Convex Sets of Robust Recurrent Neural Networks
Convex Sets of Robust Recurrent Neural Networks
复制标题
鲁棒循环神经网络的凸集
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
I. Manchester
中科院分区：
文献类型：
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作者：
Max Revay;Ruigang Wang;I. Manchester
递归神经网络（RNN）是一类非线性动态系统，通常用于对序列到序列映射进行建模。RNN已被证明具有出色的表达能力，但缺乏安全关键应用所需的稳定性或鲁棒性保证。在本文中，我们制定凸集的RNN保证稳定性和鲁棒性。的保证是使用差分IQC方法，可以确保收缩（所有解决方案的全局指数稳定性）和增量L2增益（学习序列到序列映射的Lipschitz常数）的界限。隐式模型结构被用来构造RNN的联合凸表示及其稳定性或鲁棒性证书。我们证明了所提出的模型结构包括所有以前提出的收缩RNN的凸集作为特例，也包括所有稳定的线性动力系统。我们证明了所提出的模型类的非线性系统识别的背景下的效用。
Recurrent neural networks (RNNs) are a class of nonlinear dynamical systems often used to model sequence-to-sequence maps. RNNs have been shown to have excellent expressive power but lack stability or robustness guarantees that would be necessary for safety-critical applications. In this paper we formulate convex sets of RNNs with guaranteed stability and robustness properties. The guarantees are derived using differential IQC methods and can ensure contraction (global exponential stability of all solutions) and bounds on incremental l2 gain (the Lipschitz constant of the learnt sequence-to-sequence mapping). An implicit model structure is employed to construct a jointly-convex representation of an RNN and its certificate of stability or robustness. We prove that the proposed model structure includes all previously-proposed convex sets of contracting RNNs as special cases, and also includes all stable linear dynamical systems. We demonstrate the utility of the proposed model class in the context of nonlinear system identification.
影响因子：
6.8
作者：
Fazlyab, Mahyar;Morari, Manfred;Pappas, George J.
通讯作者：
Pappas, George J.