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We propose a constrained linear data-feature-mapping model as aninterpretable mathematical model for image classification using a convolutionalneural network (CNN). From this viewpoint, we establish detailed connectionsbetween the traditional iterative schemes for linear systems and thearchitectures of the basic blocks of ResNet- and MgNet-type models. Using theseconnections, we present some modified ResNet models that compared with theoriginal models have fewer parameters and yet can produce more accurateresults, thereby demonstrating the validity of this constrained learningdata-feature-mapping assumption. Based on this assumption, we further propose ageneral data-feature iterative scheme to show the rationality of MgNet. We alsoprovide a systematic numerical study on MgNet to show its success andadvantages in image classification problems and demonstrate its advantages incomparison with established networks.

An Interpretive Constrained Linear Model for ResNet and MgNet