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Zero Stability Well Predicts Performance of Convolutional Neural Networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Set PreResNet-32 feature coefficient α to 1 rather than a non-zero-stable setting such as α=2 (ablation) | PreResNet-32 · CIFAR-10 | test accuracy: 79.13$\pm$0.30 -> 93.19$\pm$0.17 | Helped |
| Set LM-ResNet-44 coefficient k to 0.5 rather than k=-1.5 (ablation) | LM-ResNet-44 · CIFAR-10 | test accuracy: 81.43$\pm$0.19 -> 93.69$\pm$0.21 | Helped |
| Use zero-stable rather than non-zero-stable third-order coefficients (ablation) | Third-order-discretization CNNs · CIFAR-10, 32-, 44-, and 56-layer models | test accuracy: 77.55$\pm$0.15 to 93.28$\pm$0.12; 77.91$\pm$0.62 to 93.72$\pm$0.10; 78.29$\pm$0.09 to 94.04$\pm$0.12 | Helped |
| Use theoretically optimal coefficients (root moduli 0.33, 0.33, 1.00) (ablation) | Third-order-discretization CNNs · CIFAR-10, 32-, 44-, and 56-layer models | test accuracy: 93.28$\pm$0.12; 93.68$\pm$0.15; 94.04$\pm$0.12 | Helped |
| Use zero-stable rather than non-zero-stable root moduli (ablation) | Third-order-discretization CNNs · CIFAR-10, 56 layers, uniform noise [-0.08, 0] | test accuracy: 69.38$\pm$0.40 -> 88.31$\pm$0.33 | Helped |
| Use zero-stable rather than non-zero-stable root moduli (ablation) | Third-order-discretization CNNs · CIFAR-10, 56 layers, Gaussian noise δ=0.04 | test accuracy: 50.2$\pm$0.96 -> 76.74$\pm$0.13 | Helped |
| Use optimal root moduli 0.33, 0.33, 1.00 rather than non-zero-stable roots (ablation) | Third-order-discretization CNNs · CIFAR-10, PGD adversarial examples, ε=8/255 | adversarial accuracy: 48.80 -> 63.76 | Helped |
| Use optimal root moduli 0.33, 0.33, 1.00 rather than non-zero-stable roots (ablation) | Third-order-discretization CNNs · MNIST, FGSM adversarial examples, ε=0.3 | adversarial accuracy: 12 -> 59 | Helped |
| Reduce root moduli from 1, 0.87, 0.87 to 1, 0.33, 0.33 (ablation) | ZeroSNet44 · CIFAR-100 | generalization gap: 26.45 -> 26.43 | Helped |
| Use ZeroSNet-Opt instead of LM-ResNet | 20-layer CNNs · CIFAR-10 | accuracy: 91.67$^{\dagger}$ -> 92.01$\pm$0.35 | Helped |
| Use ZeroSNet-Opt instead of LM-ResNet | 110-layer CNNs · CIFAR-100 | accuracy: 74.13$^{\dagger}$ -> 74.50$\pm$0.28 | Helped |
| Use ZeroSNet-Opt instead of PreResNet | 18-layer CNNs · ImageNet validation | Top-1 accuracy: 69.66 -> 69.84 | Helped |
Closest papers by meaning
- Zeroth-Order Optimization at the Edge of Stability (ICML 2026 · similarity 0.88)
- Improving the Robustness of Deep Neural Networks via Stability Training (CVPR 2016 · similarity 0.88)
- NAIS-Net: Stable Deep Networks from Non-Autonomous Differential Equations (NeurIPS 2018 · similarity 0.87)
- Limitless Stability for Graph Convolutional Networks (ICLR 2023 · similarity 0.86)
- On the Stability of Graph Convolutional Neural Networks: A Probabilistic Perspective (NeurIPS 2025 · similarity 0.85)
- Stable Minima of ReLU Neural Networks Suffer from the Curse of Dimensionality: The Neural Shattering Phenomenon (NeurIPS 2025 · similarity 0.85)
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