Convolutional networks have achieved great success in various vision tasks. This is mainly due to a considerable amount of research on network structure. In this study, instead of focusing on architectures, we focused on the convolution unit itself. The existing convolution unit has a fixed shape, and is limited to observing restricted receptive fields. In an earlier work, we proposed the active convolution unit (ACU), which can freely define its shape and learn by itself. In this paper, we propose a detailed analysis of the proposed unit and show that it is an efficient representation of a sparse weight convolution. Furthermore, we expand the unit to a grouped ACU, which can observe multiple receptive fields in one layer. We found that the performance of a naive grouped convolution is degraded by increasing the number of groups; however, the proposed unit retains the accuracy even though the number of parameters reduces. Based on this result, we suggest a depthwise ACU, and various experiments have shown that our unit is efficient and can replace the existing convolutions.
Depthwise (or channelwise) convolution is a special case of grouped convolution, in which the number of input and output channels is the same as the number of groups. This implies that each output channel is calculated using only a corresponding input channel. Xception @cite_48 uses separable convolution, which first applies the depthwise convolution, followed by the pointwise convolution. This operation reduces the number of weight parameters efficiently, and the corresponding network achieves better result with less parameters. MobileNet @cite_19 @cite_22 also employs the depthwise convolution to reduce the network size and run fast in embedded devices.
@cite_19 @cite_48 @cite_22
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Depthwise separable convolution has shown great efficiency in network design, but requires time-consuming training procedure with full training-set available. This paper first analyzes the mathematical relationship between regular convolutions and depthwise separable convolutions, and proves that the former one could be approximated with the latter one in closed form. We show depthwise separable convolutions are principal components of regular convolutions. And then we propose network decoupling (ND), a training-free method to accelerate convolutional neural networks (CNNs) by transferring pre-trained CNN models into the MobileNet-like depthwise separable convolution structure, with a promising speedup yet negligible accuracy loss. We further verify through experiments that the proposed method is orthogonal to other training-free methods like channel decomposition, spatial decomposition, etc. Combining the proposed method with them will bring even larger CNN speedup. For instance, ND itself achieves about 2X speedup for the widely used VGG16, and combined with other methods, it reaches 3.7X speedup with graceful accuracy degradation. We demonstrate that ND is widely applicable to classification networks like ResNet, and object detection network like SSD300. Deep convolutional neural networks achieve remarkable visual recognition performance, at the cost of high computational complexity. In this paper, we have a new design of efficient convolutional layers based on three schemes. The 3D convolution operation in a convolutional layer can be considered as performing spatial convolution in each channel and linear projection across channels simultaneously. By unravelling them and arranging the spatial convolution sequentially, the proposed layer is composed of a single intra-channel convolution, of which the computation is negligible, and a linear channel projection. A topological subdivisioning is adopted to reduce the connection between the input channels and output channels. Additionally, we also introduce a spatial "bottleneck" structure that utilizes a convolution-projection-deconvolution pipeline to take advantage of the correlation between adjacent pixels in the input. Our experiments demonstrate that the proposed layers remarkably outperform the standard convolutional layers with regard to accuracy complexity ratio. Our models achieve similar accuracy to VGG, ResNet-50, ResNet-101 while requiring 42, 4.5, 6.5 times less computation respectively. This paper explores the complexity of deep feedforward networks with linear pre-synaptic couplings and rectified linear activations. This is a contribution to the growing body of work contrasting the representational power of deep and shallow network architectures. In particular, we offer a framework for comparing deep and shallow models that belong to the family of piecewise linear functions based on computational geometry. We look at a deep rectifier multi-layer perceptron (MLP) with linear outputs units and compare it with a single layer version of the model. In the asymptotic regime, when the number of inputs stays constant, if the shallow model has @math hidden units and @math inputs, then the number of linear regions is @math . For a @math layer model with @math hidden units on each layer it is @math . The number @math grows faster than @math when @math tends to infinity or when @math tends to infinity and @math . Additionally, even when @math is small, if we restrict @math to be @math , we can show that a deep model has considerably more linear regions that a shallow one. We consider this as a first step towards understanding the complexity of these models and specifically towards providing suitable mathematical tools for future analysis. Deep convolutional neural networks achieve better than human level visual recognition accuracy, at the cost of high computational complexity. We propose to factorize the convolutional layers to improve their efficiency. In traditional convolutional layers, the 3D convolution can be considered as performing in-channel spatial convolution and linear channel projection simultaneously, leading to highly redundant computation. By unravelling them apart, the proposed layer only involves single in-channel convolution and linear channel projection. When stacking such layers together, we achieves similar accuracy with significantly less computation. Additionally, we propose a topological connection framework between the input channels and output channels that further improves the layer's efficiency. Our experiments demonstrate that the proposed method remarkably outperforms the standard convolutional layer with regard to accuracy complexity ratio. Our model achieves accuracy of GoogLeNet while consuming 3.4 times less computation.