{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:2XNCTDPVHVJGSXC63TCKJQ3GLN","short_pith_number":"pith:2XNCTDPV","schema_version":"1.0","canonical_sha256":"d5da298df53d52695c5edcc4a4c3665b72cc9eb732ba5ac8b21f26bbaaa8e1c7","source":{"kind":"arxiv","id":"2304.06847","version":1},"attestation_state":"computed","paper":{"title":"High-dimensional limit of one-pass SGD on least squares","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Elizabeth Collins-Woodfin, Elliot Paquette","submitted_at":"2023-04-13T22:31:01Z","abstract_excerpt":"We give a description of the high-dimensional limit of one-pass single-batch stochastic gradient descent (SGD) on a least squares problem. This limit is taken with non-vanishing step-size, and with proportionally related number of samples to problem-dimensionality. The limit is described in terms of a stochastic differential equation in high dimensions, which is shown to approximate the state evolution of SGD. As a corollary, the statistical risk is shown to be approximated by the solution of a convolution-type Volterra equation with vanishing errors as dimensionality tends to infinity. The se"},"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":"2304.06847","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-04-13T22:31:01Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"fc2e73d2ba428bb90e0cad67a62ba343063bc68f0e5dd75b750e1391c3d80ea8","abstract_canon_sha256":"945846a01dcc2f3e5ea321b9f8e4fadc750ec3484a3f622724b954db77c3fb6c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:01:02.586208Z","signature_b64":"5hQ6WnBw3o9iNDnVRts9vbdlZZ6Ee1u0R6apbxJdEUvxOcqs3QoNUTE8AIaU0tclXA+43/Ka2Im8ES2yB1LlCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5da298df53d52695c5edcc4a4c3665b72cc9eb732ba5ac8b21f26bbaaa8e1c7","last_reissued_at":"2026-07-05T06:01:02.585787Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:01:02.585787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"High-dimensional limit of one-pass SGD on least squares","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Elizabeth Collins-Woodfin, Elliot Paquette","submitted_at":"2023-04-13T22:31:01Z","abstract_excerpt":"We give a description of the high-dimensional limit of one-pass single-batch stochastic gradient descent (SGD) on a least squares problem. This limit is taken with non-vanishing step-size, and with proportionally related number of samples to problem-dimensionality. The limit is described in terms of a stochastic differential equation in high dimensions, which is shown to approximate the state evolution of SGD. As a corollary, the statistical risk is shown to be approximated by the solution of a convolution-type Volterra equation with vanishing errors as dimensionality tends to infinity. The se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.06847","kind":"arxiv","version":1},"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/2304.06847/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":"2304.06847","created_at":"2026-07-05T06:01:02.585842+00:00"},{"alias_kind":"arxiv_version","alias_value":"2304.06847v1","created_at":"2026-07-05T06:01:02.585842+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.06847","created_at":"2026-07-05T06:01:02.585842+00:00"},{"alias_kind":"pith_short_12","alias_value":"2XNCTDPVHVJG","created_at":"2026-07-05T06:01:02.585842+00:00"},{"alias_kind":"pith_short_16","alias_value":"2XNCTDPVHVJGSXC6","created_at":"2026-07-05T06:01:02.585842+00:00"},{"alias_kind":"pith_short_8","alias_value":"2XNCTDPV","created_at":"2026-07-05T06:01:02.585842+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.01032","citing_title":"The Fourth Quadrant: A Stylized View of Benign Misfitting","ref_index":52,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2XNCTDPVHVJGSXC63TCKJQ3GLN","json":"https://pith.science/pith/2XNCTDPVHVJGSXC63TCKJQ3GLN.json","graph_json":"https://pith.science/api/pith-number/2XNCTDPVHVJGSXC63TCKJQ3GLN/graph.json","events_json":"https://pith.science/api/pith-number/2XNCTDPVHVJGSXC63TCKJQ3GLN/events.json","paper":"https://pith.science/paper/2XNCTDPV"},"agent_actions":{"view_html":"https://pith.science/pith/2XNCTDPVHVJGSXC63TCKJQ3GLN","download_json":"https://pith.science/pith/2XNCTDPVHVJGSXC63TCKJQ3GLN.json","view_paper":"https://pith.science/paper/2XNCTDPV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2304.06847&json=true","fetch_graph":"https://pith.science/api/pith-number/2XNCTDPVHVJGSXC63TCKJQ3GLN/graph.json","fetch_events":"https://pith.science/api/pith-number/2XNCTDPVHVJGSXC63TCKJQ3GLN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2XNCTDPVHVJGSXC63TCKJQ3GLN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2XNCTDPVHVJGSXC63TCKJQ3GLN/action/storage_attestation","attest_author":"https://pith.science/pith/2XNCTDPVHVJGSXC63TCKJQ3GLN/action/author_attestation","sign_citation":"https://pith.science/pith/2XNCTDPVHVJGSXC63TCKJQ3GLN/action/citation_signature","submit_replication":"https://pith.science/pith/2XNCTDPVHVJGSXC63TCKJQ3GLN/action/replication_record"}},"created_at":"2026-07-05T06:01:02.585842+00:00","updated_at":"2026-07-05T06:01:02.585842+00:00"}