Randomized Smoothing Threshold Certificate

Randomized smoothing turns an arbitrary base classifier into one with a mathematically guaranteed certified radius against adversarial perturbations. By injecting Gaussian noise to the input and voting on the resulting predictions, the smoothed model behaves predictably under bounded shifts.

Experiment: Interactive Validation

Use the interactive module to verify the mathematical properties of the smoothing certificate. You can adjust the following controls:

1. Set Input x to different values and observe the certified radius matches |x|.
2. Adjust Noise sigma and notice how the probabilities change, but the theoretical absolute certified radius for this specific exact-probability linear threshold remains |x|.
3. Change Attack delta to values beyond the certified radius (e.g., x=1, δ=-1) and see how it falls outside the strictly certified set.