  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.
