Research map / Adversarial robustness and security / Certified and empirical robustness
Effects of Exponential Gaussian Distribution on (Double Sampling) Randomized Smoothing
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Studies Exponential Standard Gaussian (ESG) and Exponential General Gaussian (EGG) smoothing distributions for randomized smoothing and double-sampling RS, deriving an η-independent certified radius formula for ESG and showing EGG tightens DSRS lower bounds.
Problem
Randomized smoothing's ℓ2 certified radius depends on the choice of smoothing distribution, and the interaction between distribution shape and certification (including the curse of dimensionality in DSRS) is poorly understood.
Approach
Generalizes Gaussian smoothing to exponential-power families (ESG, with exponent η) and General Gaussian to EGG; shows that ESG's certified radius converges to the Gaussian (Cohen et al.) formula in high dimension regardless of η, and that EGG with suitable η gives tighter Ω(√d) constant factors in DSRS under a concentration assumption.
Key results
- ESG's certified accuracy is nearly unchanged across eta in {1,2,4,8} on CIFAR-10 and ImageNet under DSRS.
- EGG with eta=8 outperforms the DSRS General Gaussian (eta=2) baseline, with up to 6.4% certified accuracy gain on ImageNet.
- Theorem shows EGG with eta in (0,2) certifies r >= 0.02 sigma sqrt(d) lower bound under the concentration property.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| increase EGG exponent from η=2.0 to η=8.0 (ablation) | DSRS · CIFAR10, r=1.00 | certified accuracy: 20.2% -> 20.6% | Helped |
| increase EGG exponent from η=2.0 to η=8.0 (ablation) | DSRS · ImageNet, r=1.00 | certified accuracy: 35.2% -> 36.8% | Helped |
| vary ESG exponent η across 1.0, 2.0, 4.0, and 8.0 (ablation) | DSRS · CIFAR10 and ImageNet | certified accuracy | No clear effect |
| use smaller EGG η for the tight-constant-factor lower bound (ablation) | DSRS with a classifier satisfying the concentration property · ℓ2 certified radius lower bound | tight constant factor | Helped |
| use larger EGG η on real classifiers (ablation) | DSRS · CIFAR10 and ImageNet | certified accuracy | Helped |
Surprising findings
- Larger EGG exponent (eta=8) improves real-classifier certification, contrary to the theory under the concentration assumption which favors smaller eta.
- ESG certification is almost insensitive to the exponent eta, so Gaussian is not uniquely optimal.
Limitations
- Theoretical EGG lower bounds rely on the (sigma,p,2)-concentration property, which real classifiers only partly satisfy.
- ESG analytic formula relies on high-dimension approximations (d >> eta, ln(-nu) << d/eta).
- Improvements in DSRS are finite and appear to be upper-bounded by the Gaussian certification.
Experimental setup
Datasets: CIFAR-10 ImageNet
Benchmarks: CIFAR-10 ImageNet
Metrics: certified accuracy average certified radius
Baselines: Neyman-Pearson certification (Cohen et al.) DSRS (General Gaussian, eta=2)
Builds on: randomized smoothing double sampling randomized smoothing Neyman-Pearson certification
Closest papers by meaning
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