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A popular recent method,mixup<\/jats:italic>, uses convex combinations of pairs of original samples to generate new samples. However, as we show in our experiments,mixup<\/jats:italic>\u00a0can produce undesirable synthetic samples, where the data is sampled off the manifold and can contain incorrect labels. We propose$$\\zeta $$<\/jats:tex-math>\u03b6<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>-mixup<\/jats:italic>, a generalization ofmixup<\/jats:italic>\u00a0with provably and demonstrably desirable properties that allows convex combinations of$${T} \\ge 2$$<\/jats:tex-math>T<\/mml:mi>\u2265<\/mml:mo>2<\/mml:mn><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>samples, leading to more realistic and diverse outputs that incorporate information from$${T}$$<\/jats:tex-math>T<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>original samples by using ap<\/jats:italic>-series interpolant. We show that, compared tomixup<\/jats:italic>,$$\\zeta $$<\/jats:tex-math>\u03b6<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>-mixup<\/jats:italic>\u00a0better preserves the intrinsic dimensionality of the original datasets, which is a desirable property for training generalizable models. Furthermore, we show that our implementation of$$\\zeta $$<\/jats:tex-math>\u03b6<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>-mixup<\/jats:italic>\u00a0is faster thanmixup<\/jats:italic>, and extensive evaluation on controlled synthetic and 26 diverse real-world natural and medical image classification datasets shows that$$\\zeta $$<\/jats:tex-math>\u03b6<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>-mixup<\/jats:italic>\u00a0outperformsmixup<\/jats:italic>, CutMix,\u00a0and traditional data augmentation techniques. The code will be released athttps:\/\/github.com\/kakumarabhishek\/zeta-mixup<\/jats:ext-link>.<\/jats:p>","DOI":"10.1186\/s40537-024-00898-6","type":"journal-article","created":{"date-parts":[[2024,3,23]],"date-time":"2024-03-23T12:01:52Z","timestamp":1711195312000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Multi-sample $$\\zeta $$-mixup: richer, more realistic synthetic samples from a p-series interpolant"],"prefix":"10.1186","volume":"11","author":[{"given":"Kumar","family":"Abhishek","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Colin J.","family":"Brown","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ghassan","family":"Hamarneh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,3,23]]},"reference":[{"key":"898_CR1","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1016\/j.neunet.2014.09.003","volume":"61","author":"J Schmidhuber","year":"2015","unstructured":"Schmidhuber J. 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