Computer, Electrical and Mathematical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia.
Computer, Electrical and Mathematical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia; Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA.
Neural Netw. 2023 May;162:384-392. doi: 10.1016/j.neunet.2023.03.011. Epub 2023 Mar 11.
We propose a constrained linear data-feature-mapping model as an interpretable mathematical model for image classification using a convolutional neural network (CNN). From this viewpoint, we establish detailed connections between the traditional iterative schemes for linear systems and the architectures of the basic blocks of ResNet- and MgNet-type models. Using these connections, we present some modified ResNet models that, compared with the original models, have fewer parameters but can produce more accurate results, thereby demonstrating the validity of this constrained learning data-feature-mapping assumption. Based on this assumption, we further propose a general data-feature iterative scheme to demonstrate the rationality of MgNet. We also provide a systematic numerical study on MgNet to show its success and advantages in image classification problems, particularly in comparison with established networks.
我们提出了一个约束线性数据特征映射模型，作为使用卷积神经网络（CNN）进行图像分类的可解释数学模型。从这个角度来看，我们建立了传统线性系统迭代方案与 ResNet 和 MgNet 类型模型基本块结构之间的详细联系。利用这些联系，我们提出了一些改进的 ResNet 模型，与原始模型相比，这些模型具有更少的参数，但可以产生更准确的结果，从而证明了这种约束学习数据特征映射假设的有效性。基于这一假设，我们进一步提出了一种通用的数据特征迭代方案，以证明 MgNet 的合理性。我们还对 MgNet 进行了系统的数值研究，以展示其在图像分类问题中的成功和优势，特别是与已建立的网络相比。
