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Efficient Neural Network Robustness Certification with General Activation Functions
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use adaptive linear activation bounds instead of Fast-Lin bounds | ReLU networks · MNIST 4×[1024], ℓ1 | certified lower bound: 1.57649 -> 1.88217; +19% | Helped |
| Use adaptive linear activation bounds instead of Fast-Lin bounds | ReLU networks · MNIST 4×[1024], ℓ2 | certified lower bound: 0.18891 -> 0.22811; +21% | Helped |
| Use adaptive linear activation bounds instead of Fast-Lin bounds | ReLU networks · MNIST 4×[1024], ℓ∞ | certified lower bound: 0.00823 -> 0.00997; +21% | Helped |
| Use adaptive linear activation bounds instead of Fast-Lin bounds | ReLU networks · CIFAR-10 7×[1024], ℓ1 | certified lower bound: 0.86468 -> 1.09067; +26% | Helped |
| Use adaptive linear activation bounds instead of Fast-Lin bounds | ReLU networks · CIFAR-10 7×[1024], ℓ2 | certified lower bound: 0.05937 -> 0.07496; +26% | Helped |
| Use adaptive linear activation bounds instead of Fast-Lin bounds | ReLU networks · CIFAR-10 7×[1024], ℓ∞ | certified lower bound: 0.00134 -> 0.00169; +26% | Helped |
| Use adaptive activation bounds rather than fixed Fast-Lin-style bounds | ReLU networks · large ReLU networks | certified lower bound: up to 28% | Helped |
| Use quadratic activation bounds | CROWN on 2-layer ReLU networks · MNIST 2×[20] | certified lower bound | Helped |
| Use tanh activations rather than ReLU | CROWN, MNIST 3×[1024] · MNIST 3×[1024], ℓ2 | certified lower bound: 0.50841 -> 0.27287 | Hurt |
| Use sigmoid activations rather than ReLU | CROWN, MNIST 3×[1024] · MNIST 3×[1024], ℓ2 | certified lower bound: 0.50841 -> 0.44471 | Hurt |
| Use arctan activations rather than ReLU | CROWN, MNIST 3×[1024] · MNIST 3×[1024], ℓ2 | certified lower bound: 0.50841 -> 0.30345 | Hurt |
| Use general activations instead of piecewise-linear ReLU | CROWN on large networks · MNIST and CIFAR-10 | computation time: about 20% additional computational overhead | Hurt |
Closest papers by meaning
- SOL: Sampling-based Optimal Linear bounding of arbitrary scalar functions (NeurIPS 2023 · similarity 0.91)
- Towards Fast Computation of Certified Robustness for ReLU Networks (ICML 2018 · similarity 0.90)
- Training for Faster Adversarial Robustness Verification via Inducing ReLU Stability (ICLR 2019 · similarity 0.89)
- DeepBern-Nets: Taming the Complexity of Certifying Neural Networks Using Bernstein Polynomial Activations and Precise Bound Propagation (AAAI 2024 · similarity 0.88)
- Probably Approximately Global Robustness Certification (ICML 2025 · similarity 0.88)
- Learning Better Certified Models from Empirically-Robust Teachers (NeurIPS 2026 · similarity 0.88)
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