{"paper":{"title":"Z(2) Gauge Neural Network and its Phase Structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-lat"],"primary_cat":"cond-mat.dis-nn","authors_text":"Tetsuo Matsui, Yuki Nakano, Yusuke Takafuji","submitted_at":"2012-06-06T02:36:06Z","abstract_excerpt":"We study general phase structures of neural-network models that have Z(2) local gauge symmetry. The Z(2) spin variable Si = \\pm1 on the i-th site describes a neuron state as in the Hopfield model, and the Z(2) gauge variable Jij = \\pm1 describes a state of the synaptic connection between j-th and i-th neurons. The gauge symmetry allows for a self-coupling energy among Jij's such as JijJjkJki, which describes reverberation of signals. Explicitly, we consider the three models; (I) annealed model with full and partial connections of Jij, (II) quenched model with full connections where Jij is trea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1110","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":""},"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"}