Paper:
Global Gated Mixture of Second-order Pooling for Improving Deep Convolutional Neural Networks
In most of existing deep convolutional neural networks (CNNs) for classification, global average (first-order) pooling (GAP) has become a standard module to summarize activations of the last convolution layer as final representation for prediction. Recent researches show integration of higher-order pooling (HOP) methods clearly improves performance of deep CNNs. However, both GAP and existing HOP methods assume unimodal distributions, which cannot fully capture statistics of convolutional activations, limiting representation ability of deep CNNs, especially for samples with complex contents. To overcome the above limitation, this paper proposes a global Gated Mixture of Second-order Pooling (GM-SOP) method to further improve representation ability of deep CNNs. To this end, we introduce a sparsity-constrained gating mechanism and propose a novel parametric SOP as component of mixture model. Given a bank of SOP candidates, our method can adaptively choose Top-K(K > 1) candidates for each input sample through the sparsity-constrained gating module, and performs weighted sum of outputs of K selected candidates as representation of the sample. The proposed GM-SOP can flexibly accommodate a large number of personalized SOP candidates in an efficient way, leading to richer representations. The deep networks with our GM-SOP can be end-to-end trained, having potential to characterize complex, multi-modal distributions. The proposed method is evaluated on two large scale image benchmarks (i.e., downsampled ImageNet-1K and Places365), and experimental results show our GM-SOP is superior to its counterparts and achieves very competitive performance. The source code will be available at http://www.peihuali.org/GM-SOP.

Review:
The idea behind a Sparse Gated Mixture (GM) of Expert model has already been proposed in [1]. The main novelty of this paper is in the way the sparse mixture model is applied, namely to modify the 2nd order pooling layer within a deep CNN model to have a bank of candidates. The way GM works is as follow: Given an input sample, the sparsity-constrained gating module adaptively selects Top-K experts from N candidates according to assigned weights and outputs the weighted sum of the outputs of the K selected experts.  Another contribution of this paper is to define a parameterized architecture for pooling: For the choice of expert, the authors use a modified learnable version of matrix square-root normalized second-order pooling (SR-SOP) [2] .  --------------- The idea of using sparsely gated experts is very promising and finding new ways to apply it within model architectures, as it is the case in this work, is important.  The experiments first show that SR-SOP is advantageous over regular SOP, both are prior work, but it's good to justify why use SR-SOP in the first place. It then shows results on the new parameterized version (which slightly improves results) and then results on adding the GM which makes 2+% overall improvements.  While the presented results show advantage of this method, the experiments could be stronger and more convincing. A down-sampled ImageNet is used as dataset and a modified ResNet is used for baseline. Why not experimenting with the standard-size ImageNet, or CIFAR10-100 datasets (especially, if choosing to go with a smaller size image)? Much more research has been done on these 2 datasets and improving over those strong baselines would be a much more convincing result.    Have the authors tried increasing the number of CMs (component modules, aka experts) to multiple hundreds or thousands, to see the limit of adding capacity to the model? The maximum # of CMs in this paper is 32 and it looks like the best overall result is achieved with that many CMs. In a prior work [1], some of the best results are achieved by having 1-2k experts.    [1] N. Shazeer, A. Mirhoseini, K. Maziarz, A. Davis, Q. V. Le, G. E. Hinton, and J. Dean. Outrageously large neural networks: The sparsely-gated mixture-of-experts layer. In ICLR, 2017. [2] P. Li, J. Xie, Q. Wang, and W. Zuo. Is second-order information helpful for large-scale visual recognition? In ICCV, 2017