Convolutional kernels are basic and vital components of deep Convolutional Neural Networks (CNN). In this paper, we equip convolutional kernels with shape attributes to generate the deep Irregular Convolutional Neural Networks (ICNN). Compared to traditional CNN applying regular convolutional kernels like @math , our approach trains irregular kernel shapes to better fit the geometric variations of input features. In other words, shapes are learnable parameters in addition to weights. The kernel shapes and weights are learned simultaneously during end-to-end training with the standard back-propagation algorithm. Experiments for semantic segmentation are implemented to validate the effectiveness of our proposed ICNN.
Dilated convolution @cite_10 expands distances between every two adjacent weights in a kernel, and generates a more discrete distribution. The presented dilated convolution is able to aggregate large scale contextual information without losing resolution. It is a variant of traditional compact kernels. In addition, our proposed ICNN is a further generalized version of dilated convolution.
@cite_10
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In this paper, we analyze the spatial information of deep features, and propose two complementary regressions for robust visual tracking. First, we propose a kernelized ridge regression model wherein the kernel value is defined as the weighted sum of similarity scores of all pairs of patches between two samples. We show that this model can be formulated as a neural network and thus can be efficiently solved. Second, we propose a fully convolutional neural network with spatially regularized kernels, through which the filter kernel corresponding to each output channel is forced to focus on a specific region of the target. Distance transform pooling is further exploited to determine the effectiveness of each output channel of the convolution layer. The outputs from the kernelized ridge regression model and the fully convolutional neural network are combined to obtain the ultimate response. Experimental results on two benchmark datasets validate the effectiveness of the proposed method. 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. This paper describes a novel approach of packing sparse convolutional neural networks for their efficient systolic array implementations. By combining subsets of columns in the original filter matrix associated with a convolutional layer, we increase the utilization efficiency of the systolic array substantially (e.g., 4x) due to the increased density of nonzeros in the resulting packed filter matrix. In combining columns, for each row, all filter weights but one with the largest magnitude are pruned. We retrain the remaining weights to preserve high accuracy. We demonstrate that in mitigating data privacy concerns the retraining can be accomplished with only fractions of the original dataset (e.g., 10 for CIFAR-10). We study the effectiveness of this joint optimization for both high utilization and classification accuracy with ASIC and FPGA designs based on efficient bit-serial implementations of multiplier-accumulators. We present analysis and empirical evidence on the superior performance of our column combining approach against prior arts under metrics such as energy efficiency (3x) and inference latency (12x).