{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:RLSOPAARIOV6GCKI2V6RGFLERO","short_pith_number":"pith:RLSOPAAR","canonical_record":{"source":{"id":"1603.00988","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-03-03T06:26:31Z","cross_cats_sorted":[],"title_canon_sha256":"b857264f6f78a09a745314b74eb124f4581488260d5e25a52f03bbcf1b283eb5","abstract_canon_sha256":"1f44d2763d40a59cdba3effb64f740290081284f28d8cacff5d9eca90ed6025b"},"schema_version":"1.0"},"canonical_sha256":"8ae4e7801143abe30948d57d1315648ba6150f76d97bb98beae79f16ab6558d8","source":{"kind":"arxiv","id":"1603.00988","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.00988","created_at":"2026-05-18T01:13:23Z"},{"alias_kind":"arxiv_version","alias_value":"1603.00988v4","created_at":"2026-05-18T01:13:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00988","created_at":"2026-05-18T01:13:23Z"},{"alias_kind":"pith_short_12","alias_value":"RLSOPAARIOV6","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RLSOPAARIOV6GCKI","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RLSOPAAR","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:RLSOPAARIOV6GCKI2V6RGFLERO","target":"record","payload":{"canonical_record":{"source":{"id":"1603.00988","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-03-03T06:26:31Z","cross_cats_sorted":[],"title_canon_sha256":"b857264f6f78a09a745314b74eb124f4581488260d5e25a52f03bbcf1b283eb5","abstract_canon_sha256":"1f44d2763d40a59cdba3effb64f740290081284f28d8cacff5d9eca90ed6025b"},"schema_version":"1.0"},"canonical_sha256":"8ae4e7801143abe30948d57d1315648ba6150f76d97bb98beae79f16ab6558d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:23.509302Z","signature_b64":"4QJpmBsy38jC/WH5LzoW/PYeKnm5IUc6IX7T+Q5lX92v4Kpq7EfoRKF1CqYof1uFxaI5ti957WHNB+hj85NoBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ae4e7801143abe30948d57d1315648ba6150f76d97bb98beae79f16ab6558d8","last_reissued_at":"2026-05-18T01:13:23.508821Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:23.508821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.00988","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:13:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+DgHtK5EdeRZJIr2+ZOw5+DRm4ZCOJCJJj9X/sJkavihOqsrL+BswgOKb5K1NT3ClXyDl/ASKW4HrcbeAsmzCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T07:55:47.943026Z"},"content_sha256":"8242b197db2c19f52f1e6583085c2807661f92eeef37e768df704727e4a9e574","schema_version":"1.0","event_id":"sha256:8242b197db2c19f52f1e6583085c2807661f92eeef37e768df704727e4a9e574"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:RLSOPAARIOV6GCKI2V6RGFLERO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning Functions: When Is Deep Better Than Shallow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Hrushikesh Mhaskar, Qianli Liao, Tomaso Poggio","submitted_at":"2016-03-03T06:26:31Z","abstract_excerpt":"While the universal approximation property holds both for hierarchical and shallow networks, we prove that deep (hierarchical) networks can approximate the class of compositional functions with the same accuracy as shallow networks but with exponentially lower number of training parameters as well as VC-dimension. This theorem settles an old conjecture by Bengio on the role of depth in networks. We then define a general class of scalable, shift-invariant algorithms to show a simple and natural set of requirements that justify deep convolutional networks."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00988","kind":"arxiv","version":4},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:13:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uKcYgX0eOtBF4Gi8uHhCO0CkMMN1eAnaHnZcCz+u1Kf8tYFXimj4wNZEr7jVjiyoesznKmXx1MU+KXeawShzCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T07:55:47.943690Z"},"content_sha256":"b89385c7e2f89de93a2bcd8e68b9f0ba9d1d6989d5e21e51137fb3d7944c3889","schema_version":"1.0","event_id":"sha256:b89385c7e2f89de93a2bcd8e68b9f0ba9d1d6989d5e21e51137fb3d7944c3889"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RLSOPAARIOV6GCKI2V6RGFLERO/bundle.json","state_url":"https://pith.science/pith/RLSOPAARIOV6GCKI2V6RGFLERO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RLSOPAARIOV6GCKI2V6RGFLERO/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":"2026-05-22T07:55:47Z","links":{"resolver":"https://pith.science/pith/RLSOPAARIOV6GCKI2V6RGFLERO","bundle":"https://pith.science/pith/RLSOPAARIOV6GCKI2V6RGFLERO/bundle.json","state":"https://pith.science/pith/RLSOPAARIOV6GCKI2V6RGFLERO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RLSOPAARIOV6GCKI2V6RGFLERO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RLSOPAARIOV6GCKI2V6RGFLERO","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":"1f44d2763d40a59cdba3effb64f740290081284f28d8cacff5d9eca90ed6025b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-03-03T06:26:31Z","title_canon_sha256":"b857264f6f78a09a745314b74eb124f4581488260d5e25a52f03bbcf1b283eb5"},"schema_version":"1.0","source":{"id":"1603.00988","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.00988","created_at":"2026-05-18T01:13:23Z"},{"alias_kind":"arxiv_version","alias_value":"1603.00988v4","created_at":"2026-05-18T01:13:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00988","created_at":"2026-05-18T01:13:23Z"},{"alias_kind":"pith_short_12","alias_value":"RLSOPAARIOV6","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RLSOPAARIOV6GCKI","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RLSOPAAR","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:b89385c7e2f89de93a2bcd8e68b9f0ba9d1d6989d5e21e51137fb3d7944c3889","target":"graph","created_at":"2026-05-18T01:13:23Z","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"},"paper":{"abstract_excerpt":"While the universal approximation property holds both for hierarchical and shallow networks, we prove that deep (hierarchical) networks can approximate the class of compositional functions with the same accuracy as shallow networks but with exponentially lower number of training parameters as well as VC-dimension. This theorem settles an old conjecture by Bengio on the role of depth in networks. We then define a general class of scalable, shift-invariant algorithms to show a simple and natural set of requirements that justify deep convolutional networks.","authors_text":"Hrushikesh Mhaskar, Qianli Liao, Tomaso Poggio","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-03-03T06:26:31Z","title":"Learning Functions: When Is Deep Better Than Shallow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00988","kind":"arxiv","version":4},"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":"sha256:8242b197db2c19f52f1e6583085c2807661f92eeef37e768df704727e4a9e574","target":"record","created_at":"2026-05-18T01:13:23Z","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":"1f44d2763d40a59cdba3effb64f740290081284f28d8cacff5d9eca90ed6025b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-03-03T06:26:31Z","title_canon_sha256":"b857264f6f78a09a745314b74eb124f4581488260d5e25a52f03bbcf1b283eb5"},"schema_version":"1.0","source":{"id":"1603.00988","kind":"arxiv","version":4}},"canonical_sha256":"8ae4e7801143abe30948d57d1315648ba6150f76d97bb98beae79f16ab6558d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ae4e7801143abe30948d57d1315648ba6150f76d97bb98beae79f16ab6558d8","first_computed_at":"2026-05-18T01:13:23.508821Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:23.508821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4QJpmBsy38jC/WH5LzoW/PYeKnm5IUc6IX7T+Q5lX92v4Kpq7EfoRKF1CqYof1uFxaI5ti957WHNB+hj85NoBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:23.509302Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.00988","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8242b197db2c19f52f1e6583085c2807661f92eeef37e768df704727e4a9e574","sha256:b89385c7e2f89de93a2bcd8e68b9f0ba9d1d6989d5e21e51137fb3d7944c3889"],"state_sha256":"f56d000e36d7f00d1b0128063b117a874dcb8f7779c2aafcfe2237e0da73107d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E/RM3DxFEItcGDhWq5YswnjQ2OeRzYhzjCI3Wlb31hFNOroBd0Y42iKj8BXah2v6ITH8VZ6301ZGgz/17NitBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T07:55:47.946970Z","bundle_sha256":"20063089daebf15bab69c034f6d17f437206be3f9083b199d6102b47e14e3e81"}}