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Sharpened Generalization Bounds based on Conditional Mutual Information and an Application to Noisy, Iterative Algorithms
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the CMI-based bound with a trajectory-informed hypothesis-test prior instead of Prior bound A | Langevin dynamics · MNIST-MLP | generalization bound: 67.93± 16.25 % -> 44.65± 4.27 % | Helped |
| Use the CMI-based bound with a trajectory-informed hypothesis-test prior instead of Prior bound A | Langevin dynamics · MNIST-CNN | generalization bound: 20.98± 5.01 % -> 16.51± 1.41 % | Helped |
| Use the CMI-based bound with a trajectory-informed hypothesis-test prior instead of Prior bound A | Langevin dynamics · CIFAR10-CNN | generalization bound: 4112.63 ± 567.08 % -> 71.76 ± 4.82 % | Helped |
| Use the CMI-based bound with a trajectory-informed hypothesis-test prior instead of Prior bound A | Langevin dynamics · FMNIST-CNN | generalization bound: 82.89 ± 12.64 % -> 48.01 ± 4.22 % | Helped |
| Optimize the decision function θ rather than use the default decision function (ablation) | CMI generalization bound · MNIST-MLP | generalization bound: 44.65± 4.27 % -> 39.06± 5.52 % | Helped |
| Optimize the decision function θ rather than use the default decision function (ablation) | CMI generalization bound · MNIST-CNN | generalization bound: 16.51± 1.41 % -> 13.24±1.53 % | Helped |
| Optimize the decision function θ rather than use the default decision function (ablation) | CMI generalization bound · CIFAR10-CNN | generalization bound: 71.76 ± 4.82 % -> 63.00 ± 5.97 % | Helped |
| Optimize the decision function θ rather than use the default decision function (ablation) | CMI generalization bound · FMNIST-CNN | generalization bound: 48.01 ± 4.22 % -> 41.17 ±5.85 % | Helped |
| Use the CMI-based bound instead of Prior bound B | Langevin dynamics · MNIST-MLP | generalization bound: 600.29± 1.99 % -> 44.65± 4.27 % | Helped |
| Use the CMI-based bound instead of Prior bound B | Langevin dynamics · MNIST-CNN | generalization bound: 245.03± 2.37 % -> 16.51± 1.41 % | Helped |
| Use the CMI-based bound instead of Prior bound B | Langevin dynamics · CIFAR10-CNN | generalization bound: 20754.32 ± 75.95 % -> 71.76 ± 4.82 % | Helped |
| Use the CMI-based bound instead of Prior bound B | Langevin dynamics · FMNIST-CNN | generalization bound: 598.62 ± 3.21 % -> 48.01 ± 4.22 % | Helped |
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