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This work makes a substantial step in the field of split computing, i.e., how to split a deep neural network to host its early part on an embedded device and the rest on a server. So far, potential split locations have been identified exploiting uniquely architectural aspects, i.e., based on the layer sizes. Under this paradigm, the efficacy of the split in terms of accuracy can be evaluated only after having performed the split and retrained the entire pipeline, making an exhaustive evaluation of all the plausible splitting points prohibitive in terms of time. Here we show that not only the architecture of the layers does matter, but the importance of the neurons contained therein too. A neuron is important if its gradient with respect to the correct class decision is high. It follows that a split should be applied right after a layer with a high density of important neurons, in order to preserve the information flowing until then. Upon this idea, we propose Interpretable Split (I-SPLIT): a procedure that identifies the most suitable splitting points by providing a reliable prediction on how well this split will perform in terms of classification accuracy, beforehand of its effective implementation. As a further major contribution of I-SPLIT, we show that the best choice for the splitting point on a multiclass categorization problem depends also on which specific classes the network has to deal with. Exhaustive experiments have been carried out on two networks, VGG16 and ResNet-50, and three datasets, Tiny-Imagenet-200, notMNIST, and Chest X-Ray Pneumonia. The source code is available at https://github.com/vips4/I-Split.