{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,26]],"date-time":"2025-11-26T16:30:58Z","timestamp":1764174658251},"reference-count":47,"publisher":"MIT Press - Journals","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2019,6]]},"abstract":"<jats:p> Recurrent neural networks have been extensively studied in the context of neuroscience and machine learning due to their ability to implement complex computations. While substantial progress in designing effective learning algorithms has been achieved, a full understanding of trained recurrent networks is still lacking. Specifically, the mechanisms that allow computations to emerge from the underlying recurrent dynamics are largely unknown. Here we focus on a simple yet underexplored computational setup: a feedback architecture trained to associate a stationary output to a stationary input. As a starting point, we derive an approximate analytical description of global dynamics in trained networks, which assumes uncorrelated connectivity weights in the feedback and in the random bulk. The resulting mean-field theory suggests that the task admits several classes of solutions, which imply different stability properties. Different classes are characterized in terms of the geometrical arrangement of the readout with respect to the input vectors, defined in the high-dimensional space spanned by the network population. We find that such an approximate theoretical approach can be used to understand how standard training techniques implement the input-output task in finite-size feedback networks. In particular, our simplified description captures the local and the global stability properties of the target solution, and thus predicts training performance. <\/jats:p>","DOI":"10.1162\/neco_a_01187","type":"journal-article","created":{"date-parts":[[2019,4,13]],"date-time":"2019-04-13T00:05:57Z","timestamp":1555113957000},"page":"1139-1182","source":"Crossref","is-referenced-by-count":12,"title":["A Geometrical Analysis of Global Stability in Trained Feedback Networks"],"prefix":"10.1162","volume":"31","author":[{"given":"Francesca","family":"Mastrogiuseppe","sequence":"first","affiliation":[{"name":"Laboratoire de Neurosciences Cognitives et Computationelles, INSERM U960, and Laboratoire de Physique Statistique, CNRS UMR 8550, Ecole Normale Sup\u00e9rieure\u2013PSL Research University, Paris 75005, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Srdjan","family":"Ostojic","sequence":"additional","affiliation":[{"name":"Laboratoire de Neurosciences Cognitives et Computationelles, INSERM U960, Ecole Normale Sup\u00e9rieure\u2013PSL Research University, Paris 75005, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"281","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1109\/72.846741"},{"key":"B2","doi-asserted-by":"publisher","DOI":"10.1016\/j.conb.2017.06.003"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.1109\/72.279181"},{"key":"B4","doi-asserted-by":"publisher","DOI":"10.1109\/9.61020"},{"key":"B5","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1003258"},{"key":"B6","author":"Bretscher O.","year":"2009","journal-title":"Linear algebra with applications"},{"key":"B7","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(94)90024-8"},{"key":"B8","first-page":"2777","volume":"6","author":"Doya K.","year":"1992","journal-title":"IEEE Symp. 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