Research map / Learning theory and algorithms / Sample complexity
Provable Benefit of Mixup for Finding Optimal Decision Boundaries
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Mixup (pairwise convex combinations) instead of ERM training | logistic regression on D_kappa · synthetic D_kappa, kappa=2.0 | alignment with Bayes optimal direction | Helped |
| Use masking-based Mixup (CutMix-style) instead of ERM | logistic regression on D_kappa · synthetic D_kappa, kappa=0.5 and 2.0 | alignment with Bayes optimal direction | Hurt |
| Increase separability kappa for ERM | ERM sample complexity · theory, D_kappa | sample complexity to near Bayes optimal: exp(Omega(kappa^2)) vs Mixup kappa^2 | Hurt |
| Use Mixup instead of ERM | sample complexity theory · theory, D_kappa | sample complexity to near Bayes optimal: exp(Omega(kappa^2)) to Omega(kappa^2) | Helped |
| Use 2D two-layer ReLU network with Mixup instead of ERM on highly separable sine data | 2-layer ReLU network, 2D synthetic data · 2D sine-shaped synthetic data, small noise | decision boundary shape | Helped |
| Use Mixup instead of ERM on CIFAR-10 | VGG19 and ResNet18 · CIFAR-10 decision boundary distance (input perturbation norm) | distance of decision boundary from data | Helped |
| Use CutMix instead of ERM on CIFAR-10 | VGG19 and ResNet18 · CIFAR-10 decision boundary distance | distance of decision boundary from data | Mixed |
Closest papers by meaning
- Selective Mixup Helps with Distribution Shifts, But Not (Only) because of Mixup (ICML 2024 · similarity 0.88)
- Pushing Boundaries: Mixup's Influence on Neural Collapse (ICLR 2024 · similarity 0.87)
- Optimal Algorithms for Augmented Testing of Discrete Distributions (NeurIPS 2024 · similarity 0.85)
- MixMin: Finding Data Mixtures via Convex Minimization (ICML 2025 · similarity 0.85)
- Provably Reliable Classifier Guidance via Cross-Entropy Control (NeurIPS 2026 · similarity 0.84)
- Optimal Sample Complexity of Contrastive Learning (ICLR 2024 · similarity 0.84)
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