Conventional Convolutional Neural Networks (CNNs) use either a linear or non-linear filter to extract features from an image patch (region) of spatial size @math (Typically, @math is small and is equal to @math , e.g., @math is 5 or 7). Generally, the size of the filter is equal to the size @math of the input patch. We argue that the representation ability of equal-size strategy is not strong enough. To overcome the drawback, we propose to use subpatch filter whose spatial size @math is smaller than @math . The proposed subpatch filter consists of two subsequent filters. The first one is a linear filter of spatial size @math and is aimed at extracting features from spatial domain. The second one is of spatial size @math and is used for strengthening the connection between different input feature channels and for reducing the number of parameters. The subpatch filter convolves with the input patch and the resulting network is called a subpatch network. Taking the output of one subpatch network as input, we further repeat constructing subpatch networks until the output contains only one neuron in spatial domain. These subpatch networks form a new network called Cascaded Subpatch Network (CSNet). The feature layer generated by CSNet is called csconv layer. For the whole input image, we construct a deep neural network by stacking a sequence of csconv layers. Experimental results on four benchmark datasets demonstrate the effectiveness and compactness of the proposed CSNet. For example, our CSNet reaches a test error of @math on the CIFAR10 dataset without model averaging. To the best of our knowledge, this is the best result ever obtained on the CIFAR10 dataset.
(1) . Some researchers paid attention to the parameters of CNN, such as the sizes of convolutional filters, the strides of filters, the number of feature channels in each layer, and the number of convolutional layers. They tried to adjust the parameters to improve the performance of CNN through exhaustive experiments. Zeiler and Fergus @cite_34 visualized the trained CNN model and found that large filter size and large stride of the first convolutional layer could cause aliasing artifacts. Therefore, they used smaller receptive window size and smaller stride. Sermanet @cite_10 utilized smaller strides in the first convolution, larger number of feature maps, and larger number of layers. They achieved better results than the AlexNet. The VGG network @cite_6 pushes the depth of CNN to up to 19 convolutional layers by using very small convolutional filters and gains a significant improvement. These above efforts can be viewed as preliminary explorations on how to construct networks with better performance.
@cite_34 @cite_10 @cite_6
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We propose local binary convolution (LBC), an efficient alternative to convolutional layers in standard convolutional neural networks (CNN). The design principles of LBC are motivated by local binary patterns (LBP). The LBC layer comprises of a set of fixed sparse pre-defined binary convolutional filters that are not updated during the training process, a non-linear activation function and a set of learnable linear weights. The linear weights combine the activated filter responses to approximate the corresponding activated filter responses of a standard convolutional layer. The LBC layer affords significant parameter savings, 9x to 169x in the number of learnable parameters compared to a standard convolutional layer. Furthermore, the sparse and binary nature of the weights also results in up to 9x to 169x savings in model size compared to a standard convolutional layer. We demonstrate both theoretically and experimentally that our local binary convolution layer is a good approximation of a standard convolutional layer. Empirically, CNNs with LBC layers, called local binary convolutional neural networks (LBCNN), achieves performance parity with regular CNNs on a range of visual datasets (MNIST, SVHN, CIFAR-10, and ImageNet) while enjoying significant computational savings. Deep learning using convolutional neural networks (CNN) gives state-of-the-art accuracy on many computer vision tasks (e.g. object detection, recognition, segmentation). Convolutions account for over 90 of the processing in CNNs for both inference testing and training, and fully convolutional networks are increasingly being used. To achieve state-of-the-art accuracy requires CNNs with not only a larger number of layers, but also millions of filters weights, and varying shapes (i.e. filter sizes, number of filters, number of channels) as shown in Fig. 14.5.1. For instance, AlexNet [1] uses 2.3 million weights (4.6MB of storage) and requires 666 million MACs per 227227 image (13kMACs pixel). VGG16 [2] uses 14.7 million weights (29.4MB of storage) and requires 15.3 billion MACs per 224224 image (306kMACs pixel). The large number of filter weights and channels results in substantial data movement, which consumes significant energy. Learning acoustic models directly from the raw waveform data with minimal processing is challenging. Current waveform-based models have generally used very few (2) convolutional layers, which might be insufficient for building high-level discriminative features. In this work, we propose very deep convolutional neural networks (CNNs) that directly use time-domain waveforms as inputs. Our CNNs, with up to 34 weight layers, are efficient to optimize over very long sequences (e.g., vector of size 32000), necessary for processing acoustic waveforms. This is achieved through batch normalization, residual learning, and a careful design of down-sampling in the initial layers. Our networks are fully convolutional, without the use of fully connected layers and dropout, to maximize representation learning. We use a large receptive field in the first convolutional layer to mimic bandpass filters, but very small receptive fields subsequently to control the model capacity. We demonstrate the performance gains with the deeper models. Our evaluation shows that the CNN with 18 weight layers outperforms the CNN with 3 weight layers by over 15 in absolute accuracy for an environmental sound recognition task and is competitive with the performance of models using log-mel features.