{"paper":{"title":"Meta-stable states in the hierarchical Dyson model drive parallel processing in the hierarchical Hopfield network","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.dis-nn","authors_text":"Adriano Barra, Andrea Galluzzi, Daniele Tantari, Elena Agliari, Flavia Tavani, Francesco Guerra","submitted_at":"2014-07-19T12:05:29Z","abstract_excerpt":"In this paper we introduce and investigate the statistical mechanics of hierarchical neural networks: First, we approach these systems \\`a la Mattis, by thinking at the Dyson model as a single-pattern hierarchical neural network and we discuss the stability of different retrievable states as predicted by the related self-consistencies obtained from a mean-field bound and from a bound that bypasses the mean-field limitation. The latter is worked out by properly reabsorbing fluctuations of the magnetization related to higher levels of the hierarchy into effective fields for the lower levels. Rem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5176","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"}