{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:KZTLCHSELA5P77CFU5X27HUDD3","short_pith_number":"pith:KZTLCHSE","schema_version":"1.0","canonical_sha256":"5666b11e44583afffc45a76faf9e831ec94949a74898bccc4679a8fb99515637","source":{"kind":"arxiv","id":"2412.08772","version":1},"attestation_state":"computed","paper":{"title":"On improving generalization in a class of learning problems with the method of small parameters for weakly-controlled optimal gradient systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"math.OC","authors_text":"Getachew K. Befekadu","submitted_at":"2024-12-11T20:50:29Z","abstract_excerpt":"In this paper, we provide a mathematical framework for improving generalization in a class of learning problems which is related to point estimations for modeling of high-dimensional nonlinear functions. In particular, we consider a variational problem for a weakly-controlled gradient system, whose control input enters into the system dynamics as a coefficient to a nonlinear term which is scaled by a small parameter. Here, the optimization problem consists of a cost functional, which is associated with how to gauge the quality of the estimated model parameters at a certain fixed final time w.r"},"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":"2412.08772","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-12-11T20:50:29Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"7887e013890721425cfd87fa5f46702daa8febb37196a14464c69718393c2743","abstract_canon_sha256":"a2cf95f5b4cfed9c0ba02e7da4596918a32cdb6c6a25affbc95b8ff70e9ca52f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:48:00.441212Z","signature_b64":"EhELtDW4gXMy64B+YpAEAUQa7Y8NRFMsDaganrG34yX1QZKgOSNkUoa1xIQcnrCWHhDp5tnro5ykSjmt5EWrBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5666b11e44583afffc45a76faf9e831ec94949a74898bccc4679a8fb99515637","last_reissued_at":"2026-07-05T09:48:00.440795Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:48:00.440795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On improving generalization in a class of learning problems with the method of small parameters for weakly-controlled optimal gradient systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"math.OC","authors_text":"Getachew K. Befekadu","submitted_at":"2024-12-11T20:50:29Z","abstract_excerpt":"In this paper, we provide a mathematical framework for improving generalization in a class of learning problems which is related to point estimations for modeling of high-dimensional nonlinear functions. In particular, we consider a variational problem for a weakly-controlled gradient system, whose control input enters into the system dynamics as a coefficient to a nonlinear term which is scaled by a small parameter. Here, the optimization problem consists of a cost functional, which is associated with how to gauge the quality of the estimated model parameters at a certain fixed final time w.r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.08772","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/2412.08772/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":"2412.08772","created_at":"2026-07-05T09:48:00.440846+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.08772v1","created_at":"2026-07-05T09:48:00.440846+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.08772","created_at":"2026-07-05T09:48:00.440846+00:00"},{"alias_kind":"pith_short_12","alias_value":"KZTLCHSELA5P","created_at":"2026-07-05T09:48:00.440846+00:00"},{"alias_kind":"pith_short_16","alias_value":"KZTLCHSELA5P77CF","created_at":"2026-07-05T09:48:00.440846+00:00"},{"alias_kind":"pith_short_8","alias_value":"KZTLCHSE","created_at":"2026-07-05T09:48:00.440846+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.16521","citing_title":"On characterizing optimal learning trajectories in a class of learning problems","ref_index":1,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KZTLCHSELA5P77CFU5X27HUDD3","json":"https://pith.science/pith/KZTLCHSELA5P77CFU5X27HUDD3.json","graph_json":"https://pith.science/api/pith-number/KZTLCHSELA5P77CFU5X27HUDD3/graph.json","events_json":"https://pith.science/api/pith-number/KZTLCHSELA5P77CFU5X27HUDD3/events.json","paper":"https://pith.science/paper/KZTLCHSE"},"agent_actions":{"view_html":"https://pith.science/pith/KZTLCHSELA5P77CFU5X27HUDD3","download_json":"https://pith.science/pith/KZTLCHSELA5P77CFU5X27HUDD3.json","view_paper":"https://pith.science/paper/KZTLCHSE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.08772&json=true","fetch_graph":"https://pith.science/api/pith-number/KZTLCHSELA5P77CFU5X27HUDD3/graph.json","fetch_events":"https://pith.science/api/pith-number/KZTLCHSELA5P77CFU5X27HUDD3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KZTLCHSELA5P77CFU5X27HUDD3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KZTLCHSELA5P77CFU5X27HUDD3/action/storage_attestation","attest_author":"https://pith.science/pith/KZTLCHSELA5P77CFU5X27HUDD3/action/author_attestation","sign_citation":"https://pith.science/pith/KZTLCHSELA5P77CFU5X27HUDD3/action/citation_signature","submit_replication":"https://pith.science/pith/KZTLCHSELA5P77CFU5X27HUDD3/action/replication_record"}},"created_at":"2026-07-05T09:48:00.440846+00:00","updated_at":"2026-07-05T09:48:00.440846+00:00"}