{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:4O3LAX6GWZS2XC2QOI6CACBTVP","short_pith_number":"pith:4O3LAX6G","canonical_record":{"source":{"id":"2010.09610","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-10-19T15:46:48Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"c603b1f2084d2afedb1add83a221ba78658237c28ff1213c57d53a2067a85abc","abstract_canon_sha256":"a82486b7086b46b7b632c8c211b3c06f7b7bc6ddb38abc629c7879e1d2183583"},"schema_version":"1.0"},"canonical_sha256":"e3b6b05fc6b665ab8b50723c200833abea09b2c45bcee9551c65ef1ebae2dbda","source":{"kind":"arxiv","id":"2010.09610","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.09610","created_at":"2026-07-05T02:46:24Z"},{"alias_kind":"arxiv_version","alias_value":"2010.09610v2","created_at":"2026-07-05T02:46:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.09610","created_at":"2026-07-05T02:46:24Z"},{"alias_kind":"pith_short_12","alias_value":"4O3LAX6GWZS2","created_at":"2026-07-05T02:46:24Z"},{"alias_kind":"pith_short_16","alias_value":"4O3LAX6GWZS2XC2Q","created_at":"2026-07-05T02:46:24Z"},{"alias_kind":"pith_short_8","alias_value":"4O3LAX6G","created_at":"2026-07-05T02:46:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:4O3LAX6GWZS2XC2QOI6CACBTVP","target":"record","payload":{"canonical_record":{"source":{"id":"2010.09610","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-10-19T15:46:48Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"c603b1f2084d2afedb1add83a221ba78658237c28ff1213c57d53a2067a85abc","abstract_canon_sha256":"a82486b7086b46b7b632c8c211b3c06f7b7bc6ddb38abc629c7879e1d2183583"},"schema_version":"1.0"},"canonical_sha256":"e3b6b05fc6b665ab8b50723c200833abea09b2c45bcee9551c65ef1ebae2dbda","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:46:24.917447Z","signature_b64":"ZKDq90S7M1DcZMg7lePYx1GB13V5MdGJzOG3oP4BXlLUlo49pBzdO6tqRrQ08PGHYqajrWu4fXFNm1x+MhD8Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3b6b05fc6b665ab8b50723c200833abea09b2c45bcee9551c65ef1ebae2dbda","last_reissued_at":"2026-07-05T02:46:24.916880Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:46:24.916880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2010.09610","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":"2026-07-05T02:46:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tg8QkhXJ3WzdoThhBWxogCGaA4AKsjKi1ocnjSGy4f9ImgRjPnmF4cTri8xlPsXf2Y5xCR1y8qPvuNeP3RQ/DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T04:44:41.945014Z"},"content_sha256":"6220eed8392ae8cd1cb7b4d88747e21093232b259938d375eaca8c5de2dd7721","schema_version":"1.0","event_id":"sha256:6220eed8392ae8cd1cb7b4d88747e21093232b259938d375eaca8c5de2dd7721"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:4O3LAX6GWZS2XC2QOI6CACBTVP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Increasing Depth Leads to U-Shaped Test Risk in Over-parameterized Convolutional Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Adityanarayanan Radhakrishnan, Caroline Uhler, Eshaan Nichani","submitted_at":"2020-10-19T15:46:48Z","abstract_excerpt":"Recent works have demonstrated that increasing model capacity through width in over-parameterized neural networks leads to a decrease in test risk. For neural networks, however, model capacity can also be increased through depth, yet understanding the impact of increasing depth on test risk remains an open question. In this work, we demonstrate that the test risk of over-parameterized convolutional networks is a U-shaped curve (i.e. monotonically decreasing, then increasing) with increasing depth. We first provide empirical evidence for this phenomenon via image classification experiments usin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.09610","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2010.09610/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:46:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sTScT9SF4WmRsqHMzjOh3Co8smdi2Tbxl5Exj/2sqF9Q3hXu9KmdrMZrs50ZiLSg1F7AKQPUWXi1f7EPhXgaDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T04:44:41.945958Z"},"content_sha256":"0b415b1030093b3e89f3003394fd1b1cb92b813d75d0aa0f27ecb9e12c232504","schema_version":"1.0","event_id":"sha256:0b415b1030093b3e89f3003394fd1b1cb92b813d75d0aa0f27ecb9e12c232504"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4O3LAX6GWZS2XC2QOI6CACBTVP/bundle.json","state_url":"https://pith.science/pith/4O3LAX6GWZS2XC2QOI6CACBTVP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4O3LAX6GWZS2XC2QOI6CACBTVP/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":"2026-08-13T04:44:41Z","links":{"resolver":"https://pith.science/pith/4O3LAX6GWZS2XC2QOI6CACBTVP","bundle":"https://pith.science/pith/4O3LAX6GWZS2XC2QOI6CACBTVP/bundle.json","state":"https://pith.science/pith/4O3LAX6GWZS2XC2QOI6CACBTVP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4O3LAX6GWZS2XC2QOI6CACBTVP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:4O3LAX6GWZS2XC2QOI6CACBTVP","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":"a82486b7086b46b7b632c8c211b3c06f7b7bc6ddb38abc629c7879e1d2183583","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-10-19T15:46:48Z","title_canon_sha256":"c603b1f2084d2afedb1add83a221ba78658237c28ff1213c57d53a2067a85abc"},"schema_version":"1.0","source":{"id":"2010.09610","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.09610","created_at":"2026-07-05T02:46:24Z"},{"alias_kind":"arxiv_version","alias_value":"2010.09610v2","created_at":"2026-07-05T02:46:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.09610","created_at":"2026-07-05T02:46:24Z"},{"alias_kind":"pith_short_12","alias_value":"4O3LAX6GWZS2","created_at":"2026-07-05T02:46:24Z"},{"alias_kind":"pith_short_16","alias_value":"4O3LAX6GWZS2XC2Q","created_at":"2026-07-05T02:46:24Z"},{"alias_kind":"pith_short_8","alias_value":"4O3LAX6G","created_at":"2026-07-05T02:46:24Z"}],"graph_snapshots":[{"event_id":"sha256:0b415b1030093b3e89f3003394fd1b1cb92b813d75d0aa0f27ecb9e12c232504","target":"graph","created_at":"2026-07-05T02:46:24Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2010.09610/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recent works have demonstrated that increasing model capacity through width in over-parameterized neural networks leads to a decrease in test risk. For neural networks, however, model capacity can also be increased through depth, yet understanding the impact of increasing depth on test risk remains an open question. In this work, we demonstrate that the test risk of over-parameterized convolutional networks is a U-shaped curve (i.e. monotonically decreasing, then increasing) with increasing depth. We first provide empirical evidence for this phenomenon via image classification experiments usin","authors_text":"Adityanarayanan Radhakrishnan, Caroline Uhler, Eshaan Nichani","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-10-19T15:46:48Z","title":"Increasing Depth Leads to U-Shaped Test Risk in Over-parameterized Convolutional Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.09610","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":"sha256:6220eed8392ae8cd1cb7b4d88747e21093232b259938d375eaca8c5de2dd7721","target":"record","created_at":"2026-07-05T02:46:24Z","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":"a82486b7086b46b7b632c8c211b3c06f7b7bc6ddb38abc629c7879e1d2183583","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-10-19T15:46:48Z","title_canon_sha256":"c603b1f2084d2afedb1add83a221ba78658237c28ff1213c57d53a2067a85abc"},"schema_version":"1.0","source":{"id":"2010.09610","kind":"arxiv","version":2}},"canonical_sha256":"e3b6b05fc6b665ab8b50723c200833abea09b2c45bcee9551c65ef1ebae2dbda","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3b6b05fc6b665ab8b50723c200833abea09b2c45bcee9551c65ef1ebae2dbda","first_computed_at":"2026-07-05T02:46:24.916880Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:46:24.916880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZKDq90S7M1DcZMg7lePYx1GB13V5MdGJzOG3oP4BXlLUlo49pBzdO6tqRrQ08PGHYqajrWu4fXFNm1x+MhD8Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:46:24.917447Z","signed_message":"canonical_sha256_bytes"},"source_id":"2010.09610","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6220eed8392ae8cd1cb7b4d88747e21093232b259938d375eaca8c5de2dd7721","sha256:0b415b1030093b3e89f3003394fd1b1cb92b813d75d0aa0f27ecb9e12c232504"],"state_sha256":"9d8b089d22024f3552de684019a68a50d18f4b74b694bdc90176ebf71da6315b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pzqvIWpHQmNp1yLlePCseToOfphIoVq1MXnbAgSvu7f3k+63MwwOUgSDdltA9qKI1JX4ElDUUXddZROqtC4UAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T04:44:41.961715Z","bundle_sha256":"f4b149e6dfe45c7355a824e2da43c1677538b28ba5d7efc1be11c9f309d536cb"}}