{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:GRHBQZTL22L35BOMYKUNZ3WY7B","short_pith_number":"pith:GRHBQZTL","canonical_record":{"source":{"id":"1506.05232","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-06-17T07:51:42Z","cross_cats_sorted":[],"title_canon_sha256":"cf633822018fcc84680e7a3ddf9717469b38f62e3cc4471ec23b7b4e164ae24e","abstract_canon_sha256":"588ca6654a41dcf173522864c9e28f67d70983ee430e5fb45d2572950a399b23"},"schema_version":"1.0"},"canonical_sha256":"344e18666bd697be85ccc2a8dceed8f8739db9dd4b0a60c6aaf50542a3b524c7","source":{"kind":"arxiv","id":"1506.05232","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.05232","created_at":"2026-05-18T01:25:46Z"},{"alias_kind":"arxiv_version","alias_value":"1506.05232v2","created_at":"2026-05-18T01:25:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.05232","created_at":"2026-05-18T01:25:46Z"},{"alias_kind":"pith_short_12","alias_value":"GRHBQZTL22L3","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GRHBQZTL22L35BOM","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GRHBQZTL","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:GRHBQZTL22L35BOMYKUNZ3WY7B","target":"record","payload":{"canonical_record":{"source":{"id":"1506.05232","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-06-17T07:51:42Z","cross_cats_sorted":[],"title_canon_sha256":"cf633822018fcc84680e7a3ddf9717469b38f62e3cc4471ec23b7b4e164ae24e","abstract_canon_sha256":"588ca6654a41dcf173522864c9e28f67d70983ee430e5fb45d2572950a399b23"},"schema_version":"1.0"},"canonical_sha256":"344e18666bd697be85ccc2a8dceed8f8739db9dd4b0a60c6aaf50542a3b524c7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:46.944590Z","signature_b64":"dooeJxL9czLizS7mPC8KZXnHWuv4TqIUq2gF1Os02DQujfX4G8c6GV6tkIM0Jg5oc/nV9lpWjrHqdaepD7LtAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"344e18666bd697be85ccc2a8dceed8f8739db9dd4b0a60c6aaf50542a3b524c7","last_reissued_at":"2026-05-18T01:25:46.944024Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:46.944024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.05232","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:25:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"19FsCHKzFQ/DnbKPTKueuS0cH9lSjv8Pf86AjU19XsYou3qA341yEOaufnhX+0Fd8YTLDx/I7Nin4+92gvaKCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:13:26.703733Z"},"content_sha256":"1d9e83e7514e3332093434e5e46da5bf276540084ef5371db739d36e4ae63b19","schema_version":"1.0","event_id":"sha256:1d9e83e7514e3332093434e5e46da5bf276540084ef5371db739d36e4ae63b19"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:GRHBQZTL22L35BOMYKUNZ3WY7B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Depth of Deep Neural Networks: A Theoretical View","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Liwei Wang, Shizhao Sun, Tie-Yan Liu, Wei Chen, Xiaoguang Liu","submitted_at":"2015-06-17T07:51:42Z","abstract_excerpt":"People believe that depth plays an important role in success of deep neural networks (DNN). However, this belief lacks solid theoretical justifications as far as we know. We investigate role of depth from perspective of margin bound. In margin bound, expected error is upper bounded by empirical margin error plus Rademacher Average (RA) based capacity term. First, we derive an upper bound for RA of DNN, and show that it increases with increasing depth. This indicates negative impact of depth on test performance. Second, we show that deeper networks tend to have larger representation power (meas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05232","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:25:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BvK54adi5Xy9bO6qMknVepNj2GWh5xjd5Q5ofq36h7vZzjE4fz2d3xBSVe+rTc6puXbC6WHi3x17iEXguxkoCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:13:26.704076Z"},"content_sha256":"1fd024cbcbb7460d9027a5d4d5f74806a926c6c90a2e1ca68d268ae0b60c5c46","schema_version":"1.0","event_id":"sha256:1fd024cbcbb7460d9027a5d4d5f74806a926c6c90a2e1ca68d268ae0b60c5c46"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GRHBQZTL22L35BOMYKUNZ3WY7B/bundle.json","state_url":"https://pith.science/pith/GRHBQZTL22L35BOMYKUNZ3WY7B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GRHBQZTL22L35BOMYKUNZ3WY7B/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":"2026-05-28T12:13:26Z","links":{"resolver":"https://pith.science/pith/GRHBQZTL22L35BOMYKUNZ3WY7B","bundle":"https://pith.science/pith/GRHBQZTL22L35BOMYKUNZ3WY7B/bundle.json","state":"https://pith.science/pith/GRHBQZTL22L35BOMYKUNZ3WY7B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GRHBQZTL22L35BOMYKUNZ3WY7B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GRHBQZTL22L35BOMYKUNZ3WY7B","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":"588ca6654a41dcf173522864c9e28f67d70983ee430e5fb45d2572950a399b23","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-06-17T07:51:42Z","title_canon_sha256":"cf633822018fcc84680e7a3ddf9717469b38f62e3cc4471ec23b7b4e164ae24e"},"schema_version":"1.0","source":{"id":"1506.05232","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.05232","created_at":"2026-05-18T01:25:46Z"},{"alias_kind":"arxiv_version","alias_value":"1506.05232v2","created_at":"2026-05-18T01:25:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.05232","created_at":"2026-05-18T01:25:46Z"},{"alias_kind":"pith_short_12","alias_value":"GRHBQZTL22L3","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GRHBQZTL22L35BOM","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GRHBQZTL","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:1fd024cbcbb7460d9027a5d4d5f74806a926c6c90a2e1ca68d268ae0b60c5c46","target":"graph","created_at":"2026-05-18T01:25:46Z","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":"People believe that depth plays an important role in success of deep neural networks (DNN). However, this belief lacks solid theoretical justifications as far as we know. We investigate role of depth from perspective of margin bound. In margin bound, expected error is upper bounded by empirical margin error plus Rademacher Average (RA) based capacity term. First, we derive an upper bound for RA of DNN, and show that it increases with increasing depth. This indicates negative impact of depth on test performance. Second, we show that deeper networks tend to have larger representation power (meas","authors_text":"Liwei Wang, Shizhao Sun, Tie-Yan Liu, Wei Chen, Xiaoguang Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-06-17T07:51:42Z","title":"On the Depth of Deep Neural Networks: A Theoretical View"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05232","kind":"arxiv","version":2},"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":"sha256:1d9e83e7514e3332093434e5e46da5bf276540084ef5371db739d36e4ae63b19","target":"record","created_at":"2026-05-18T01:25:46Z","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":"588ca6654a41dcf173522864c9e28f67d70983ee430e5fb45d2572950a399b23","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-06-17T07:51:42Z","title_canon_sha256":"cf633822018fcc84680e7a3ddf9717469b38f62e3cc4471ec23b7b4e164ae24e"},"schema_version":"1.0","source":{"id":"1506.05232","kind":"arxiv","version":2}},"canonical_sha256":"344e18666bd697be85ccc2a8dceed8f8739db9dd4b0a60c6aaf50542a3b524c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"344e18666bd697be85ccc2a8dceed8f8739db9dd4b0a60c6aaf50542a3b524c7","first_computed_at":"2026-05-18T01:25:46.944024Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:46.944024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dooeJxL9czLizS7mPC8KZXnHWuv4TqIUq2gF1Os02DQujfX4G8c6GV6tkIM0Jg5oc/nV9lpWjrHqdaepD7LtAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:46.944590Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.05232","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d9e83e7514e3332093434e5e46da5bf276540084ef5371db739d36e4ae63b19","sha256:1fd024cbcbb7460d9027a5d4d5f74806a926c6c90a2e1ca68d268ae0b60c5c46"],"state_sha256":"752ea931c2a0d3b2aa934b9feb0d25ad37075052c8cddbb4816b8a4bcb6e8e03"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7GuvFq/t3c8eIuxC0v2AhUqwcvkV2B+swJDKASrJ2Jt2hvEmQStscuZ0lcifTl9N/TEhZ4JICi9rra1W1XO4Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T12:13:26.706011Z","bundle_sha256":"8a63fccf6d86a65179ad7ce05f41b7ca2b9850bf282df51d60914b87591eb950"}}