回声状态网络的分形维数分析
Analyzing Echo-state Networks Using Fractal Dimension
摘要：
这项工作加入了水库优化，信息理论的最佳编码，并在其中心分形分析方面。我们建立在观察，由于递归神经网络的递归性质，输入序列出现在其隐藏状态表示的分形图案。这些图案的分形维数低于储层中的单元数。我们展示了这种分形维数在优化递归神经网络初始化方面的潜在用途。我们连接的想法“理想”水库无损最佳编码使用算术编码器。我们的研究表明，从输入到隐藏状态的映射的分形维数应接近网络中的单元数。分形维数和网络连通性之间的这种联系是递归神经网络初始化和储备池计算的一个有趣的新方向。
英文摘要：
This work joins aspects of reservoir optimization, information-theoretic optimal encoding, and at its center fractal analysis. We build on the observation that, due to the recursive nature of recurrent neural networks, input sequences appear as fractal patterns in their hidden state representation. These patterns have a fractal dimension that is lower than the number of units in the reservoir. We show potential usage of this fractal dimension with regard to optimization of recurrent neural network initialization. We connect the idea of `ideal' reservoirs to lossless optimal encoding using arithmetic encoders. Our investigation suggests that the fractal dimension of the mapping from input to hidden state shall be close to the number of units in the network. This connection between fractal dimension and network connectivity is an interesting new direction for recurrent neural network initialization and reservoir computing.
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