Research map / Adversarial robustness and security / Certified and empirical robustness
Adversarial Risk and Robustness: General Definitions and Implications for the Uniform Distribution
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the error-region definition instead of prediction-change or corrupted-instance robustness | Monotone conjunction hypotheses under U_n · Monotone conjunctions under U_n | Robustness scaling: Θ(min{|h|, |c|}) versus Θ(|h|) | Mixed |
| Use error-region risk and robustness definitions that require actual misclassification at the perturbed point | Adversarial risk and robustness definitions · General classification problems | Guarantee that perturbed instances are misclassified | Helped |
| Apply Hamming perturbations to instances from U_n | Any classifier with initial risk 0.01 · Uniform hypercube U_n | Risk increase to 0.50: ≈ 1.17 √n | Hurt |
| Apply Hamming perturbations to instances from U_n | Any classifier with initial risk 0.01 · Uniform hypercube U_n | Risk increase to 0.99: ≈ 2.34 √n | Hurt |
| Use the same order of perturbation budget to increase risk to 1 | Any classifier with constant initial risk under U_n · Uniform hypercube U_n | Expected Hamming perturbation robustness: O(√n) | Hurt |
| Set h equal to c | Monotone conjunctions under U_n · Monotone conjunctions under U_n | Error-region risk: 0 | Helped |
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