{"paper":{"title":"Exact ensemble controllability for neural differential equations via neural interpolation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Control, Department of Mathematics, Erlangen, Germany), Lehrstuhl f\\\"ur Dynamics, Machine Learning, Martin Gugat (Friedrich-Alexander-Universit\\\"at Erlangen-N\\\"urnberg (FAU), Numerics","submitted_at":"2026-07-23T09:41:13Z","abstract_excerpt":"We study a system that is governed by neural dynamics. Neural dynamics are a model for deep neural networks with a large number of layers. For a differential equation where the right-hand side is given by a neural network, we analyze the exact ensemble controllability of the system. This property plays an essential role in Machine Learning. It concerns the ability to learn to perform different tasks simultaneously with a single neural dynamics: Exact ensemble controllability requires that $N$ different initial states are steered to corresponding $N$ target states with a single set of control p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.21112","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/2607.21112/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"}