# A Lightweight Convolutional Neural Network Method for Two-Dimensional PhotoPlethysmoGraphy Signals
## 2 Methods
### Lightweight Convolutional Neural Network, LW-CNN  
Since this paper studies identity authentication based on wearable devices and considers the resource-limited characteristics of wearable devices, we propose a lightweight convolutional neural network LW-CNN with deep separable convolution ideas and residual connections. Compared with traditional convolutional neural networks (CNN), LW-CNN significantly reduces the complexity of the model by reducing the number of network layers, using smaller convolution kernels and a more straightforward network structure. Additionally, because of its simpler structure and fewer parameters, both forward and backward calculations require less computation, resulting in improved efficiency. Moreover, because the residual structure is introduced, the network structure is more stable, which improves the network's performance and enhances its robustness. Depthwise separable convolution can be regarded as a special convolution operation. In traditional convolution operations, each convolution kernel performs convolution operations simultaneously on all channels of the input feature map, thereby generating channels of the output feature map. If the input feature map has N channels, each convolution kernel requires N convolution sub-kernels for the input channels. However, depthwise separable convolution divides this process into two stages. The first part is the Depthwise Convolution layer, in which each input channel has its own 3 \(\times\) 3 convolution kernel for independent convolution operations. This means there will be N convolution kernels if there are N input channels, and each kernel will only convolve one input channel. In this way, the deep convolutional layer can extract the features of each channel without increasing the number of parameters. Secondly, the pointwise convolution layer (Pointwise Convolution), after the depth convolution, uses a 1 \(\times\) 1 convolution kernel to convolve the output of the depth convolution. This 1 \(\times\) 1 convolution kernel is a cross-channel linear transformation. Its function is to fuse and combine the features of all channels to generate the final output feature map. In this way, depthwise separable convolution can significantly reduce the model's parameters while maintaining the convolution operation's spatial filtering capabilities. Specifically, for a traditional convolutional layer with N input channels and M output channels, the number of parameters is N \(\times\) M \(\times\) K \(\times\) K (where K is the size of the convolution kernel). The number of parameters of the corresponding depth-separable convolution layer is reduced to N \(\times\) K \(\times\) K (depth convolution layer) + M \(\times\) N (point-by-point convolution layer). Usually, M and N are both large, so this reduction is very significant. Figure 3 is a schematic diagram of depthwise separable convolution. The residual structure is proposed to solve the problem of gradient explosion or dispersion in neural network training. The core idea is to build a neural network by introducing residual blocks (Residual blocks). These residual blocks create a shortcut connection between the input and output, allowing information to pass more smoothly through the network. Specifically, each residual block contains multiple convolutional layers used to extract and transform features. At the same time, short-circuit connections allow the input signal to skip one or more layers and be added directly to the output  
Figure 3: Illustration of Depthwise Separable Convolution. of subsequent layers. This structural innovation ensures that gradients can flow back to previous layers more effectively during backpropagation, thereby avoiding the problem of vanishing gradients.