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Certified Robustness via Randomized Smoothing (2D)

Interactive 2D top-down simulator of certified adversarial robustness: Monte Carlo Gaussian smoothing around a classifier's decision boundary, the Cohen et al. certified radius R = sigma*Phi^-1(p_A), and whether a chosen perturbation stays inside the certified ball.

AI & Machine Learning2DAdvanced60 FPS📱 Mobile-adapted⇄ 3D version

Most adversarial-defense visualizations show an attack breaking a model. This one shows the opposite: a mathematical guarantee that no attack below a certain size can succeed. The top-down view renders a wavy binary decision boundary, plants an input point on it, and surrounds that point with a cloud of Gaussian-noise samples whose votes build the Cohen et al. (2019) randomized-smoothing certificate — a certified radius R = σ·Φ⁻¹(p_A) inside which the prediction is provably stable. The lower panel plots that same formula as a curve so you can see exactly how p_A maps to R. Tune the noise level, sample count and boundary curvature to watch the certified ball grow and shrink, then drag the attack-perturbation slider to see whether a given adversarial step falls safely inside it or breaches it. Drag the main view to pan, scroll to zoom.

⚙ Under the hood

Watch a top-down decision boundary get wrapped in a Monte Carlo cloud of Gaussian noise samples, computing the Cohen et al. certified radius R = σ·Φ⁻¹(p_A) and testing whether a chosen adversarial perturbation stays inside the provably-safe ball. A linked analytics panel plots the R(p) formula itself alongside a live vote histogram.

adversarial robustnessrandomized smoothingmachine learningcertified defenseAI security

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install