Published as a conference paper at ICLR 2018 WAVELET POOLING FOR CONVOLUTIONAL NEURAL NETWORKS
Convolutional Neural Networks continuously advance the progress of 2D and 3D image and object classification. The steadfast usage of this algorithm requires constant evaluation and upgrading of foundational concepts to maintain progress. Network regularization techniques typically focus on convolutional layer operations, while leaving pooling layer operations without suitable options. We introduce Wavelet Pooling as another alternative to traditional neighborhood pooling. This method decomposes features into a second level decomposition, and discards the first-level subbands to reduce feature dimensions. This method addresses the overfitting problem encountered by max pooling, while reducing features in a more structurally compact manner than pooling via neighborhood regions. Experimental results on four benchmark classification datasets demonstrate our proposed method outperforms or performs comparatively with methods like max, mean, mixed, and stochastic pooling.
The paper proposes "wavelet pooling" as an alternative for traditional subsampling methods, e.g. max/average/global pooling, etc., within convolutional neural networks. 
Experiments on the MNIST, CIFAR-10, SHVN and KDEF datasets, shows the proposed wavelet-based method has
competitive performance with existing methods while still being able to address the overfitting behavior of max pooling.
Strong points
- The method is sound and well motivated.
- The proposes method achieves competitive performance.
Weak points
- No information about added computational costs is given.
- Experiments are conducted in relatively low-scale datasets.
Overall the method is well presented and properly motivated. The paper as a good flow and is easy to follow. The authors effectively demonstrate with few toy examples the weaknesses of traditional methods, i.e max pooling and average pooling. Moreover, their extended evaluation on several datasets show the performance of the proposed method in different scenarios.
My main concerns with the manuscript are the following.
Compared to traditional methods, the proposed methods seems to require higher computation costs. In a deep neural network setting where operations are conducted a large number of times, this is a of importance. However, no indication is given on what are the added computation costs of the proposed method and how that compares to existing methods. A comparison on that regard would strengthen the paper.
In many of the experiments, the manuscript stresses the overfitting behavior of max pooling. This makes me wonder whether this is caused by the fact that experiments are conducted or relatively smaller datasets. While the currently tested datasets are a good indication of the performance of the proposed method, an evaluation on a large scale scenario, e.g. ILSVRC'12, could solidify the message sent by this manuscript. Moreover, it would increase the relevance of this work in the computer vision community.
Finally, related to the presentation, I would recommend presenting the plots, i.e. Fig. 8,10,12,14, for the training and validation image subsets in two separate plots. Currently, results for training and validation sets are mixed in the same plot, and due to the clutter it is not possible to see the trends clearly.
Similarly, I would recommend referring to the Tables added in the paper when discussing the performance of the proposed method w.r.t. traditional alternatives.
I encourage the authors to address my concerns in their rebuttal