Research map / Learning theory and algorithms / Sample complexity
Lipschitz constant estimation of Neural Networks via sparse polynomial optimization
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use LiPopt-4 instead of SDP | Lipschitz estimation · MNIST, label 8 | Lipschitz bound: 98.8 -> 88.3 | Helped |
| Increase the LiPopt hierarchy degree from 3 to 4 (ablation) | LiPopt · MNIST, label 8 | Lipschitz bound: 94.6 -> 88.3 | Helped |
| Use LiPopt-3 instead of SDP | Lipschitz estimation · MNIST, label 8 | Lipschitz bound: 98.8 -> 94.6 | Helped |
| Use LiPopt-4 instead of the product of layer-wise bounds | Lipschitz estimation · MNIST, label 8 | Lipschitz bound: 691.5 -> 88.3 | Helped |
| Use tighter activation-derivative bounds from the restricted input region (ablation) | LiPopt-3 · Local Lipschitz estimation on random networks | Lipschitz bound | Helped |
| Increase LiPopt hierarchy degree by 1 beyond the minimum degree (ablation) | LiPopt-k · Random networks with one or two hidden layers | Relative error | Helped |
| Exploit network sparsity in the LP certificate (ablation) | LiPopt-k · Random networks with one or two hidden layers | Computation time | Helped |
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