{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GR7EEYS33ATMHGQSPDLYIR5VZH","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":"29735a4aeafc83938d6b5c52c18cd125798c5bbe30422911bfff2f6cb9f05b21","cross_cats_sorted":["cs.DS","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-02-20T19:40:32Z","title_canon_sha256":"91ab2c129791934e317ec60ed34f090782d5cd1cdb8748ecf01964888702f58d"},"schema_version":"1.0","source":{"id":"1802.07301","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.07301","created_at":"2026-05-18T00:03:41Z"},{"alias_kind":"arxiv_version","alias_value":"1802.07301v3","created_at":"2026-05-18T00:03:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.07301","created_at":"2026-05-18T00:03:41Z"},{"alias_kind":"pith_short_12","alias_value":"GR7EEYS33ATM","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GR7EEYS33ATMHGQS","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GR7EEYS3","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:a717daafd403ed05fcde6322c2b6dbb28d0c6ed664bab132920b98c758426f4a","target":"graph","created_at":"2026-05-18T00:03:41Z","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":"We establish connections between the problem of learning a two-layer neural network and tensor decomposition. We consider a model with feature vectors $\\boldsymbol x \\in \\mathbb R^d$, $r$ hidden units with weights $\\{\\boldsymbol w_i\\}_{1\\le i \\le r}$ and output $y\\in \\mathbb R$, i.e., $y=\\sum_{i=1}^r \\sigma( \\boldsymbol w_i^{\\mathsf T}\\boldsymbol x)$, with activation functions given by low-degree polynomials. In particular, if $\\sigma(x) = a_0+a_1x+a_3x^3$, we prove that no polynomial-time learning algorithm can outperform the trivial predictor that assigns to each example the response variabl","authors_text":"Andrea Montanari, Marco Mondelli","cross_cats":["cs.DS","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-02-20T19:40:32Z","title":"On the Connection Between Learning Two-Layers Neural Networks and Tensor Decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07301","kind":"arxiv","version":3},"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":"sha256:138404d4a43a41218354142f690aa75001007aaef21f793713a95f3e6fc458ed","target":"record","created_at":"2026-05-18T00:03:41Z","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":"29735a4aeafc83938d6b5c52c18cd125798c5bbe30422911bfff2f6cb9f05b21","cross_cats_sorted":["cs.DS","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-02-20T19:40:32Z","title_canon_sha256":"91ab2c129791934e317ec60ed34f090782d5cd1cdb8748ecf01964888702f58d"},"schema_version":"1.0","source":{"id":"1802.07301","kind":"arxiv","version":3}},"canonical_sha256":"347e42625bd826c39a1278d78447b5c9d61779aafcbdea6d4228ea0440ffd400","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"347e42625bd826c39a1278d78447b5c9d61779aafcbdea6d4228ea0440ffd400","first_computed_at":"2026-05-18T00:03:41.521455Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:41.521455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/dn8lH/FvcFsBi64WcTuxcQV2m8X4kxO7Fui9EZ6tWa77UG8JM42A5AiizG6ZRZuHOhPOkvmPsN63ggEfuEWBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:41.521849Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.07301","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:138404d4a43a41218354142f690aa75001007aaef21f793713a95f3e6fc458ed","sha256:a717daafd403ed05fcde6322c2b6dbb28d0c6ed664bab132920b98c758426f4a"],"state_sha256":"628061240bfef63d46abb1123a9ea2fd4b19bf872365ac4d2e4a5c9c1e322030"}