{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:APTFPWDTUGL7WUGD4EYX5V27LB","short_pith_number":"pith:APTFPWDT","schema_version":"1.0","canonical_sha256":"03e657d873a197fb50c3e1317ed75f5850e53a2d5fddde3639d9587c9786ab1f","source":{"kind":"arxiv","id":"1808.05587","version":2},"attestation_state":"computed","paper":{"title":"Deep Convolutional Networks as shallow Gaussian Processes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Adri\\`a Garriga-Alonso, Carl Edward Rasmussen, Laurence Aitchison","submitted_at":"2018-08-16T17:20:58Z","abstract_excerpt":"We show that the output of a (residual) convolutional neural network (CNN) with an appropriate prior over the weights and biases is a Gaussian process (GP) in the limit of infinitely many convolutional filters, extending similar results for dense networks. For a CNN, the equivalent kernel can be computed exactly and, unlike \"deep kernels\", has very few parameters: only the hyperparameters of the original CNN. Further, we show that this kernel has two properties that allow it to be computed efficiently; the cost of evaluating the kernel for a pair of images is similar to a single forward pass t"},"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":"1808.05587","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2018-08-16T17:20:58Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"2b4bff4402581d78d281b8e4e651dda244aefdd317cdfdfbac847044c6da4c30","abstract_canon_sha256":"876a16c4bd71b1ff53ca3041d980dfd7190486ad07e0849321d5a5f2d7a04f84"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:02.962377Z","signature_b64":"4AIWNNBtHtIrbm3srMClUi3Y1EOas14Tf6WZLx3OfKS+JS47xi/LyTeil1wpFYERH5IC8OmqmvavfidYfr2HBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03e657d873a197fb50c3e1317ed75f5850e53a2d5fddde3639d9587c9786ab1f","last_reissued_at":"2026-05-17T23:47:02.961641Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:02.961641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Deep Convolutional Networks as shallow Gaussian Processes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Adri\\`a Garriga-Alonso, Carl Edward Rasmussen, Laurence Aitchison","submitted_at":"2018-08-16T17:20:58Z","abstract_excerpt":"We show that the output of a (residual) convolutional neural network (CNN) with an appropriate prior over the weights and biases is a Gaussian process (GP) in the limit of infinitely many convolutional filters, extending similar results for dense networks. For a CNN, the equivalent kernel can be computed exactly and, unlike \"deep kernels\", has very few parameters: only the hyperparameters of the original CNN. Further, we show that this kernel has two properties that allow it to be computed efficiently; the cost of evaluating the kernel for a pair of images is similar to a single forward pass t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05587","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":""},"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":"1808.05587","created_at":"2026-05-17T23:47:02.961755+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.05587v2","created_at":"2026-05-17T23:47:02.961755+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.05587","created_at":"2026-05-17T23:47:02.961755+00:00"},{"alias_kind":"pith_short_12","alias_value":"APTFPWDTUGL7","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_16","alias_value":"APTFPWDTUGL7WUGD","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_8","alias_value":"APTFPWDT","created_at":"2026-05-18T12:32:13.499390+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":3,"sample":[{"citing_arxiv_id":"2006.12024","citing_title":"Bayesian Neural Networks: An Introduction and Survey","ref_index":87,"is_internal_anchor":true},{"citing_arxiv_id":"2508.03810","citing_title":"Viability of perturbative expansion for quantum field theories on neurons","ref_index":28,"is_internal_anchor":true},{"citing_arxiv_id":"2003.03485","citing_title":"Neural Operator: Graph Kernel Network for Partial Differential Equations","ref_index":122,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/APTFPWDTUGL7WUGD4EYX5V27LB","json":"https://pith.science/pith/APTFPWDTUGL7WUGD4EYX5V27LB.json","graph_json":"https://pith.science/api/pith-number/APTFPWDTUGL7WUGD4EYX5V27LB/graph.json","events_json":"https://pith.science/api/pith-number/APTFPWDTUGL7WUGD4EYX5V27LB/events.json","paper":"https://pith.science/paper/APTFPWDT"},"agent_actions":{"view_html":"https://pith.science/pith/APTFPWDTUGL7WUGD4EYX5V27LB","download_json":"https://pith.science/pith/APTFPWDTUGL7WUGD4EYX5V27LB.json","view_paper":"https://pith.science/paper/APTFPWDT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.05587&json=true","fetch_graph":"https://pith.science/api/pith-number/APTFPWDTUGL7WUGD4EYX5V27LB/graph.json","fetch_events":"https://pith.science/api/pith-number/APTFPWDTUGL7WUGD4EYX5V27LB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/APTFPWDTUGL7WUGD4EYX5V27LB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/APTFPWDTUGL7WUGD4EYX5V27LB/action/storage_attestation","attest_author":"https://pith.science/pith/APTFPWDTUGL7WUGD4EYX5V27LB/action/author_attestation","sign_citation":"https://pith.science/pith/APTFPWDTUGL7WUGD4EYX5V27LB/action/citation_signature","submit_replication":"https://pith.science/pith/APTFPWDTUGL7WUGD4EYX5V27LB/action/replication_record"}},"created_at":"2026-05-17T23:47:02.961755+00:00","updated_at":"2026-05-17T23:47:02.961755+00:00"}