Research map / Learning theory and algorithms / Sample complexity
Sorting Out Lipschitz Function Approximation
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use FullSort rather than ReLU | 2-norm-constrained networks · Circular cones, input dim. 512, depth 3 | Wasserstein objective: 0.46 -> 1.00 | Helped |
| Use FullSort rather than MaxMin | 2-norm-constrained networks · Circular cones, input dim. 512, depth 3 | Wasserstein objective: 0.72 -> 1.00 | Helped |
| Increase depth from 3 to 7 | ReLU networks · Circular cones, input dim. 512 | Wasserstein objective: 0.46 -> 0.49 | Helped |
| Increase depth from 3 to 7 | MaxMin networks · Circular cones, input dim. 512 | Wasserstein objective: 0.72 -> 0.88 | Helped |
| Use Björck instead of Spectral weight constraints with ReLU | ReLU networks · MNIST GAN distributions | Wasserstein distance estimate: 0.95 ± 0.01 -> 1.40 ± 0.01 | Helped |
| Use GroupSort(4) rather than ReLU with Björck constraints | 1-Lipschitz networks · MNIST GAN distributions | Wasserstein distance estimate: 1.40 ± 0.01 -> 2.31 ± 0.01 | Helped |
| Use GroupSort(9) rather than ReLU with Björck constraints | 1-Lipschitz networks · CIFAR10 GAN distributions | Wasserstein distance estimate: 1.39 ± 0.01 -> 2.23 ± 0.02 | Helped |
| Use GroupSort(9) rather than GroupSort(4) with Björck constraints | 1-Lipschitz networks · CIFAR10 GAN distributions | Wasserstein distance estimate: 2.17 ± 0.02 -> 2.23 ± 0.02 | Helped |
| Use GroupSort(4) rather than GroupSort(9) with Björck constraints | 1-Lipschitz networks · MNIST GAN distributions | Wasserstein distance estimate: 2.31 ± 0.01 -> 2.31 ± 0.01 | No clear effect |
| Use Björck rather than Spectral weight constraints with GroupSort(4) | GroupSort(4) networks · CIFAR10 GAN distributions | Wasserstein distance estimate: 1.63 ± 0.03 -> 2.17 ± 0.02 | Helped |
Closest papers by meaning
- ECLipsE: Efficient Compositional Lipschitz Constant Estimation for Deep Neural Networks (NeurIPS 2024 · similarity 0.89)
- Approximation theory for 1-Lipschitz ResNets (NeurIPS 2025 · similarity 0.89)
- A Recipe for Improved Certifiable Robustness (ICLR 2024 · similarity 0.89)
- Novel Quadratic Constraints for Extending LipSDP beyond Slope-Restricted Activations (ICLR 2024 · similarity 0.89)
- Some Fundamental Aspects about Lipschitz Continuity of Neural Networks (ICLR 2024 · similarity 0.89)
- DP-SGD Without Clipping: The Lipschitz Neural Network Way (ICLR 2024 · similarity 0.87)
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