when the scale of BDNN is increased (higher complexity), the performance becomes better.

The convolutional neural network
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In deep learning research, the structure of CNN is widely used for image classification. Therefore, in the experiments, we also tested the CNN structure. As shown in Fig. \[cnn\], we used a CNN structure of five layers. The first layer is the input data, followed by two layers of feature maps (calculated by the convolutional kernels). The last two layers are the fully connected neurons and one of them is used as output layer. In most of the CNNs, after convolutional operation, the feature map size is then decreased by pooling. Nevertheless, since it is hard to realize the pooling operation on binary values, thus the feature map size is controlled by skipping every other pixel in the convolutional operation.

With different sizes of the feature maps and kernels, three different CNN structures are obtained as follows.

-   Structure C: Layer 1 is the input image, the size is $29 \times 29$; Layer 2 contains $7$ feature maps of size $13 \times 13$, obtained by using $7$ kernels of size $5 \times 5$; Layer 3 contains $51$ feature maps of size $5 