Spectral Roll-off Points: Estimating Useful Information Under the Basis of Low-frequency Data Representations

Useful information is the basis for model decisions. Estimating useful information in feature maps promotes the understanding of the mechanisms of neural networks. Low frequency is a prerequisite for useful information in data representations, because downscaling operations reduce the communication bandwidth. This study proposes the use of spectral roll-off points (SROPs) to integrate the low-frequency condition when estimating useful information. The computation of an SROP is extended from a 1-D signal to a 2-D image by the required rotation invariance in image classification tasks. SROP statistics across feature maps are implemented for layer-wise useful information estimation. Sanity checks demonstrate that the variation of layer-wise SROP distributions among model input can be used to recognize useful components that support model decisions. Moreover, the variations of SROPs and accuracy, the ground truth of useful information of models, are synchronous when adopting sufficient training in various model structures. Therefore, SROP is an accurate and convenient estimation of useful information. It promotes the explainability of artificial intelligence with respect to frequency-domain knowledge.