{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:SAQAFVKKNA2JSPYPVSL4ZRKVGM","short_pith_number":"pith:SAQAFVKK","schema_version":"1.0","canonical_sha256":"902002d54a6834993f0fac97ccc555330436c9966e188b0171c38a84fec96aa2","source":{"kind":"arxiv","id":"1611.04231","version":3},"attestation_state":"computed","paper":{"title":"Identity Matters in Deep Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NE","stat.ML"],"primary_cat":"cs.LG","authors_text":"Moritz Hardt, Tengyu Ma","submitted_at":"2016-11-14T02:44:18Z","abstract_excerpt":"An emerging design principle in deep learning is that each layer of a deep artificial neural network should be able to easily express the identity transformation. This idea not only motivated various normalization techniques, such as \\emph{batch normalization}, but was also key to the immense success of \\emph{residual networks}.\n  In this work, we put the principle of \\emph{identity parameterization} on a more solid theoretical footing alongside further empirical progress. We first give a strikingly simple proof that arbitrarily deep linear residual networks have no spurious local optima. The "},"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":"1611.04231","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-11-14T02:44:18Z","cross_cats_sorted":["cs.NE","stat.ML"],"title_canon_sha256":"11352b7283eb17a0a51b02097ae7e085fe082b4852549b7bd599c0aed109e470","abstract_canon_sha256":"788790a9aa6edbf9d6453e5d1f9f3662913fb677ad2f1e7be47e6a1c9697835d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:19.553091Z","signature_b64":"0/UWESuBB0l4WJcfNjsmeoVNoMrgg78+h7sFiDswXe8cvn2C3kLJmyeTU4odDrfm6sSyu2rTmrWjOhYpVEjJBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"902002d54a6834993f0fac97ccc555330436c9966e188b0171c38a84fec96aa2","last_reissued_at":"2026-05-18T00:10:19.552500Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:19.552500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Identity Matters in Deep Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NE","stat.ML"],"primary_cat":"cs.LG","authors_text":"Moritz Hardt, Tengyu Ma","submitted_at":"2016-11-14T02:44:18Z","abstract_excerpt":"An emerging design principle in deep learning is that each layer of a deep artificial neural network should be able to easily express the identity transformation. This idea not only motivated various normalization techniques, such as \\emph{batch normalization}, but was also key to the immense success of \\emph{residual networks}.\n  In this work, we put the principle of \\emph{identity parameterization} on a more solid theoretical footing alongside further empirical progress. We first give a strikingly simple proof that arbitrarily deep linear residual networks have no spurious local optima. The "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04231","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":""},"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":"1611.04231","created_at":"2026-05-18T00:10:19.552585+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.04231v3","created_at":"2026-05-18T00:10:19.552585+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04231","created_at":"2026-05-18T00:10:19.552585+00:00"},{"alias_kind":"pith_short_12","alias_value":"SAQAFVKKNA2J","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_16","alias_value":"SAQAFVKKNA2JSPYP","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_8","alias_value":"SAQAFVKK","created_at":"2026-05-18T12:30:44.179134+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1906.11148","citing_title":"Chaining Meets Chain Rule: Multilevel Entropic Regularization and Training of Neural Nets","ref_index":5,"is_internal_anchor":true},{"citing_arxiv_id":"2104.13478","citing_title":"Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges","ref_index":37,"is_internal_anchor":false},{"citing_arxiv_id":"2605.09209","citing_title":"Select-then-differentiate: Solving Bilevel Optimization with Manifold Lower-level Solution Sets","ref_index":41,"is_internal_anchor":false},{"citing_arxiv_id":"2605.06959","citing_title":"Locally Near Optimal Piecewise Linear Regression in High Dimensions via Difference of Max-Affine Functions","ref_index":109,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SAQAFVKKNA2JSPYPVSL4ZRKVGM","json":"https://pith.science/pith/SAQAFVKKNA2JSPYPVSL4ZRKVGM.json","graph_json":"https://pith.science/api/pith-number/SAQAFVKKNA2JSPYPVSL4ZRKVGM/graph.json","events_json":"https://pith.science/api/pith-number/SAQAFVKKNA2JSPYPVSL4ZRKVGM/events.json","paper":"https://pith.science/paper/SAQAFVKK"},"agent_actions":{"view_html":"https://pith.science/pith/SAQAFVKKNA2JSPYPVSL4ZRKVGM","download_json":"https://pith.science/pith/SAQAFVKKNA2JSPYPVSL4ZRKVGM.json","view_paper":"https://pith.science/paper/SAQAFVKK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.04231&json=true","fetch_graph":"https://pith.science/api/pith-number/SAQAFVKKNA2JSPYPVSL4ZRKVGM/graph.json","fetch_events":"https://pith.science/api/pith-number/SAQAFVKKNA2JSPYPVSL4ZRKVGM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SAQAFVKKNA2JSPYPVSL4ZRKVGM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SAQAFVKKNA2JSPYPVSL4ZRKVGM/action/storage_attestation","attest_author":"https://pith.science/pith/SAQAFVKKNA2JSPYPVSL4ZRKVGM/action/author_attestation","sign_citation":"https://pith.science/pith/SAQAFVKKNA2JSPYPVSL4ZRKVGM/action/citation_signature","submit_replication":"https://pith.science/pith/SAQAFVKKNA2JSPYPVSL4ZRKVGM/action/replication_record"}},"created_at":"2026-05-18T00:10:19.552585+00:00","updated_at":"2026-05-18T00:10:19.552585+00:00"}