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arXiv · 2104.12174

Demystification of Few-shot and One-shot Learning

Ivan Y. Tyukin·Alexander N. Gorban·Muhammad H. Alkhudaydi·Qinghua Zhou
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Abstract

Few-shot and one-shot learning have been the subject of active and intensive research in recent years, with mounting evidence pointing to successful implementation and exploitation of few-shot learning algorithms in practice. Classical statistical learning theories do not fully explain why few- or one-shot learning is at all possible since traditional generalisation bounds normally require large training and testing samples to be meaningful. This sharply contrasts with numerous examples of successful one- and few-shot learning systems and applications. In this work we present mathematical foundations for a theory of one-shot and few-shot learning and reveal conditions specifying when such learning schemes are likely to succeed. Our theory is based on intrinsic properties of high-dimensional spaces. We show that if the ambient or latent decision space of a learning machine is sufficiently high-dimensional than a large class of objects in this space can indeed be easily learned from few examples provided that certain data non-concentration conditions are met.

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Ivan Y. Tyukin, Alexander N. Gorban, Muhammad H. Alkhudaydi, Qinghua Zhou. 2021-05-29. Demystification of Few-shot and One-shot Learning. https://doi.org/10.1109/ijcnn52387.2021.9534395.

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