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Useful information (UI) is an elusive concept in neural networks. Aquantitative measurement of UI is absent, despite the variations of UI can berecognized by prior knowledge. The communication bandwidth of feature mapsdecreases after downscaling operations, but UI flows smoothly after trainingdue to lower Nyquist frequency. Inspired by the low-Nyqusit-frequency nature ofUI, we propose the use of spectral roll-off points (SROPs) to estimate UI onvariations. The computation of an SROP is extended from a 1-D signal to a 2-Dimage by the required rotation invariance in image classification tasks. SROPstatistics across feature maps are implemented as layer-wise useful informationestimates. We design sanity checks to explore SROP variations when UIvariations are produced by variations in model input, model architecture andtraining stages. The variations of SROP is synchronizes with UI variations invarious randomized and sufficiently trained model structures. Therefore, SROPvariations is an accurate and convenient sign of UI variations, which promotesthe explainability of data representations with respect to frequency-domainknowledge.

Spectral Roll-off Points Variations: Exploring Useful Information in Feature Maps by Its Variations