Journal
NEURAL NETWORKS
Volume 83, Issue -, Pages 11-20Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.neunet.2016.07.007
Keywords
Recurrent networks; Linear dynamical systems; Over-actuated systems; Sparse input; l(1) minimization
Funding
- Burroughs-Wellcome Fund
- US Air Force Office of Scientific Research [AFOSR 15RT0189]
- US National Science Foundation [NSF ECCS 1509342, NSF CMMI 1537015]
- Div Of Civil, Mechanical, & Manufact Inn
- Directorate For Engineering [1537015] Funding Source: National Science Foundation
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In this paper, we study how the dynamics of recurrent networks, formulated as general dynamical systems, mediate the recovery of sparse, time-varying signals. Our formulation resembles the well described problem of compressed sensing, but in a dynamic setting. We specifically consider the problem of recovering a high-dimensional network input, over time, from observation of only a subset of the network states (i.e., the network output). Our goal is to ascertain how the network dynamics may enable recovery, even if classical methods fail at each time instant. We are particularly interested in understanding performance in scenarios where both the input and output are corrupted by disturbance and noise, respectively. Our main results consist of the development of analytical conditions, including a generalized observability criterion, that ensure exact and stable input recovery in a dynamic, recurrent network setting. (C) 2016 Elsevier Ltd. All rights reserved.
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