{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:TIEOIC7KB3KO6ATOP54I6NUIJJ","short_pith_number":"pith:TIEOIC7K","schema_version":"1.0","canonical_sha256":"9a08e40bea0ed4ef026e7f788f36884a540c89aa5ee6d5a0dc16629b9e084b32","source":{"kind":"arxiv","id":"1910.12478","version":3},"attestation_state":"computed","paper":{"title":"Tensor Programs I: Wide Feedforward or Recurrent Neural Networks of Any Architecture are Gaussian Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.LG","math-ph","math.MP"],"primary_cat":"cs.NE","authors_text":"Greg Yang","submitted_at":"2019-10-28T07:31:59Z","abstract_excerpt":"Wide neural networks with random weights and biases are Gaussian processes, as originally observed by Neal (1995) and more recently by Lee et al. (2018) and Matthews et al. (2018) for deep fully-connected networks, as well as by Novak et al. (2019) and Garriga-Alonso et al. (2019) for deep convolutional networks. We show that this Neural Network-Gaussian Process correspondence surprisingly extends to all modern feedforward or recurrent neural networks composed of multilayer perceptron, RNNs (e.g. LSTMs, GRUs), (nD or graph) convolution, pooling, skip connection, attention, batch normalization,"},"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":"1910.12478","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2019-10-28T07:31:59Z","cross_cats_sorted":["cond-mat.dis-nn","cs.LG","math-ph","math.MP"],"title_canon_sha256":"e6f0522c55ebe84d0bc13f718406d0063a5e5c5779e89693db0b4c31cf92a652","abstract_canon_sha256":"4a63c430c964400df2693383771865f2de34dbdc8027a2c233fae33018ae2681"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:38:27.785438Z","signature_b64":"b9+U36uDiiAZUzHHyr4Tu5RFcQRw5XscdVAlMtH9iKrZLOvPtSUNt0A5ltD7/SYCX0yWMBJiNlj83az21SdnAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a08e40bea0ed4ef026e7f788f36884a540c89aa5ee6d5a0dc16629b9e084b32","last_reissued_at":"2026-07-05T02:38:27.784723Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:38:27.784723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tensor Programs I: Wide Feedforward or Recurrent Neural Networks of Any Architecture are Gaussian Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.LG","math-ph","math.MP"],"primary_cat":"cs.NE","authors_text":"Greg Yang","submitted_at":"2019-10-28T07:31:59Z","abstract_excerpt":"Wide neural networks with random weights and biases are Gaussian processes, as originally observed by Neal (1995) and more recently by Lee et al. (2018) and Matthews et al. (2018) for deep fully-connected networks, as well as by Novak et al. (2019) and Garriga-Alonso et al. (2019) for deep convolutional networks. We show that this Neural Network-Gaussian Process correspondence surprisingly extends to all modern feedforward or recurrent neural networks composed of multilayer perceptron, RNNs (e.g. LSTMs, GRUs), (nD or graph) convolution, pooling, skip connection, attention, batch normalization,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.12478","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/1910.12478/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":"1910.12478","created_at":"2026-07-05T02:38:27.784804+00:00"},{"alias_kind":"arxiv_version","alias_value":"1910.12478v3","created_at":"2026-07-05T02:38:27.784804+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.12478","created_at":"2026-07-05T02:38:27.784804+00:00"},{"alias_kind":"pith_short_12","alias_value":"TIEOIC7KB3KO","created_at":"2026-07-05T02:38:27.784804+00:00"},{"alias_kind":"pith_short_16","alias_value":"TIEOIC7KB3KO6ATO","created_at":"2026-07-05T02:38:27.784804+00:00"},{"alias_kind":"pith_short_8","alias_value":"TIEOIC7K","created_at":"2026-07-05T02:38:27.784804+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2508.03810","citing_title":"Viability of perturbative expansion for quantum field theories on neurons","ref_index":30,"is_internal_anchor":false},{"citing_arxiv_id":"2604.27050","citing_title":"Optimal Architecture and Fundamental Bounds in Neural Network Field Theory","ref_index":24,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TIEOIC7KB3KO6ATOP54I6NUIJJ","json":"https://pith.science/pith/TIEOIC7KB3KO6ATOP54I6NUIJJ.json","graph_json":"https://pith.science/api/pith-number/TIEOIC7KB3KO6ATOP54I6NUIJJ/graph.json","events_json":"https://pith.science/api/pith-number/TIEOIC7KB3KO6ATOP54I6NUIJJ/events.json","paper":"https://pith.science/paper/TIEOIC7K"},"agent_actions":{"view_html":"https://pith.science/pith/TIEOIC7KB3KO6ATOP54I6NUIJJ","download_json":"https://pith.science/pith/TIEOIC7KB3KO6ATOP54I6NUIJJ.json","view_paper":"https://pith.science/paper/TIEOIC7K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1910.12478&json=true","fetch_graph":"https://pith.science/api/pith-number/TIEOIC7KB3KO6ATOP54I6NUIJJ/graph.json","fetch_events":"https://pith.science/api/pith-number/TIEOIC7KB3KO6ATOP54I6NUIJJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TIEOIC7KB3KO6ATOP54I6NUIJJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TIEOIC7KB3KO6ATOP54I6NUIJJ/action/storage_attestation","attest_author":"https://pith.science/pith/TIEOIC7KB3KO6ATOP54I6NUIJJ/action/author_attestation","sign_citation":"https://pith.science/pith/TIEOIC7KB3KO6ATOP54I6NUIJJ/action/citation_signature","submit_replication":"https://pith.science/pith/TIEOIC7KB3KO6ATOP54I6NUIJJ/action/replication_record"}},"created_at":"2026-07-05T02:38:27.784804+00:00","updated_at":"2026-07-05T02:38:27.784804+00:00"}