研究循环神经网络动力学的多重可见性图
Multiplex visibility graphs to investigate recurrent neural networks dynamics
摘要：
递归神经网络（RNN）是动力系统的一种通用逼近器，其性能往往依赖于敏感的超参数。调整这样的超参数可能是困难的，并且通常基于试错法。在这项工作中，我们采用了一个基于图的框架来解释和表征内部RNN动态。通过这种洞察力，我们能够设计一种原则性的无监督方法，以获得在预测误差和记忆容量方面具有最大性能的配置。特别是，我们建议建模神经元激活的时间序列与最近推出的水平可见性图，其拓扑性质反映了重要的动力学特征的基础动力系统。接下来，每个图都成为一个更大结构的一层，称为多路复用。我们表明，这样一个多路复用的拓扑性质反映了RNN动力学的重要特征，并用于指导调谐过程。为了验证所提出的方法，我们考虑一类称为回声状态网络的RNN。我们进行实验，并讨论了几个基准和现实世界的呼叫数据记录的数据集的结果。
英文摘要：
A recurrent neural network (RNN) is a universal approximator of dynamical systems, whose performance often depends on sensitive hyperparameters. Tuning of such hyperparameters may be difficult and, typically, based on a trial-and-error approach. In this work, we adopt a graph-based framework to interpret and characterize the internal RNN dynamics. Through this insight, we are able to design a principled unsupervised method to derive configurations with maximized performances, in terms of prediction error and memory capacity. In particular, we propose to model time series of neurons activations with the recently introduced horizontal visibility graphs, whose topological properties reflect important dynamical features of the underlying dynamic system. Successively, each graph becomes a layer of a larger structure, called multiplex. We show that topological properties of such a multiplex reflect important features of RNN dynamics and are used to guide the tuning procedure. To validate the proposed method, we consider a class of RNNs called echo state networks. We perform experiments and discuss results on several benchmarks and real-world dataset of call data records.
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