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On the Importance of Gradient Norm in PAC-Bayesian Bounds
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use the gradient-norm PAC-Bayesian bound instead of the compared prior bounds | PAC-Bayesian bounds · MNIST | generalization bound: 3.36 -> 0.04; 1.86 -> 0.04; 0.41 -> 0.04 | Helped |
| use the gradient-norm PAC-Bayesian bound instead of the compared prior bounds | PAC-Bayesian bounds · CIFAR-10 | generalization bound: 4.81 -> 0.05; 8.37 -> 0.05 | Helped |
| remove skip connections (ablation) | ResNet18 · CIFAR10 | test loss: 0.722±0.01 -> 0.631±0.02 | No clear effect |
| remove batch normalization (ablation) | ResNet18 · CIFAR10 | test loss: 0.722±0.01 -> 0.603±0.05 | No clear effect |
| remove skip connections and batch normalization (ablation) | ResNet18 · CIFAR10 | train loss: 0.541±0.06 -> 2.31±0.02 | Hurt |
| remove skip connections and batch normalization (ablation) | ResNet18 · CIFAR10 | bound on C(√m, p): 0.185±0.006 -> 0.01±0.0004 | Helped |
| increase network depth | MLPs on MNIST and CNNs on CIFAR · MNIST and CIFAR | mean gradient norm: MNIST: 0.00224 -> 0.00088 -> 0.00036; CIFAR: 0.0258 -> 0.011 -> 0.0049 | Hurt |
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