As a general type of machine learning approach, artificial neural networks have established state-of-art benchmarks in many pattern recognition and data analysis tasks. Among various kinds of neural networks architectures, polynomial neural networks (PNNs) have been recently shown to be analyzable by spectrum analysis via neural tangent kernel, and particularly effective at image generation and face recognition. However, acquiring theoretical insight into the computation and sample complexity of PNNs remains an open problem. In this paper, we extend the analysis in previous literature to PNNs and obtain novel results on sample complexity of PNNs, which provides some insights in explaining the generalization ability of PNNs.

翻译：作为一种一般的机器学习方法,人工神经网络在许多模式识别和数据分析任务中确立了最先进的基准,在各种神经网络结构中,最近通过神经相切内核的频谱分析表明,多元神经网络(PNN)是可分析的,在图像生成和面部识别方面特别有效,然而,从理论上深入了解PNN的计算和样本复杂性仍然是一个尚未解决的问题。在本文件中,我们将先前文献中的分析扩大到PNNN,并获得关于PNN的样本复杂性的新结果,这为解释PNN的通用能力提供了一些见解。