标题： 如何神经网络学习对混沌时间序列进行分类 显示英文标题

标题： How neural networks learn to classify chaotic time series

摘要： 神经网络被越来越多地用于对从物理学到生物学的非线性动态系统进行建模、分析和控制。 由于它们的通用逼近能力，在准确性、计算速度和/或控制能力方面，它们通常优于最先进的模型驱动方法。 另一方面，神经网络经常被视为黑箱，其可解释性受到大量可训练参数的挑战。 在本文中，我们解决了一个重要的问题，即分析训练用于分类规则与混沌时间序列的神经网络的内部工作机制。 这种设置在动力系统中已被广泛研究，使得可以进行彻底的形式分析。 我们特别关注由Boullé等人（2021年）最近引入的一类网络，称为大核卷积神经网络（LKCNN）。 这些非递归网络已被证明在此分类任务中优于其他成熟的架构（例如残差网络、浅层神经网络和全卷积网络）。 此外，它们优于基于李雅普诺夫指数直接重构的“手动”分类方法。 我们发现LKCNN使用输入序列的定性特性。 特别是，我们表明输入周期性和激活周期性之间的关系是LKCNN模型性能的关键。 实际上，表现不佳的模型显示出与随机未训练模型类似的周期性激活。 这可能为事先识别准确性较差的训练模型提供非常一般的标准。 显示英文摘要

摘要： Neural networks are increasingly employed to model, analyze and control non-linear dynamical systems ranging from physics to biology. Owing to their universal approximation capabilities, they regularly outperform state-of-the-art model-driven methods in terms of accuracy, computational speed, and/or control capabilities. On the other hand, neural networks are very often they are taken as black boxes whose explainability is challenged, among others, by huge amounts of trainable parameters. In this paper, we tackle the outstanding issue of analyzing the inner workings of neural networks trained to classify regular-versus-chaotic time series. This setting, well-studied in dynamical systems, enables thorough formal analyses. We focus specifically on a family of networks dubbed Large Kernel Convolutional Neural Networks (LKCNN), recently introduced by Boull\'{e} et al. (2021). These non-recursive networks have been shown to outperform other established architectures (e.g. residual networks, shallow neural networks and fully convolutional networks) at this classification task. Furthermore, they outperform ``manual'' classification approaches based on direct reconstruction of the Lyapunov exponent. We find that LKCNNs use qualitative properties of the input sequence. In particular, we show that the relation between input periodicity and activation periodicity is key for the performance of LKCNN models. Low performing models show, in fact, analogous periodic activations to random untrained models. This could give very general criteria for identifying, a priori, trained models that have poor accuracy.