"},{"alias_kind":"pith_short_8","alias_value":"6KA3GEFY","created_at":"2026-07-05T04:37:18.076103+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6KA3GEFYTO5SIOHI2MSKV4QI6G","json":"https://pith.science/pith/6KA3GEFYTO5SIOHI2MSKV4QI6G.json","graph_json":"https://pith.science/api/pith-number/6KA3GEFYTO5SIOHI2MSKV4QI6G/graph.json","events_json":"https://pith.science/api/pith-number/6KA3GEFYTO5SIOHI2MSKV4QI6G/events.json","paper":"https://pith.science/paper/6KA3GEFY"},"agent_actions":{"view_html":"https://pith.science/pith/6KA3GEFYTO5SIOHI2MSKV4QI6G","download_json":"https://pith.science/pith/6KA3GEFYTO5SIOHI2MSKV4QI6G.json","view_paper":"https://pith.science/paper/6KA3GEFY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2108.12862&json=true","fetch_graph":"https://pith.science/api/pith-number/6KA3GEFYTO5SIOHI2MSKV4QI6G/graph.json","fetch_events":"https://pith.science/api/pith-number/6KA3GEFYTO5SIOHI2MSKV4QI6G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6KA3GEFYTO5SIOHI2MSKV4QI6G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6KA3GEFYTO5SIOHI2MSKV4QI6G/action/storage_attestation","attest_author":"https://pith.science/pith/6KA3GEFYTO5SIOHI2MSKV4QI6G/action/author_attestation","sign_citation":"https://pith.science/pith/6KA3GEFYTO5SIOHI2MSKV4QI6G/action/citation_signature","submit_replication":"https://pith.science/pith/6KA3GEFYTO5SIOHI2MSKV4QI6G/action/replication_record"}},"created_at":"2026-07-05T04:37:18.076103+00:00","updated_at":"2026-07-05T04:37:18.076103+00:00"}