Research map / Adversarial robustness and security / Certified and empirical robustness
Certifying Ensembles: A General Certification Theory with S-Lipschitzness
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the exact gradient set for certification instead of a norm-ball overapproximation | S-Lipschitz classifier certification · Pointwise robustness certificates | certified perturbation set | Helped |
| Certify class-difference functions directly rather than combining separate class gradient sets | Class-wise S-certification · Pointwise robustness certificates | certified perturbation set | Helped |
| Require constituent classifiers to share the same top prediction | Ensembles of classifiers · Ensemble certification regime | certified-set inclusion | Helped |
| Ensemble classifiers that agree on both their top and second predictions in the uniform-continuity setting | Uniform-continuity ensembles · Ensemble certification regime | certified-set inclusion | No clear effect |
| Ensemble classifiers with different top predictions | Ensembles of robust classifiers · Pointwise robustness | ensemble certified-set size: 0.09 -> 0.0069 | Hurt |
| Use a uniform-weight ensemble of smoothed classifiers | CIFAR10 ResNet20 ensembles · CIFAR10 test split | inputs in regime R1 | Hurt |
| Use a uniform-weight ensemble of smoothed classifiers | ImageNet ResNet50 ensemble · ImageNet test split | inputs in regime R1: 1.4% | Helped |
| Use a uniform-weight ensemble of smoothed classifiers | Real-world smoothed classifier ensembles · CIFAR10 and ImageNet test inputs | inputs in regime R3: 3.9%, 4.1%, 3.3%; 10.2% | Hurt |
| Increase the best constituent classifier's prediction gap | Ensemble prediction-gap upper bound · Normalized K-class classifiers | maximum ensemble gap gain: r^g_{c_B} ≤ overline r + (1-overline r)/2 - (1-overline r)/(2(K-1)) | Hurt |
| Average classifiers with different top predictions using weights that place the input on the ensemble decision boundary | Ensembles of robust classifiers · Pointwise robustness | ensemble prediction gap: r^g_{c_B}=0; Q_g={0} | Hurt |
| Ensemble the smoothed classifiers rather than smooth the ensemble | Randomized-smoothing ensembles · Certification analysis | certified perturbation set | Mixed |
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