{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:6OG5ULT7H36SBKQ7N7C6IUK6UQ","short_pith_number":"pith:6OG5ULT7","schema_version":"1.0","canonical_sha256":"f38dda2e7f3efd20aa1f6fc5e4515ea404cd137fa1ed17328634ec81aab5631a","source":{"kind":"arxiv","id":"2303.01372","version":2},"attestation_state":"computed","paper":{"title":"High-dimensional analysis of double descent for linear regression with random projections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Francis Bach (SIERRA)","submitted_at":"2023-03-02T15:58:09Z","abstract_excerpt":"We consider linear regression problems with a varying number of random projections, where we provably exhibit a double descent curve for a fixed prediction problem, with a high-dimensional analysis based on random matrix theory. We first consider the ridge regression estimator and review earlier results using classical notions from non-parametric statistics, namely degrees of freedom, also known as effective dimensionality. We then compute asymptotic equivalents of the generalization performance (in terms of squared bias and variance) of the minimum norm least-squares fit with random projectio"},"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":"2303.01372","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-03-02T15:58:09Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"22f0ff309de9ae8399641bf1672171898259336c4e6a26cbebc8ff68a6861bd3","abstract_canon_sha256":"9c7580c030b8250a4714d57bca04312498e88427334d8ea50a754e7afa6357fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:51:03.635417Z","signature_b64":"tH6hvO46WUxJjbWkrb0JlyjaQAIvFHXCfv1ms2k3TXydVAEHPc/VE2T/yhmY/hD+SI0Spkr50w+F/BjMOyJRBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f38dda2e7f3efd20aa1f6fc5e4515ea404cd137fa1ed17328634ec81aab5631a","last_reissued_at":"2026-07-05T05:51:03.635053Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:51:03.635053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"High-dimensional analysis of double descent for linear regression with random projections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Francis Bach (SIERRA)","submitted_at":"2023-03-02T15:58:09Z","abstract_excerpt":"We consider linear regression problems with a varying number of random projections, where we provably exhibit a double descent curve for a fixed prediction problem, with a high-dimensional analysis based on random matrix theory. We first consider the ridge regression estimator and review earlier results using classical notions from non-parametric statistics, namely degrees of freedom, also known as effective dimensionality. We then compute asymptotic equivalents of the generalization performance (in terms of squared bias and variance) of the minimum norm least-squares fit with random projectio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.01372","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/2303.01372/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":"2303.01372","created_at":"2026-07-05T05:51:03.635115+00:00"},{"alias_kind":"arxiv_version","alias_value":"2303.01372v2","created_at":"2026-07-05T05:51:03.635115+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.01372","created_at":"2026-07-05T05:51:03.635115+00:00"},{"alias_kind":"pith_short_12","alias_value":"6OG5ULT7H36S","created_at":"2026-07-05T05:51:03.635115+00:00"},{"alias_kind":"pith_short_16","alias_value":"6OG5ULT7H36SBKQ7","created_at":"2026-07-05T05:51:03.635115+00:00"},{"alias_kind":"pith_short_8","alias_value":"6OG5ULT7","created_at":"2026-07-05T05:51:03.635115+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.24668","citing_title":"Impact of Bottleneck Layers and Skip Connections on the Generalization of Linear Denoising Autoencoders","ref_index":5,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6OG5ULT7H36SBKQ7N7C6IUK6UQ","json":"https://pith.science/pith/6OG5ULT7H36SBKQ7N7C6IUK6UQ.json","graph_json":"https://pith.science/api/pith-number/6OG5ULT7H36SBKQ7N7C6IUK6UQ/graph.json","events_json":"https://pith.science/api/pith-number/6OG5ULT7H36SBKQ7N7C6IUK6UQ/events.json","paper":"https://pith.science/paper/6OG5ULT7"},"agent_actions":{"view_html":"https://pith.science/pith/6OG5ULT7H36SBKQ7N7C6IUK6UQ","download_json":"https://pith.science/pith/6OG5ULT7H36SBKQ7N7C6IUK6UQ.json","view_paper":"https://pith.science/paper/6OG5ULT7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2303.01372&json=true","fetch_graph":"https://pith.science/api/pith-number/6OG5ULT7H36SBKQ7N7C6IUK6UQ/graph.json","fetch_events":"https://pith.science/api/pith-number/6OG5ULT7H36SBKQ7N7C6IUK6UQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6OG5ULT7H36SBKQ7N7C6IUK6UQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6OG5ULT7H36SBKQ7N7C6IUK6UQ/action/storage_attestation","attest_author":"https://pith.science/pith/6OG5ULT7H36SBKQ7N7C6IUK6UQ/action/author_attestation","sign_citation":"https://pith.science/pith/6OG5ULT7H36SBKQ7N7C6IUK6UQ/action/citation_signature","submit_replication":"https://pith.science/pith/6OG5ULT7H36SBKQ7N7C6IUK6UQ/action/replication_record"}},"created_at":"2026-07-05T05:51:03.635115+00:00","updated_at":"2026-07-05T05:51:03.635115+00:00"}