  We introduce Harmonic Robustness, a powerful and intuitive method to test the
robustness of any machine-learning model either during training or in black-box
real-time inference monitoring without ground-truth labels. It is based on
functional deviation from the harmonic mean value property, indicating
instability and lack of explainability. We show implementation examples in
low-dimensional trees and feedforward NNs, where the method reliably identifies
overfitting, as well as in more complex high-dimensional models such as
ResNet-50 and Vision Transformer where it efficiently measures adversarial
vulnerability across image classes.
