An Interpretive Constrained Linear Model for ResNet and MgNet
This work provides an interpretable mathematical framework for CNNs, potentially aiding researchers in understanding and improving network architectures, though it appears incremental in its modifications to existing models.
The authors tackled the problem of interpreting convolutional neural networks (CNNs) for image classification by proposing a constrained linear data-feature-mapping model, which led to modified ResNet models with fewer parameters and higher accuracy, and demonstrated the advantages of MgNet in numerical studies.
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 and yet 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 show the rationality of MgNet. We also provide a systematic numerical study on MgNet to show its success and advantages in image classification problems and demonstrate its advantages in comparison with established networks.