Lyapunov exponent analysis for multilayer neural networks
Lyapunov exponent analysis for multilayer neural networks
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DOI：
10.1587/nolta.12.674
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Misaki Kondo;S. Sunada;T. Niiyama
中科院分区：
文献类型：
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作者：
Misaki Kondo;S. Sunada;T. Niiyama
多层神经网络可以看作是一类离散时间动力系统，因为层与层之间的信息传播可以表示为特定动力系统的时间演化。在这项研究中，我们用finite-time最大Lyapunov指数研究了经典fi阳离子问题多层神经网络的信息传播的稳定性，并讨论了多层神经网络如何对输入进行分类。本文的动态稳定性分析揭示了训练好的多层神经网络的输入相关稳定性。对多层神经网络进行训练，使得信息传播对Classifi决策边界附近的输入数据向量高度敏感，而对远离决策边界的输入数据向量不那么敏感。这意味着经典fi阳离子问题的决策边界是一个信息传播的fi时间最大Lyapunov指数较大的集合。这些结果为用多层神经网络估计经典ff阳离子的不确定度提供了一个新的视角。
: A multilayer neural network can be regarded as a type of discrete-time dynamical system in the sense that layer-to-layer information propagation can be expressed as the time evolution of a particular dynamical system. In this study, we investigate the stability of information propagation in multilayer neural networks for classification problems using finite-time maximum Lyapunov exponents, and we discuss how multilayer neural networks classify inputs. The dynamical stability analysis in this study reveals the input-dependent stability of trained multilayer neural networks. Multilayer neural networks are trained such that the information propagation is highly sensitive to input data vectors near a decision boundary for classification whereas it is less sensitive to input data vectors far from the decision boundary. This implies that the decision boundary in classification problems is characterized by a set where the finite-time maximum Lyapunov exponents of the information propagation are relatively large. These results offer a new perspective on the estimation of uncertainty of classification using multilayer neural networks.