{"paper":{"title":"Empirical Analysis of the Necessary and Sufficient Conditions of the Echo State Property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.NE","authors_text":"Sebasti\\'an Basterrech","submitted_at":"2017-03-20T10:49:36Z","abstract_excerpt":"The Echo State Network (ESN) is a specific recurrent network, which has gained popularity during the last years. The model has a recurrent network named reservoir, that is fixed during the learning process. The reservoir is used for transforming the input space in a larger space. A fundamental property that provokes an impact on the model accuracy is the Echo State Property (ESP). There are two main theoretical results related to the ESP. First, a sufficient condition for the ESP existence that involves the singular values of the reservoir matrix. Second, a necessary condition for the ESP. The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06664","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"}