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首页> 外文期刊>Neural Networks and Learning Systems, IEEE Transactions on >Nonlinear System Modeling With Random Matrices: Echo State Networks Revisited
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Nonlinear System Modeling With Random Matrices: Echo State Networks Revisited

机译：带有随机矩阵的非线性系统建模：再探回声状态网络

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摘要

Echo state networks (ESNs) are a novel form of recurrent neural networks (RNNs) that provide an efficient and powerful computational model approximating nonlinear dynamical systems. A unique feature of an ESN is that a large number of neurons (the “reservoir”) are used, whose synaptic connections are generated randomly, with only the connections from the reservoir to the output modified by learning. Why a large randomly generated fixed RNN gives such excellent performance in approximating nonlinear systems is still not well understood. In this brief, we apply random matrix theory to examine the properties of random reservoirs in ESNs under different topologies (sparse or fully connected) and connection weights (Bernoulli or Gaussian). We quantify the asymptotic gap between the scaling factor bounds for the necessary and sufficient conditions previously proposed for the echo state property. We then show that the state transition mapping is contractive with high probability when only the necessary condition is satisfied, which corroborates and thus analytically explains the observation that in practice one obtains echo states when the spectral radius of the reservoir weight matrix is smaller than 1.
机译：回声状态网络（ESN）是递归神经网络（RNN）的一种新颖形式，它提供了逼近非线性动力学系统的高效且强大的计算模型。 ESN的独特功能是使用了大量的神经元（“储存器”），它们的突触连接是随机生成的，只有从储存器到输出的连接通过学习来修改。为什么大型随机生成的固定RNN在逼近非线性系统中具有如此出色的性能，人们仍然不甚了解。在本文中，我们应用随机矩阵理论来研究不同拓扑结构（稀疏或完全连接）和连接权重（伯努利或高斯）下ESN中随机油藏的性质。我们量化缩放系数范围之间的渐进间隙，用于先前为回波状态属性建议的必要条件和充分条件。然后我们表明，仅满足必要条件时，状态转换映射具有较高的收缩率，这印证了这一点，从而分析性地解释了以下观察结果：在实践中，当储层权重矩阵的光谱半径小于1时，人们会获得回波状态。

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