# Confidence Dimension for Deep Learning based on Hoeffding Inequality and Relative Evaluation Source: [Confidence Dimension for Deep Learning based on Hoeffding Inequality and Relative Evaluation]() Collection index: [llms.txt]() Data updated: 2025-10-26T00:02:49.336Z Authors: Runqi Wang, Linlin Yang, Baochang Zhang, Wentao Zhu, David Doermann, Guodong Guo Published: 2022-03-17T04:43:43.000Z ## Abstract Research on the generalization ability of deep neural networks (DNNs) has recently attracted a great deal of attention. However, due to their complex architectures and large numbers of parameters, measuring the generalization ability of specific DNN models remains an open challenge. In this paper, we propose to use multiple factors to measure and rank the relative generalization of DNNs based on a new concept of confidence dimension (CD). Furthermore, we provide a feasible framework in our CD to theoretically calculate the upper bound of generalization based on the conventional Vapnik-Chervonenk dimension (VC-dimension) and Hoeffding's inequality. Experimental results on image classification and object detection demonstrate that our CD can reflect the relative generalization ability for different DNNs. In addition to full-precision DNNs, we also analyze the generalization ability of binary neural networks (BNNs), whose generalization ability remains an unsolved problem. Our CD yields a consistent and reliable measure and ranking for both full-precision DNNs and BNNs on all the tasks. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()