# Hartley Spectral Pooling for Deep Learning

arXiv: https://arxiv.org/abs/1810.04028 · HTML: https://mlsanity.com/paper/1810.04028/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Oct 2018.

## Built on by (most cited first, 6 of 6)

- [Learning strides in convolutional neural networks](https://mlsanity.com/paper/2202.01653/) (2022)
- [Modality specific U-Net variants for biomedical image segmentation: A survey](https://mlsanity.com/paper/2107.04537/) (2021)
- [Maximal function pooling with applications](https://mlsanity.com/paper/2103.01292/) (2021)
- [Exploring Inter-frequency Guidance of Image for Lightweight Gaussian Denoising](https://mlsanity.com/paper/2112.11779/) (2021)
- [Legal-HNet: Mixing Legal Long-Context Tokens with Hartley Transform](https://mlsanity.com/paper/2311.05089/) (2023)
- [Hybrid of DiffStride and Spectral Pooling in Convolutional Neural Networks](https://mlsanity.com/paper/2401.09008/) (2024)

## Abstract (arXiv)

In most convolution neural networks (CNNs), downsampling hidden layers is adopted for increasing computation efficiency and the receptive field size. Such operation is commonly so-called pooling. Maximation and averaging over sliding windows (max/average pooling), and plain downsampling in the form of strided convolution are popular pooling methods. Since the pooling is a lossy procedure, a motivation of our work is to design a new pooling approach for less lossy in the dimensionality reduction. Inspired by the Fourier spectral pooling(FSP) proposed by Rippel et. al. [1], we present the Hartley transform based spectral pooling method in CNNs. Compared with FSP, the proposed spectral pooling avoids the use of complex arithmetic for frequency representation and reduces the computation. Spectral pooling preserves more structure features for network's discriminability than max and average pooling. We empirically show that Hartley spectral pooling gives rise to the convergence of training CNNs on MNIST and CIFAR-10 datasets.