Research map / Adversarial robustness and security / Certified and empirical robustness
Verification of Non-Linear Specifications for Neural Networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use convex-relaxable specifications and convex optimization to verify nonlinear properties | Neural network verification · CIFAR-10 semantic consistency | adversarial bound minus verification bound: .9% | Helped |
| Use convex-relaxable specifications and convex optimization to verify nonlinear properties | Neural network verification · Digit-sum error, N=2 | adversarial bound minus verification bound: 1.5% | Helped |
| Use the convex relaxation instead of exhaustive verification | Pendulum energy verification · Damped pendulum, perturbation radius 0.02 | verification bound: 73.98% -> 70.00% | Hurt |
| Add an energy-consistency penalty during training | Pendulum dynamics model · Damped pendulum, perturbation radius .06 | verification bound: 34.53% -> 64.16% | Helped |
| Train for higher verification of semantic consistency | CIFAR-10 classifier · CIFAR-10 semantic specification | verification bound: 84.3% -> 93.5% | Helped |
| Add the SDP constraint to the quadratic relaxation (ablation) | Pendulum model B verification · Damped pendulum, small perturbation radius δ≤0.02 | additional test points verified: 0.9% | Helped |
| Add the SDP constraint to the quadratic relaxation (ablation) | Pendulum model B verification · Damped pendulum, increasing perturbation radius | additional test points verified: 4.8% | Helped |
| Increase the number of summed digits from 2 to 4 (ablation) | Digit-sum verification · Digit sum, δ=2/255 | adversarial bound minus verification bound: 4.2%, ~14.1%, ~26.1% | Hurt |
| Increase the number of summed digits from 2 to 4 (ablation) | Digit-sum verification · Digit sum, δ=6/255 | adversarial bound minus verification bound: 19.9%,~49.7%,~51.8% | Hurt |
| Use a convex-relaxation verifier rather than falsification alone | Verification of nonlinear specifications · Damped pendulum energy specification, perturbation radius 0.06 | verification bound: 70.00%; 22.05% | Mixed |
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