{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:AEAK4QPNEXWQBERJYKID2UTFVW","short_pith_number":"pith:AEAK4QPN","schema_version":"1.0","canonical_sha256":"0100ae41ed25ed009229c2903d5265adb1a806a737e3dedb42d914abede87e46","source":{"kind":"arxiv","id":"1506.08473","version":3},"attestation_state":"computed","paper":{"title":"Beating the Perils of Non-Convexity: Guaranteed Training of Neural Networks using Tensor Methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NE","stat.ML"],"primary_cat":"cs.LG","authors_text":"Anima Anandkumar, Hanie Sedghi, Majid Janzamin","submitted_at":"2015-06-28T23:19:49Z","abstract_excerpt":"Training neural networks is a challenging non-convex optimization problem, and backpropagation or gradient descent can get stuck in spurious local optima. We propose a novel algorithm based on tensor decomposition for guaranteed training of two-layer neural networks. We provide risk bounds for our proposed method, with a polynomial sample complexity in the relevant parameters, such as input dimension and number of neurons. While learning arbitrary target functions is NP-hard, we provide transparent conditions on the function and the input for learnability. Our training method is based on tenso"},"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":"1506.08473","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2015-06-28T23:19:49Z","cross_cats_sorted":["cs.NE","stat.ML"],"title_canon_sha256":"030efa5187853fe6d86e366df27387612541ee3d7a7042c8101432b1f4dc1200","abstract_canon_sha256":"bdbf0c10fc461acfb20e23d96d7a451be72c849ade62c3eabd3e8acf81c1c67b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:03.812011Z","signature_b64":"PqTQrkSscF3oxWAYaA4Ge7dMsicNwPPx+etI667nWkH/HBFlZfCDiWyIfY2SgktBLNpp5CRi5tXifUQ12bdFCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0100ae41ed25ed009229c2903d5265adb1a806a737e3dedb42d914abede87e46","last_reissued_at":"2026-05-18T01:23:03.811390Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:03.811390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Beating the Perils of Non-Convexity: Guaranteed Training of Neural Networks using Tensor Methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NE","stat.ML"],"primary_cat":"cs.LG","authors_text":"Anima Anandkumar, Hanie Sedghi, Majid Janzamin","submitted_at":"2015-06-28T23:19:49Z","abstract_excerpt":"Training neural networks is a challenging non-convex optimization problem, and backpropagation or gradient descent can get stuck in spurious local optima. We propose a novel algorithm based on tensor decomposition for guaranteed training of two-layer neural networks. We provide risk bounds for our proposed method, with a polynomial sample complexity in the relevant parameters, such as input dimension and number of neurons. While learning arbitrary target functions is NP-hard, we provide transparent conditions on the function and the input for learnability. Our training method is based on tenso"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08473","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":"1506.08473","created_at":"2026-05-18T01:23:03.811496+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.08473v3","created_at":"2026-05-18T01:23:03.811496+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.08473","created_at":"2026-05-18T01:23:03.811496+00:00"},{"alias_kind":"pith_short_12","alias_value":"AEAK4QPNEXWQ","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"AEAK4QPNEXWQBERJ","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"AEAK4QPN","created_at":"2026-05-18T12:29:10.953037+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":6,"internal_anchor_count":4,"sample":[{"citing_arxiv_id":"1907.00485","citing_title":"Robust and Resource Efficient Identification of Two Hidden Layer Neural Networks","ref_index":32,"is_internal_anchor":true},{"citing_arxiv_id":"2605.20353","citing_title":"Synchronous and Asynchronous Parallelism Approaches for Generalized Canonical Polyadic Tensor Decomposition with GenTen","ref_index":15,"is_internal_anchor":true},{"citing_arxiv_id":"2605.07005","citing_title":"Equivalence of Coarse and Fine-Grained Models for Learning with Distribution Shift","ref_index":205,"is_internal_anchor":true},{"citing_arxiv_id":"2401.01335","citing_title":"Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models","ref_index":58,"is_internal_anchor":true},{"citing_arxiv_id":"2604.10858","citing_title":"Tensor-based Multi-layer Decoupling","ref_index":15,"is_internal_anchor":false},{"citing_arxiv_id":"2605.07005","citing_title":"Equivalence of Coarse and Fine-Grained Models for Learning with Distribution Shift","ref_index":205,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AEAK4QPNEXWQBERJYKID2UTFVW","json":"https://pith.science/pith/AEAK4QPNEXWQBERJYKID2UTFVW.json","graph_json":"https://pith.science/api/pith-number/AEAK4QPNEXWQBERJYKID2UTFVW/graph.json","events_json":"https://pith.science/api/pith-number/AEAK4QPNEXWQBERJYKID2UTFVW/events.json","paper":"https://pith.science/paper/AEAK4QPN"},"agent_actions":{"view_html":"https://pith.science/pith/AEAK4QPNEXWQBERJYKID2UTFVW","download_json":"https://pith.science/pith/AEAK4QPNEXWQBERJYKID2UTFVW.json","view_paper":"https://pith.science/paper/AEAK4QPN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.08473&json=true","fetch_graph":"https://pith.science/api/pith-number/AEAK4QPNEXWQBERJYKID2UTFVW/graph.json","fetch_events":"https://pith.science/api/pith-number/AEAK4QPNEXWQBERJYKID2UTFVW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AEAK4QPNEXWQBERJYKID2UTFVW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AEAK4QPNEXWQBERJYKID2UTFVW/action/storage_attestation","attest_author":"https://pith.science/pith/AEAK4QPNEXWQBERJYKID2UTFVW/action/author_attestation","sign_citation":"https://pith.science/pith/AEAK4QPNEXWQBERJYKID2UTFVW/action/citation_signature","submit_replication":"https://pith.science/pith/AEAK4QPNEXWQBERJYKID2UTFVW/action/replication_record"}},"created_at":"2026-05-18T01:23:03.811496+00:00","updated_at":"2026-05-18T01:23:03.811496+00:00"}