{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:LTM75RXSVRNBORRCC7DUHKYHGN","short_pith_number":"pith:LTM75RXS","schema_version":"1.0","canonical_sha256":"5cd9fec6f2ac5a17462217c743ab073359e6e4492b81b96060902086c343f52a","source":{"kind":"arxiv","id":"2307.14528","version":1},"attestation_state":"computed","paper":{"title":"Function Value Learning: Adaptive Learning Rates Based on the Polyak Stepsize and Function Splitting in ERM","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Fabian Schaipp, Guillaume Garrigos, Robert M. Gower","submitted_at":"2023-07-26T22:12:31Z","abstract_excerpt":"Here we develop variants of SGD (stochastic gradient descent) with an adaptive step size that make use of the sampled loss values. In particular, we focus on solving a finite sum-of-terms problem, also known as empirical risk minimization. We first detail an idealized adaptive method called $\\texttt{SPS}_+$ that makes use of the sampled loss values and assumes knowledge of the sampled loss at optimality. This $\\texttt{SPS}_+$ is a minor modification of the SPS (Stochastic Polyak Stepsize) method, where the step size is enforced to be positive. We then show that $\\texttt{SPS}_+$ achieves the be"},"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":"2307.14528","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-07-26T22:12:31Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"8115fa6a4c4aefafc565ff6df0796ff40f08291b95ed8562f02c4bb9a849a5ae","abstract_canon_sha256":"b170b073965a2aa59629253a66a6a410049af65e787b79d081f27e9d779379e0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:35:14.358310Z","signature_b64":"QykGWtt9poydMl/VQ9MQk0MjUpfOw4VHVKL296jY/wLRQNgQt5lDRTuno89jGrYCWI6nuvbMlhYTGkXd3NL3Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cd9fec6f2ac5a17462217c743ab073359e6e4492b81b96060902086c343f52a","last_reissued_at":"2026-07-05T06:35:14.357900Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:35:14.357900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Function Value Learning: Adaptive Learning Rates Based on the Polyak Stepsize and Function Splitting in ERM","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Fabian Schaipp, Guillaume Garrigos, Robert M. Gower","submitted_at":"2023-07-26T22:12:31Z","abstract_excerpt":"Here we develop variants of SGD (stochastic gradient descent) with an adaptive step size that make use of the sampled loss values. In particular, we focus on solving a finite sum-of-terms problem, also known as empirical risk minimization. We first detail an idealized adaptive method called $\\texttt{SPS}_+$ that makes use of the sampled loss values and assumes knowledge of the sampled loss at optimality. This $\\texttt{SPS}_+$ is a minor modification of the SPS (Stochastic Polyak Stepsize) method, where the step size is enforced to be positive. We then show that $\\texttt{SPS}_+$ achieves the be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.14528","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/2307.14528/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":"2307.14528","created_at":"2026-07-05T06:35:14.357959+00:00"},{"alias_kind":"arxiv_version","alias_value":"2307.14528v1","created_at":"2026-07-05T06:35:14.357959+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.14528","created_at":"2026-07-05T06:35:14.357959+00:00"},{"alias_kind":"pith_short_12","alias_value":"LTM75RXSVRNB","created_at":"2026-07-05T06:35:14.357959+00:00"},{"alias_kind":"pith_short_16","alias_value":"LTM75RXSVRNBORRC","created_at":"2026-07-05T06:35:14.357959+00:00"},{"alias_kind":"pith_short_8","alias_value":"LTM75RXS","created_at":"2026-07-05T06:35:14.357959+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.01827","citing_title":"Adaptive Sharpness-Aware Minimization with a Polyak-type Step size: A Theory-Grounded Scheduler","ref_index":4,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LTM75RXSVRNBORRCC7DUHKYHGN","json":"https://pith.science/pith/LTM75RXSVRNBORRCC7DUHKYHGN.json","graph_json":"https://pith.science/api/pith-number/LTM75RXSVRNBORRCC7DUHKYHGN/graph.json","events_json":"https://pith.science/api/pith-number/LTM75RXSVRNBORRCC7DUHKYHGN/events.json","paper":"https://pith.science/paper/LTM75RXS"},"agent_actions":{"view_html":"https://pith.science/pith/LTM75RXSVRNBORRCC7DUHKYHGN","download_json":"https://pith.science/pith/LTM75RXSVRNBORRCC7DUHKYHGN.json","view_paper":"https://pith.science/paper/LTM75RXS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2307.14528&json=true","fetch_graph":"https://pith.science/api/pith-number/LTM75RXSVRNBORRCC7DUHKYHGN/graph.json","fetch_events":"https://pith.science/api/pith-number/LTM75RXSVRNBORRCC7DUHKYHGN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LTM75RXSVRNBORRCC7DUHKYHGN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LTM75RXSVRNBORRCC7DUHKYHGN/action/storage_attestation","attest_author":"https://pith.science/pith/LTM75RXSVRNBORRCC7DUHKYHGN/action/author_attestation","sign_citation":"https://pith.science/pith/LTM75RXSVRNBORRCC7DUHKYHGN/action/citation_signature","submit_replication":"https://pith.science/pith/LTM75RXSVRNBORRCC7DUHKYHGN/action/replication_record"}},"created_at":"2026-07-05T06:35:14.357959+00:00","updated_at":"2026-07-05T06:35:14.357959+00:00"}