Mixup Augmentation with Multiple Interpolations

TL;DR

This work extends mixup data augmentation by introducing multi-mix, which generates $K>1$ interpolations per sample pair using interpolants $\lambda_k$ drawn from $\Beta(\alpha,\alpha)$. The authors provide a variance-reduction analysis showing that increasing $K$ reduces gradient variance, and they derive an empirical loss that averages over all interpolations along the mixup path. They extend multiple mixup variants (input, manifold, cutmix, puzzle-mix) to the multi-interpolation setting and demonstrate across synthetic data, CIFAR-100, Tiny-Imagenet, ImageNet-1K, WSOL, corruption robustness, transfer learning to CUB, and speech tasks that multi-mix improves generalization, robustness, and calibration compared to standard mixup and baselines. The results indicate notable gains in accuracy and reliability with only modest computational overhead, making multi-mix a practical enhancement to the mixup family for diverse domains.

Abstract

Mixup and its variants form a popular class of data augmentation techniques.Using a random sample pair, it generates a new sample by linear interpolation of the inputs and labels. However, generating only one single interpolation may limit its augmentation ability. In this paper, we propose a simple yet effective extension called multi-mix, which generates multiple interpolations from a sample pair. With an ordered sequence of generated samples, multi-mix can better guide the training process than standard mixup. Moreover, theoretically, this can also reduce the stochastic gradient variance. Extensive experiments on a number of synthetic and large-scale data sets demonstrate that multi-mix outperforms various mixup variants and non-mixup-based baselines in terms of generalization, robustness, and calibration.

Figures (8)

• Figure 1: An example of mixup training. Here, a cat and a dog are mixed with a mixing coefficient $\lambda=0.5$. The symbol $\succ$ describes relative ordering along the mixup transformation paths (cat $\succ$ (half-cat+half-dog) $\succ$ dog) in both input and output spaces. Mixup training improves performance by leveraging order relationship along with mixup transformation paths in the hidden space of $\mathcal{F}$.
• Figure 2: Examples of input mixup and saliency-based mixup techniques.
• Figure 3: Examples interpolations ($\hat{h}^0_1, \hat{h}^0_2, \hat{h}^0_3, \hat{h}^0_4$) generated by input mixup (top), cutmix (middle), and puzzle-mix (bottom).
• Figure 4: The noisy $\textit{spiral}$ data and decision boundaries learned without mixup, with manifold mixup, and manifold mixup with multiple interpolations. Values in brackets are the top-1 test accuracies obtained.
• Figure 5: Example localization results on CUB 200-2011 from networks pretrained with different mixup methods. Red: Predicted bounding box; Green: Ground-truth bounding box.

Theorems & Definitions (2)

• Proposition 3.1
• Proposition 3.2