Compact convolutional neural networks gain efficiency mainly through depthwise convolutions, expanded channels and complex topologies, which contrarily aggravate the training efforts. In this work, we identify the shift problem occurs in even-sized kernel (2x2, 4x4) convolutions, and eliminate it by proposing symmetric padding on each side of the feature maps (C2sp, C4sp). Symmetric padding enlarges the receptive fields of even-sized kernels with little computational cost. In classification tasks, C2sp outperforms the conventional 3x3 convolution and obtains comparable accuracies to existing compact convolution blocks, but consumes less memory and time during training. In generation tasks, C2sp and C4sp both achieve improved image qualities and stabilized training. Symmetric padding coupled with even-sized convolution is easy to be implemented into deep learning frameworks, providing promising building units for architecture designs that emphasize training efforts on online and continual learning occasions.
In @cite_33 , the authors randomly shift 3 @math 3 kernels in the down-sampling layers (strided convolution or pooling) to reduce information loss. It can be viewed as a feature augmentation method applied during training. ShiftNet @cite_30 sidesteps spatial convolutions entirely by using shift operations followed with pointwise convolutions. Though shift kernels contain no parameter or FLOP, ShiftNet expands too many FMs and is not such efficient regarding their evaluations. Deformable convolution @cite_23 augments the spatial sampling locations of kernels by additional 2D offsets, and learning the offsets directly from the target tasks. Therefore, deformable kernels shift at pixel level and are more focused on geometric transformations.
@cite_30 @cite_33 @cite_23
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Neural networks rely on convolutions to aggregate spatial information. However, spatial convolutions are expensive in terms of model size and computation, both of which grow quadratically with respect to kernel size. In this paper, we present a parameter-free, FLOP-free "shift" operation as an alternative to spatial convolutions. We fuse shifts and point-wise convolutions to construct end-to-end trainable shift-based modules, with a hyperparameter characterizing the tradeoff between accuracy and efficiency. To demonstrate the operation's efficacy, we replace ResNet's 3x3 convolutions with shift-based modules for improved CIFAR10 and CIFAR100 accuracy using 60 fewer parameters; we additionally demonstrate the operation's resilience to parameter reduction on ImageNet, outperforming ResNet family members. We finally show the shift operation's applicability across domains, achieving strong performance with fewer parameters on image classification, face verification and style transfer. Convolutional neural networks have shown great success on feature extraction from raw input data such as images. Although convolutional neural networks are invariant to translations on the inputs, they are not invariant to other transformations, including rotation and flip. Recent attempts have been made to incorporate more invariance in image recognition applications, but they are not applicable to dense prediction tasks, such as image segmentation. In this paper, we propose a set of methods based on kernel rotation and flip to enable rotation and flip invariance in convolutional neural networks. The kernel rotation can be achieved on kernels of 3 × 3, while kernel flip can be applied on kernels of any size. By rotating in eight or four angles, the convolutional layers could produce the corresponding number of feature maps based on eight or four different kernels. By using flip, the convolution layer can produce three feature maps. By combining produced feature maps using maxout, the resource requirement could be significantly reduced while still retain the invariance properties. Experimental results demonstrate that the proposed methods can achieve various invariance at reasonable resource requirements in terms of both memory and time. Convolutional Neural Networks (CNNs) with Bilinear Pooling, initially in their full form and later using compact representations, have yielded impressive performance gains on a wide range of visual tasks, including fine-grained visual categorization, visual question answering, face recognition, and description of texture and style. The key to their success lies in the spatially invariant modeling of pairwise (2nd order) feature interactions. In this work, we propose a general pooling framework that captures higher order interactions of features in the form of kernels. We demonstrate how to approximate kernels such as Gaussian RBF up to a given order using compact explicit feature maps in a parameter-free manner. Combined with CNNs, the composition of the kernel can be learned from data in an end-to-end fashion via error back-propagation. The proposed kernel pooling scheme is evaluated in terms of both kernel approximation error and visual recognition accuracy. Experimental evaluations demonstrate state-of-the-art performance on commonly used fine-grained recognition datasets. Kernel normalization methods have been employed to improve robustness of optimization methods to reparametrization of convolution kernels, covariate shift, and to accelerate training of Convolutional Neural Networks (CNNs). However, our understanding of theoretical properties of these methods has lagged behind their success in applications. We develop a geometric framework to elucidate underlying mechanisms of a diverse range of kernel normalization methods. Our framework enables us to expound and identify geometry of space of normalized kernels. We analyze and delineate how state-of-the-art kernel normalization methods affect the geometry of search spaces of the stochastic gradient descent (SGD) algorithms in CNNs. Following our theoretical results, we propose a SGD algorithm with assurance of almost sure convergence of the methods to a solution at single minimum of classification loss of CNNs. Experimental results show that the proposed method achieves state-of-the-art performance for major image classification benchmarks with CNNs.