{"paper":{"title":"Semi-supervised Hopfield model: Theoretical and Numerical results","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"Andrea Ladiana, Andrea Lepre, Linda Albanese","submitted_at":"2026-07-30T13:10:05Z","abstract_excerpt":"In the daily practice of Machine Learning, fully labeled datasets are a luxury: labels demand expensive and time-consuming human annotation, whereas raw, unlabeled data can be harvested automatically and in bulk. Semi-supervised learning, where the network jointly exploits the few labeled and the many unlabeled examples at its disposal, is the standard answer to this asymmetry, yet a statistical mechanical theory of semi-supervised Hebbian learning is still lacking. In this paper we fill this gap for the Hopfield network: we prescribe a synaptic coupling given by the convex combination, weight"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28173","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/2607.28173/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"}