Useful information (UI) is an elusive concept in neural networks. A quantitative measurement of UI is absent, despite the variations of UI can be recognized by prior knowledge. The communication bandwidth of feature maps decreases after downscaling operations, but UI flows smoothly after training due to lower Nyquist frequency. Inspired by the low-Nyqusit-frequency nature of UI, we propose the use of spectral roll-off points (SROPs) to estimate UI on variations. 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 as layer-wise useful information estimates. We design sanity checks to explore SROP variations when UI variations are produced by variations in model input, model architecture and training stages. The variations of SROP is synchronizes with UI variations in various randomized and sufficiently trained model structures. Therefore, SROP variations is an accurate and convenient sign of UI variations, which promotes the explainability of data representations with respect to frequency-domain knowledge.
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