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Modern deep learning training procedures rely on model regularizationtechniques such as data augmentation methods, which generate training samplesthat increase the diversity of data and richness of label information. Apopular recent method, mixup, uses convex combinations of pairs of originalsamples to generate new samples. However, as we show in our experiments, mixupcan produce undesirable synthetic samples, where the data is sampled off themanifold and can contain incorrect labels. We propose $\zeta$-mixup, ageneralization of mixup with provably and demonstrably desirable propertiesthat allows convex combinations of $N \geq 2$ samples, leading to morerealistic and diverse outputs that incorporate information from $N$ originalsamples by using a $p$-series interpolant. We show that, compared to mixup,$\zeta$-mixup better preserves the intrinsic dimensionality of the originaldatasets, which is a desirable property for training generalizable models.Furthermore, we show that our implementation of $\zeta$-mixup is faster thanmixup, and extensive evaluation on controlled synthetic and 24 real-worldnatural and medical image classification datasets shows that $\zeta$-mixupoutperforms mixup and traditional data augmentation techniques.

Multi-Sample $\zeta$-mixup: Richer, More Realistic Synthetic Samples from a $p$-Series Interpolant