On the Study of Sample Complexity for Polynomial Neural Networks

TL;DR

This paper investigates the sample complexity of polynomial neural networks (PNNs), providing new theoretical insights into their generalization ability and extending existing spectral analysis methods.

Contribution

It extends previous spectral analysis to PNNs and derives novel results on their sample complexity, enhancing understanding of their generalization performance.

Findings

New bounds on sample complexity for PNNs

Insights into PNNs' generalization ability

Extension of spectral analysis methods to PNNs

Abstract

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.