Research map / Adversarial robustness and security / Certified and empirical robustness
A Unified Algebraic Perspective on Lipschitz Neural Networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SLL layer (Gershgorin-based diagonal T with scaling q_j/q_i) instead of AOL | 1-Lipschitz CNN, CIFAR10 small-to-large sizes · CIFAR10 | certified accuracy | Helped |
| Increase offset value from sqrt(2) to 2sqrt(2) (larger offset) (ablation) | SLL on CIFAR10/CIFAR100 · CIFAR10 natural vs provable accuracy | natural accuracy vs provable accuracy at eps=1 | Mixed |
| Erratum: the epsilon in the denominator (q_j/(q_i+eps)) makes the layer no longer 1-Lipschitz; fixing via surrogate training or exponential scaling | SLL implementation · CIFAR10 / CIFAR100 | certified accuracy | Hurt |
| Replace q_j/q_i with exponential scaling exp(q_j)/exp(q_i) in SLL (ablation) | SLL X-Large, CIFAR10 · CIFAR10 | provable accuracy eps=1: 20.6 vs 27.3 (original, uncorrected) | Hurt |
| Replace q_j/q_i with surrogate training (train with original form, evaluate with corrected form) (ablation) | SLL, CIFAR10 and CIFAR100 · CIFAR10 and CIFAR100 | provable accuracy: similar to exponential scaling results | No clear effect |
| Use AOL-style choice T=diag(sum|W^TW|) with Gershgorin generalization (Q=I) vs SLL with learned q scaling | SLL vs AOL on CIFAR100 · CIFAR100 | provable accuracy | Helped |
| Corrected SLL: AOL vs SLL on CIFAR10 at eps 72/255 and 108/255 | SLL vs AOL after erratum · CIFAR10 | provable accuracy | Mixed |
| Replace Local-Lip-B with SLL X-Large for TinyImageNet | TinyImageNet · TinyImageNet | provable accuracy | Mixed |
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