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In this paper we introduce a new problem within the growing literature ofinterpretability for convolution neural networks (CNNs). While previous workhas focused on the question of how to visually interpret CNNs, we ask what itis that we care to interpret, that is, which layers and neurons are worth ourattention? Due to the vast size of modern deep learning network architectures,automated, quantitative methods are needed to rank the relative importance ofneurons so as to provide an answer to this question. We present a newstatistical method for ranking the hidden neurons in any convolutional layer ofa network. We define importance as the maximal correlation between theactivation maps and the class score. We provide different ways in which thismethod can be used for visualization purposes with MNIST and ImageNet, and showa real-world application of our method to air pollution prediction withstreet-level images.

PCACE: A Statistical Approach to Ranking Neurons for CNN Interpretability