{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FA4DDW6AVBERIE4XM4MEOVPNYF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"692633a0654454bc7fe184790956da8839e1b0a81d0d7fcc9968794c1cb58bbf","cross_cats_sorted":["cs.DM","math.AC","math.RA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2018-03-14T13:09:35Z","title_canon_sha256":"11fc50a7fbb4d2f3e002e0fc9d6ddc6c0d455af3513ce2176fd4c666dc2f2291"},"schema_version":"1.0","source":{"id":"1803.05252","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.05252","created_at":"2026-05-18T00:20:55Z"},{"alias_kind":"arxiv_version","alias_value":"1803.05252v2","created_at":"2026-05-18T00:20:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.05252","created_at":"2026-05-18T00:20:55Z"},{"alias_kind":"pith_short_12","alias_value":"FA4DDW6AVBER","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"FA4DDW6AVBERIE4X","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"FA4DDW6A","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:6c0225c01878e10e5d63fab39e2d67f0aeba814cf2c8094467e9193d907fe760","target":"graph","created_at":"2026-05-18T00:20:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Machine learning algorithms use error function minimization to fit a large set of parameters in a preexisting model. However, error minimization eventually leads to a memorization of the training dataset, losing the ability to generalize to other datasets. To achieve generalization something else is needed, for example a regularization method or stopping the training when error in a validation dataset is minimal. Here we propose a different approach to learning and generalization that is parameter-free, fully discrete and that does not use function minimization. We use the training data to fin","authors_text":"Fernando Martin-Maroto, Gonzalo G. de Polavieja","cross_cats":["cs.DM","math.AC","math.RA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2018-03-14T13:09:35Z","title":"Algebraic Machine Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05252","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:41e7f7664cb922b18733022a323e3980903129bf546345a5f4ad88f369eea5e6","target":"record","created_at":"2026-05-18T00:20:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"692633a0654454bc7fe184790956da8839e1b0a81d0d7fcc9968794c1cb58bbf","cross_cats_sorted":["cs.DM","math.AC","math.RA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2018-03-14T13:09:35Z","title_canon_sha256":"11fc50a7fbb4d2f3e002e0fc9d6ddc6c0d455af3513ce2176fd4c666dc2f2291"},"schema_version":"1.0","source":{"id":"1803.05252","kind":"arxiv","version":2}},"canonical_sha256":"283831dbc0a84914139767184755edc1612862362ad800143dc441eb166b9ebb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"283831dbc0a84914139767184755edc1612862362ad800143dc441eb166b9ebb","first_computed_at":"2026-05-18T00:20:55.447921Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:55.447921Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E6SYT/PqP760M6lHvcnE2bCQxnkBzsoSyjUhUbPcLsNzhMpJRjtWtwlbTy0IECM9uqLZ2z5DJ6eVrTOnAfWOBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:55.448607Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.05252","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41e7f7664cb922b18733022a323e3980903129bf546345a5f4ad88f369eea5e6","sha256:6c0225c01878e10e5d63fab39e2d67f0aeba814cf2c8094467e9193d907fe760"],"state_sha256":"0f99093bd4a4f51b2493988e38d990e09041affe6c3c5a49d299f2a4cfadb693"}