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Research on the generalization ability of deep neural networks (DNNs) hasrecently attracted a great deal of attention. However, due to their complexarchitectures and large numbers of parameters, measuring the generalizationability of specific DNN models remains an open challenge. In this paper, wepropose to use multiple factors to measure and rank the relative generalizationof DNNs based on a new concept of confidence dimension (CD). Furthermore, weprovide a feasible framework in our CD to theoretically calculate the upperbound of generalization based on the conventional Vapnik-Chervonenk dimension(VC-dimension) and Hoeffding's inequality. Experimental results on imageclassification and object detection demonstrate that our CD can reflect therelative generalization ability for different DNNs. In addition tofull-precision DNNs, we also analyze the generalization ability of binaryneural networks (BNNs), whose generalization ability remains an unsolvedproblem. Our CD yields a consistent and reliable measure and ranking for bothfull-precision DNNs and BNNs on all the tasks.

Confidence Dimension for Deep Learning based on Hoeffding Inequality and Relative Evaluation