{"paper":{"title":"Local Observability and Moving Horizon Estimation-based Training of Feedforward Neural Networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.SY"],"primary_cat":"eess.SY","authors_text":"Matthias A. M\\\"uller, Victor G. Lopez, Yi Yang","submitted_at":"2026-05-27T19:10:45Z","abstract_excerpt":"In this paper, we propose a moving horizon estimation (MHE)-based training method for feedforward neural networks (FNNs) with rectified linear unit (ReLU) activation functions to determine their ideal weights from a control-theoretic perspective. This allows for a rigorous theoretical analysis of the trained network. First, we reformulate the FNN as a dynamical system with the weights as states. Then, we investigate the local observability of such a system. For two-layer FNNs with fixed output weights, we derive a sufficient condition under which the observability rank condition holds, ensurin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29013","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.29013/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"}