Deep neural networks are widely used in the field of image processing for micromachines, such as in 3D shape detection in microelectronic high-speed dispensing and object detection in microrobots. It is already known that hyperparameters and their interactions impact neural network model performance. Taking advantage of the mathematical correlations between hyperparameters and the corresponding deep learning model to adjust hyperparameters intelligently is the key to obtaining an optimal solution from a deep neural network model. Leveraging these correlations is also significant for unlocking the "black box" of deep learning by revealing the mechanism of its mathematical principle. However, there is no complete system for studying the combination of mathematical derivation and experimental verification methods to quantify the impacts of hyperparameters on the performances of deep learning models. Therefore, in this paper, the authors analyzed the mathematical relationships among four hyperparameters: the learning rate, batch size, dropout rate, and convolution kernel size. A generalized multiparameter mathematical correlation model was also established, which showed that the interaction between these hyperparameters played an important role in the neural network's performance. Different experiments were verified by running convolutional neural network algorithms to validate the proposal on the MNIST dataset. Notably, this research can help establish a universal multiparameter mathematical correlation model to guide the deep learning parameter adjustment process.
Keywords: deep neural network; hyperparameters; image processing; multiparameter mathematical correlation model.