# Convolutional Neural Networks: A Roundup and Benchmark of Their Pooling Layer Variants
## 3 Putting the Methods to the Test  
### The Benchmark Setup  
In order to choose the optimal architecture and datasets to use for our benchmark, Table 3 was compiled. which summarizes what was used for each method in the corresponding paper.  
It seems that less-potent architectures are preferred in most cases. This is probably because they usually achieve a lower overall performance, but that also means that the impact of changing the pooling layer will be better highlighted. Thus, a similar model was chosen, a LeNet5 architecture with 2 convolution layers, 2 respective interchangeable pooling layers, and 2 fully connected layers, as shown in Figure 6.  
Regarding the datasets, the MNIST, CIFAR10, and CIFAR100 were used, since it seems from Table 3 that these are commonly used in the reviewed papers. They are also ideal since we had to make sure they were interchangeable for the exact same architecture without changes to the fully connected layer(s), just by modifying the total output class parameter.  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Method** & **Model(s)** & **Datasets** \\ \hline Fractional Max [15] & Custom CNN & CIFAR-10, CIFAR-100, MNIST, CASIA-OLHWDB1.1 \\ Row-wise Max [16] & Custom CNN & ModelNet-10, ModelNet-40 \\ Rank-based [18] & Custom CNN & MNIST, CIFAR-10, CIFAR-100, NORB \\ Mixed [19] & Custom CNN & MNIST, CIFAR-10, CIFAR-100, SVHN \\ Gated [19] & Custom CNN & MNIST, CIFAR-10, CIFAR-100, SVHN \\ Tree [19] & Custom CNN & MNIST, CIFAR-10, CIFAR-100, SVHN \\ LP [20] & Custom CNN & SVHN \\ Stochastic [22] & Custom CNN & MNIST, CIFAR-10, CIFAR-100, SVHN \\ Spatial pyramid [24] & ZF-5, Convnet-5, Overfeat-5/7 & VOC 2007, Caltech 101, ILSVRC 2014, ImageNet 2012 \\ Per-pixel pyramid [26] & Custom CNN & Middlebury benchmark “training dense” [42] \\ Fuzzy [27] & LeNet & MNIST, Fashion-MNIST, CIFAR-10 \\ Overlapping [28] & Custom CNN & ILSVRC 2012/2013, ImageNet2012 \\ Super-pixel [29] & VoxResNet & IBSR, Cityscapes \\ Spectral [30] & Custom CNN & CIFAR-10, CIFAR-100 \\ Wavelet [32] & MatConvNet [43] & MNIST, CIFAR-10, SVHN, KDEF \\ Weighted [21] & Custom CNN & CIFAR-10, MNIST, PASCAL VOC 2007 \\ Intermap [33] & Custom CNN & Switchboard-I Release 2 \\ Strided convolution [34] & VGG11-19, & GoogleNet, \\  & SqueezeNet & ILSVRC 2014, ILSVRC 2012 \\ Center [35] & CenterNet & MS-COCO \\ Corner [36] & CornerNet & MS-COCO \\ Cascade corner [35] & Cascade R-CNN & MS-COCO \\ Adaptive feature [38] & Mask R-CNN (/w Caffe) & MS-COCO, Cityscapes, MVD \\ Local-importance-based [39] & ResNet, DenseNet & MS-COCO, ImageNet 1K \\ Soft [41] & ResNet, DenseNet, ResNeXt, InceptionV1 & ImageNet 1K, DIV2K, Urban 100, Manga 109, Flicker 2K, ImageNet 1K, HACS, Kinetics-700, UCF-101 \\ \hline \hline \end{tabular}
\end{table}
Table 3: A cumulative table of models and datasets used in each method’s publication.  
Figure 6: The CNN architecture used for the tests.  
Lastly, we focused on testing pooling methods that can be used as a direct drop-in replacement for the Max pooling layer, with a kernel size and stride of size 2, in order to reduce each dimension by half--applying parameters that would provide similar results wherever required (like a 0.5 scaling factor, for instance, for the spectral pooling layer). Stochastic gradient descent was used as an optimizer, with a learning rate of 0.01 and momentum of 0.9 over 300 epochs.