Research map / Learning theory and algorithms / Kernels and regression theory
On Lipschitz Regularization of Convolutional Layers using Toeplitz Matrix Theory
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add LipBound Lipschitz regularization to adversarial training | Wide ResNet on CIFAR10 · CIFAR10 test | PGD-ℓ∞ accuracy: 0.426±0.000 -> 0.457±0.002 | Helped |
| Add LipBound Lipschitz regularization to adversarial training | Wide ResNet on CIFAR10 · CIFAR10 test | Accuracy: 0.864±0.001 -> 0.808±0.022 | Hurt |
| Add LipBound Lipschitz regularization to adversarial training | Wide ResNet on CIFAR10 · CIFAR10 test | C&W-ℓ2 0.6 accuracy: 0.477±0.000 -> 0.547±0.022 | Helped |
| Add LipBound Lipschitz regularization to adversarial training | Wide ResNet on CIFAR100 · CIFAR100 test | PGD-ℓ∞ accuracy: 0.199±0.000 -> 0.215±0.004 | Helped |
| Add LipBound Lipschitz regularization to adversarial training | Wide ResNet on CIFAR100 · CIFAR100 test | Accuracy: 0.591±0.000 -> 0.552±0.019 | Hurt |
| Add LipBound Lipschitz regularization to adversarial training | ResNet-101 on ImageNet · ImageNet | PGD-ℓ∞ 0.031 accuracy: 0.118 -> 0.121; 0.118 -> 0.123 | Helped |
| Increase LipReg λ₂ from 0.0006 to 0.0010 (ablation) | AT+LipReg ResNet-101 · ImageNet | Natural accuracy: 0.515 -> 0.519 | Helped |
| Increase LipReg λ₂ from 0.0006 to 0.0010 (ablation) | AT+LipReg ResNet-101 · ImageNet | C&W-ℓ2 3.00 accuracy: 0.105 -> 0.129 | Helped |
| Use LipBound/PolyGrid instead of the convolutional power method | Lipschitz regularization of convolutional layers · 1x3x3 convolution kernels | approximation ratio: 0.973±0.006 -> 0.992±0.012 | Helped |
Closest papers by meaning
- Efficient Bound of Lipschitz Constant for Convolutional Layers by Gram Iteration (ICML 2023 · similarity 0.93)
- Lipschitz regularity of deep neural networks: analysis and efficient estimation (NeurIPS 2018 · similarity 0.92)
- ECLipsE: Efficient Compositional Lipschitz Constant Estimation for Deep Neural Networks (NeurIPS 2024 · similarity 0.90)
- Improved techniques for deterministic l2 robustness (NeurIPS 2022 · similarity 0.90)
- Some Fundamental Aspects about Lipschitz Continuity of Neural Networks (ICLR 2024 · similarity 0.88)
- Approximation theory for 1-Lipschitz ResNets (NeurIPS 2025 · similarity 0.88)
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