It is desirable for statistical models to detect signals of interest independently of their position. If the data is generated by some smooth process, this additional structure should be taken into account. We introduce a new class of neural networks that are shift invariant and preserve smoothness of the data: functional neural networks (FNNs). For this, we use methods from functional data analysis (FDA) to extend multi-layer perceptrons and convolutional neural networks to functional data. We propose different model architectures, show that the models outperform a benchmark model from FDA in terms of accuracy and successfully use FNNs to classify electroencephalography (EEG) data.

翻译：统计模型能够独立于信号位置检测感兴趣信号是理想特性。当数据由某种平滑过程生成时，这种附加结构应被纳入考量。我们提出一类兼具平移不变性并保持数据平滑性的新型神经网络：功能神经网络（FNNs）。为此，我们采用函数型数据分析（FDA）方法，将多层感知机与卷积神经网络扩展至函数型数据。我们设计了多种模型架构，实验表明这些模型在精度上优于FDA基准模型，并成功将FNNs应用于脑电图（EEG）数据的分类任务。