Convolutional neural networks (CNN) are widely used in computer vision, especially in image classification. However, the way in which information and invariance properties are encoded through in deep CNN architectures is still an open question. In this paper, we propose to modify the standard convo- lutional block of CNN in order to transfer more information layer after layer while keeping some invariance within the net- work. Our main idea is to exploit both positive and negative high scores obtained in the convolution maps. This behav- ior is obtained by modifying the traditional activation func- tion step before pooling. We are doubling the maps with spe- cific activations functions, called MaxMin strategy, in order to achieve our pipeline. Extensive experiments on two classical datasets, MNIST and CIFAR-10, show that our deep MaxMin convolutional net outperforms standard CNN.
Regarding @math , it is a non-linear function that sets to zero all negative values after the convolutional layer. This filtering is supposed to facilitate the exploitation of discriminative information by de-noising filter detections. @cite_20 introduced the @math as an extension of @math . It multiplies negative values with a learnable coefficient instead of setting them to zero. This method enables to filter less information at activation layer while keeping the non linear property of @math although at the cost of additional learnable parameters.
@cite_20
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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. We study the improper learning of multi-layer neural networks. Suppose that the neural network to be learned has @math hidden layers and that the @math -norm of the incoming weights of any neuron is bounded by @math . We present a kernel-based method, such that with probability at least @math , it learns a predictor whose generalization error is at most @math worse than that of the neural network. The sample complexity and the time complexity of the presented method are polynomial in the input dimension and in @math , where @math is a function depending on @math and on the activation function, independent of the number of neurons. The algorithm applies to both sigmoid-like activation functions and ReLU-like activation functions. It implies that any sufficiently sparse neural network is learnable in polynomial time. Conventional convolutional neural networks use either a linear or a nonlinear 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 representational 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 the cascaded subpatch network (CSNet). The feature layer generated by CSNet is called the csconv layer. For the whole input image, we construct a deep neural network by stacking a sequence of csconv layers. Experimental results on five benchmark data sets demonstrate the effectiveness and compactness of the proposed CSNet. For example, our CSNet reaches a test error of 5.68 on the CIFAR10 data set without model averaging. To the best of our knowledge, this is the best result ever obtained on the CIFAR10 data set. One of the mysteries in the success of neural networks is randomly initialized first order methods like gradient descent can achieve zero training loss even though the objective function is non-convex and non-smooth. This paper demystifies this surprising phenomenon for two-layer fully connected ReLU activated neural networks. For an @math hidden node shallow neural network with ReLU activation and @math training data, we show as long as @math is large enough and no two inputs are parallel, randomly initialized gradient descent converges to a globally optimal solution at a linear convergence rate for the quadratic loss function. Our analysis relies on the following observation: over-parameterization and random initialization jointly restrict every weight vector to be close to its initialization for all iterations, which allows us to exploit a strong convexity-like property to show that gradient descent converges at a global linear rate to the global optimum. We believe these insights are also useful in analyzing deep models and other first order methods.