{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:R3OSEMRLKVTT6N67E34FEGRMN4","short_pith_number":"pith:R3OSEMRL","schema_version":"1.0","canonical_sha256":"8edd22322b55673f37df26f8521a2c6f1487ca21b061e38fea18f68f18423a7f","source":{"kind":"arxiv","id":"2312.14922","version":4},"attestation_state":"computed","paper":{"title":"Learning from higher-order statistics, efficiently: hypothesis tests, random features, and neural networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.LG"],"primary_cat":"stat.ML","authors_text":"Eszter Sz\\'ekely, Federica Gerace, Lorenzo Bardone, Sebastian Goldt","submitted_at":"2023-12-22T18:55:25Z","abstract_excerpt":"Neural networks excel at discovering statistical patterns in high-dimensional data sets. In practice, higher-order cumulants, which quantify the non-Gaussian correlations between three or more variables, are particularly important for the performance of neural networks. But how efficient are neural networks at extracting features from higher-order cumulants? We study this question in the spiked cumulant model, where the statistician needs to recover a privileged direction or \"spike\" from the order-$p\\ge 4$ cumulants of $d$-dimensional inputs. Existing literature established the presence of a w"},"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":"2312.14922","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2023-12-22T18:55:25Z","cross_cats_sorted":["cond-mat.stat-mech","cs.LG"],"title_canon_sha256":"c900db05188ba1329699b427779306f43af239b386041eda05151ce4fbffdbbf","abstract_canon_sha256":"68155e9caa337bb8e4c3e746fa161a0b2fe4249348b954152e45611d81c9d314"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:20:38.904183Z","signature_b64":"NWQI9DHA+qtngOPaLG31XsqbthlEYw4QyqVK3MxNIPvACevlO4lWQze59U/1WiCUeV00JjHBtz87Mc5Wn1TDCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8edd22322b55673f37df26f8521a2c6f1487ca21b061e38fea18f68f18423a7f","last_reissued_at":"2026-07-05T09:20:38.903673Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:20:38.903673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Learning from higher-order statistics, efficiently: hypothesis tests, random features, and neural networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.LG"],"primary_cat":"stat.ML","authors_text":"Eszter Sz\\'ekely, Federica Gerace, Lorenzo Bardone, Sebastian Goldt","submitted_at":"2023-12-22T18:55:25Z","abstract_excerpt":"Neural networks excel at discovering statistical patterns in high-dimensional data sets. In practice, higher-order cumulants, which quantify the non-Gaussian correlations between three or more variables, are particularly important for the performance of neural networks. But how efficient are neural networks at extracting features from higher-order cumulants? We study this question in the spiked cumulant model, where the statistician needs to recover a privileged direction or \"spike\" from the order-$p\\ge 4$ cumulants of $d$-dimensional inputs. Existing literature established the presence of a w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.14922","kind":"arxiv","version":4},"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/2312.14922/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2312.14922","created_at":"2026-07-05T09:20:38.903740+00:00"},{"alias_kind":"arxiv_version","alias_value":"2312.14922v4","created_at":"2026-07-05T09:20:38.903740+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.14922","created_at":"2026-07-05T09:20:38.903740+00:00"},{"alias_kind":"pith_short_12","alias_value":"R3OSEMRLKVTT","created_at":"2026-07-05T09:20:38.903740+00:00"},{"alias_kind":"pith_short_16","alias_value":"R3OSEMRLKVTT6N67","created_at":"2026-07-05T09:20:38.903740+00:00"},{"alias_kind":"pith_short_8","alias_value":"R3OSEMRL","created_at":"2026-07-05T09:20:38.903740+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2603.26029","citing_title":"Detection Is Harder Than Estimation in Certain Regimes: Inference for Moment and Cumulant Tensors","ref_index":59,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/R3OSEMRLKVTT6N67E34FEGRMN4","json":"https://pith.science/pith/R3OSEMRLKVTT6N67E34FEGRMN4.json","graph_json":"https://pith.science/api/pith-number/R3OSEMRLKVTT6N67E34FEGRMN4/graph.json","events_json":"https://pith.science/api/pith-number/R3OSEMRLKVTT6N67E34FEGRMN4/events.json","paper":"https://pith.science/paper/R3OSEMRL"},"agent_actions":{"view_html":"https://pith.science/pith/R3OSEMRLKVTT6N67E34FEGRMN4","download_json":"https://pith.science/pith/R3OSEMRLKVTT6N67E34FEGRMN4.json","view_paper":"https://pith.science/paper/R3OSEMRL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2312.14922&json=true","fetch_graph":"https://pith.science/api/pith-number/R3OSEMRLKVTT6N67E34FEGRMN4/graph.json","fetch_events":"https://pith.science/api/pith-number/R3OSEMRLKVTT6N67E34FEGRMN4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R3OSEMRLKVTT6N67E34FEGRMN4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R3OSEMRLKVTT6N67E34FEGRMN4/action/storage_attestation","attest_author":"https://pith.science/pith/R3OSEMRLKVTT6N67E34FEGRMN4/action/author_attestation","sign_citation":"https://pith.science/pith/R3OSEMRLKVTT6N67E34FEGRMN4/action/citation_signature","submit_replication":"https://pith.science/pith/R3OSEMRLKVTT6N67E34FEGRMN4/action/replication_record"}},"created_at":"2026-07-05T09:20:38.903740+00:00","updated_at":"2026-07-05T09:20:38.903740+00:00"}