Pooling is one of the main elements in convolutional neural networks. The pooling reduces the size of the feature map, enabling training and testing with a limited amount of computation. This paper proposes a new pooling method named universal pooling. Unlike the existing pooling methods such as average pooling, max pooling, and stride pooling with fixed pooling function, universal pooling generates any pooling function, depending on a given problem and dataset. Universal pooling was inspired by attention methods and can be considered as a channel-wise form of local spatial attention. Universal pooling is trained jointly with the main network and it is shown that it includes the existing pooling methods. Finally, when applied to two benchmark problems, the proposed method outperformed the existing pooling methods and performed with the expected diversity, adapting to the given problem.
Max pooling divides the feature map into blocks and collects the maximum feature value in each block into a smaller output matrix. Max pooling is commonly used between convolution layers and is employed in AlexNet @cite_4 and VGG @cite_7 . Average pooling operates similarly to max pooling, but outputs the average of each block in the feature map. Global average pooling (GAP), which applies average pooling over the entire feature map, is commonly used in convolutional networks such as ResNet @cite_13 and DenseNet @cite_1 . In DenseNet, average pooling is applied between the convolution layers. Meanwhile, stride pooling is equivalent to importing values from a fixed position after convoluting across the entire area. This approach is adopted in ResNet.
@cite_13 @cite_1 @cite_4 @cite_7
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Deep neural networks with alternating convolutional, max-pooling and decimation layers are widely used in state of the art architectures for computer vision. Max-pooling purposefully discards precise spatial information in order to create features that are more robust, and typically organized as lower resolution spatial feature maps. On some tasks, such as whole-image classification, max-pooling derived features are well suited, however, for tasks requiring precise localization, such as pixel level prediction and segmentation, max-pooling destroys exactly the information required to perform well. Precise localization may be preserved by shallow convnets without pooling but at the expense of robustness. Can we have our max-pooled multilayered cake and eat it too? Several papers have proposed summation and concatenation based methods for combining upsampled coarse, abstract features with finer features to produce robust pixel level predictions. Here we introduce another model — dubbed Recombinator Networks — where coarse features inform finer features early in their formation such that finer features can make use of several layers of computation in deciding how to use coarse features. The model is trained once, end-to-end and performs better than summation-based architectures, reducing the error from the previous state of the art on two facial keypoint datasets, AFW and AFLW, by 30 and beating the current state-of-the-art on 300W without using extra data. We improve performance even further by adding a denoising prediction model based on a novel convnet formulation. Feature pooling layers (e.g., max pooling) in convolutional neural networks (CNNs) serve the dual purpose of providing increasingly abstract representations as well as yielding computational savings in subsequent convolutional layers. We view the pooling operation in CNNs as a two step procedure: first, a pooling window (e.g., 2&#xd7; 2) slides over the feature map with stride one which leaves the spatial resolution intact, and second, downsampling is performed by selecting one pixel from each non-overlapping pooling window in an often uniform and deterministic (e.g., top-left) manner. Our starting point in this work is the observation that this regularly spaced downsampling arising from non-overlapping windows, although intuitive from a signal processing perspective (which has the goal of signal reconstruction), is not necessarily optimal for learning (where the goal is to generalize). We study this aspect and propose a novel pooling strategy with stochastic spatial sampling (S3Pool), where the regular downsampling is replaced by a more general stochastic version. We observe that this general stochasticity acts as a strong regularizer, and can also be seen as doing implicit data augmentation by introducing distortions in the feature maps. We further introduce a mechanism to control the amount of distortion to suit different datasets and architectures. To demonstrate the effectiveness of the proposed approach, we perform extensive experiments on several popular image classification benchmarks, observing excellent improvements over baseline models. In this work, we revisit the global average pooling layer proposed in [13], and shed light on how it explicitly enables the convolutional neural network to have remarkable localization ability despite being trained on image-level labels. While this technique was previously proposed as a means for regularizing training, we find that it actually builds a generic localizable deep representation that can be applied to a variety of tasks. Despite the apparent simplicity of global average pooling, we are able to achieve 37.1 top-5 error for object localization on ILSVRC 2014, which is remarkably close to the 34.2 top-5 error achieved by a fully supervised CNN approach. We demonstrate that our network is able to localize the discriminative image regions on a variety of tasks despite not being trained for them We propose a novel discrete Fourier transform-based pooling layer for convolutional neural networks. The DFT magnitude pooling replaces the traditional max average pooling layer between the convolution and fully-connected layers to retain translation invariance and shape preserving (aware of shape difference) properties based on the shift theorem of the Fourier transform. Thanks to the ability to handle image misalignment while keeping important structural information in the pooling stage, the DFT magnitude pooling improves the classification accuracy significantly. In addition, we propose the DFT+ method for ensemble networks using the middle convolution layer outputs. The proposed methods are extensively evaluated on various classification tasks using the ImageNet, CUB 2010-2011, MIT Indoors, Caltech 101, FMD and DTD datasets. The AlexNet, VGG-VD 16, Inception-v3, and ResNet are used as the base networks, upon which DFT and DFT+ methods are implemented. Experimental results show that the proposed methods improve the classification performance in all networks and datasets.