Pruning is one of the predominant approaches for compressing deep neural
networks (DNNs). Lately, coresets (provable data summarizations) were leveraged
for pruning DNNs, adding the advantage of theoretical guarantees on the
trade-off between the compression rate and the approximation error. However,
coresets in this domain were either data-dependent or generated under
restrictive assumptions on both the model's weights and inputs. In real-world
scenarios, such assumptions are rarely satisfied, limiting the applicability of
coresets. To this end, we suggest a novel and robust framework for computing
such coresets under mild assumptions on the model's weights and without any
assumption on the training data. The idea is to compute the importance of each
neuron in each layer with respect to the output of the following layer. This is
achieved by a combination of L\"{o}wner ellipsoid and Caratheodory theorem. Our
method is simultaneously data-independent, applicable to various networks and
datasets (due to the simplified assumptions), and theoretically supported.
Experimental results show that our method outperforms existing coreset based
neural pruning approaches across a wide range of networks and datasets. For
example, our method achieved a 62% compression rate on ResNet50 on ImageNet
with 1.09% drop in accuracy