# On the Study of Sample Complexity for Polynomial Neural Networks

arXiv: https://arxiv.org/abs/2207.08896 · HTML: https://mlsanity.com/paper/2207.08896/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 14 references that are in the map.
- First posted on arXiv 18 Jul 2022.

## Builds on (most cited first, 10 of 10)

- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Norm-Based Capacity Control in Neural Networks](https://mlsanity.com/paper/1503.00036/) (2015)
- [Size-Independent Sample Complexity of Neural Networks](https://mlsanity.com/paper/1712.06541/) (2017)
- [Training Graph Neural Networks with 1000 Layers](https://mlsanity.com/paper/2106.07476/) (2021)
- [On the Power of Over-parametrization in Neural Networks with Quadratic Activation](https://mlsanity.com/paper/1803.01206/) (2018)
- [On the Computational Efficiency of Training Neural Networks](https://mlsanity.com/paper/1410.1141/) (2014)
- [Pi-nets: Deep Polynomial Neural Networks](https://mlsanity.com/paper/2003.03828/) (2020)
- [The Spectral Bias of Polynomial Neural Networks](https://mlsanity.com/paper/2202.13473/) (2022)
- [Controlling the Complexity and Lipschitz Constant improves polynomial nets](https://mlsanity.com/paper/2202.05068/) (2022)

## Built on by (most cited first, 1 of 1)

- [Regularization of polynomial networks for image recognition](https://mlsanity.com/paper/2303.13896/) (2023)

## Abstract (arXiv)

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.