{"paper":{"title":"Mean Field Theory of Dynamical Systems Driven by External Signals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.AI"],"primary_cat":"nlin.CD","authors_text":"Marc Massar, Serge Massar","submitted_at":"2012-10-31T08:22:48Z","abstract_excerpt":"Dynamical systems driven by strong external signals are ubiquituous in nature and engineering. Here we study \"echo state networks\", networks of a large number of randomly connected nodes, which represent a simple model of a neural network, and have important applications in machine learning. We develop a mean field theory of echo state networks. The dynamics of the network is captured by the evolution law, similar to a logistic map, for a single collective variable. When the network is driven by many independent external signals, this collective variable reaches a steady state. But when the ne"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.8260","kind":"arxiv","version":2},"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"}