Research map / Adversarial robustness and security / Certified and empirical robustness
Does Data Augmentation Lead to Positive Margin?
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add N spherical perturbations per training point with radius calibrated to the max-margin scale | Linear classifiers trained on linearly separable data · Linearly separable data | worst-case margin: \dfrac{1}{2\sqrt{2}}\sqrt{\dfrac{\log(N/d)}{d}}r | Helped |
| Choose perturbation radius so the lower-bound guarantee is a constant fraction of the max-margin | Spherical random DA for linear classifiers · Linearly separable data | number of augmentations for constant-factor max-margin: O(nd^2) | Helped |
| Use perturbations whose radius is comparable to the target margin and seek a margin close to that radius | Spherical random DA for linear classifiers · Linearly separable data | worst-case margin relative to perturbation radius: \left(\sqrt{\dfrac{2\ln(|S'|)+2\ln(1/\delta)}{d}}\right)r | Hurt |
| Increase the perturbation radius to at least the stated large-radius threshold while using at least 16d positive-class perturbations | Linear classifiers · Two-point linearly separable data | probability augmented data remain linearly separable: 1-2e^{-d/6} | Hurt |
| Keep the perturbation radius at or below the stated dimension- and sample-size-dependent threshold | Linear classifiers · Linearly separable data | probability augmented data remain linearly separable: 1-N^{1-\beta} | Helped |
| Add fewer than d+1 artificial points | Linear classifiers · Linearly separable data | worst-case margin: d+1 | Hurt |
| Use bounded perturbations but leave at least one positive training point without an augmentation | Linear classifiers · Constructed linearly separable data | worst-case margin: 0 | Hurt |
| Use spherical perturbations with radius r ≤ ε and at least Cd perturbations per point | ε-respectful classifiers · Data with nonempty ε-respectful classifier class | worst-case margin: \frac{1}{2\sqrt{2}}\sqrt{\frac{\log(N/d)}{d}}r | Helped |
| Use a bounded perturbation radius larger than ε | ε-respectful classifiers · Constructed data | worst-case margin: 0 | Hurt |
| Use perturbation radius of order √d times the max-margin in the stated two-point setting | ε-respectful classifiers · Two-point data | probability the augmented respectful-classifier set is empty: 1 - 2e^{-d/6} | Hurt |
Closest papers by meaning
- Data Augmentation Can Improve Robustness (NeurIPS 2021 · similarity 0.89)
- Optimizing Data Augmentation through Bayesian Model Selection (ICLR 2026 · similarity 0.89)
- Mind Your Margin and Boundary: Are Your Distilled Datasets Truly Robust? (ICML 2026 · similarity 0.87)
- A Data-Augmentation Is Worth A Thousand Samples: Analytical Moments And Sampling-Free Training (NeurIPS 2022 · similarity 0.87)
- Detecting Brittle Decisions for Free: Leveraging Margin Consistency in Deep Robust Classifiers (NeurIPS 2024 · similarity 0.86)
- Characterizing the Generalization Error of Random Feature Regression with Arbitrary Data-Augmentation (NeurIPS 2026 · similarity 0.85)
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