{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T08:11:14Z","timestamp":1778746274409,"version":"3.51.4"},"reference-count":28,"publisher":"MIT Press - Journals","issue":"7","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2016,7]]},"abstract":"<jats:p>This letter addresses the reservoir design problem in the context of delay-based reservoir computers for multidimensional input signals, parallel architectures, and real-time multitasking. First, an approximating reservoir model is presented in those frameworks that provides an explicit functional link between the reservoir architecture and its performance in the execution of a specific task. Second, the inference properties of the ridge regression estimator in the multivariate context are used to assess the impact of finite sample training on the decrease of the reservoir capacity. Finally, an empirical study is conducted that shows the adequacy of the theoretical results with the empirical performances exhibited by various reservoir architectures in the execution of several nonlinear tasks with multidimensional inputs. Our results confirm the robustness properties of the parallel reservoir architecture with respect to task misspecification and parameter choice already documented in the literature.<\/jats:p>","DOI":"10.1162\/neco_a_00845","type":"journal-article","created":{"date-parts":[[2016,5,12]],"date-time":"2016-05-12T21:17:01Z","timestamp":1463087821000},"page":"1411-1451","source":"Crossref","is-referenced-by-count":15,"title":["Nonlinear Memory Capacity of Parallel Time-Delay Reservoir Computers in the Processing of Multidimensional Signals"],"prefix":"10.1162","volume":"28","author":[{"given":"Lyudmila","family":"Grigoryeva","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Universit\u00e4t Konstanz, D-78467 Konstanz, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Julie","family":"Henriques","sequence":"additional","affiliation":[{"name":"Methodology and Quality of Life in Oncology Unit, CHRU Besan\u00e7on, F-25000 Besan\u00e7on, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Laurent","family":"Larger","sequence":"additional","affiliation":[{"name":"FEMTO-ST, UMR CNRS 6174, University Bourgogne Franche-Comt\u00e9, F-25030 Besan\u00e7on cedex, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juan-Pablo","family":"Ortega","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Statistics, Universit\u00e4t Sankt Gallen, CH-9000, Sankt Gallen, Switzerland, and Centre National de la Recherche Scientifique, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"281","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms1476"},{"key":"B2","doi-asserted-by":"publisher","DOI":"10.1109\/72.846741"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms2368"},{"key":"B4","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2006.10.148"},{"key":"B5","doi-asserted-by":"publisher","DOI":"10.1063\/1.3492712"},{"key":"B6","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2014.03.004"},{"issue":"12858","key":"B7","first-page":"1","volume":"5","author":"Grigoryeva L.","year":"2015","journal-title":"Scientific Reports"},{"key":"B8","author":"Grigoryeva L.","year":"2016","journal-title":"Singular ridge regression with homoscedastic residuals: Generalization error with estimated parameters"},{"key":"B9","author":"Gupta A.","year":"2000","journal-title":"Matrix variate distributions"},{"key":"B10","doi-asserted-by":"crossref","DOI":"10.1515\/9780691218632","author":"Hamilton J. 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