{"paper":{"title":"Thermodynamic limit in learning period three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","nlin.AO","nlin.CD"],"primary_cat":"stat.ML","authors_text":"Kohei Nakajima, Yuichiro Terasaki","submitted_at":"2024-05-12T17:57:25Z","abstract_excerpt":"A continuous one-dimensional map with period three includes all periods. This raises the following question: Can we obtain any types of periodic orbits solely by learning three data points? In this paper, we report the answer to be yes. Considering a random neural network in its thermodynamic limit, we first show that almost all learned periods are unstable, and each network has its own characteristic attractors (which can even be untrained ones). The latently acquired dynamics, which are unstable within the trained network, serve as a foundation for the diversity of characteristic attractors "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.08825","kind":"arxiv","version":4},"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/2405.08825/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"}