Title: Model-Free Energy Distance for Pruning DNNs. Abstract: We propose a novel method for compressing Deep Neural Networks (DNNs) with competitive performance to state-of-the-art methods. We measure a new model-free information between the feature maps and the output of the network. Model-freeness of our information measure guarantees that no parametric assumptions on the feature distribution are required. The new model-free information is subsequently used to prune a collection of redundant layers in the networks with skip-connections. Numerical experiments on CIFAR-10/100, SVHN, Tiny ImageNet, and ImageNet data sets show the efficacy of the proposed approach in compressing deep models. For instance, in classifying CIFAR-10 images our method achieves respectively 64.50% and 60.31% reduction in the number of parameters and FLOPs for a full DenseNet model with 0.77 million parameters while dropping only 1% in the test accuracy. Our code is available at https://github.com/suuyawu/PEDmodelcompression