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While classical in many theoretical settings - and in particular instatistical physics-inspired works - the assumption of Gaussian i.i.d. inputdata is often perceived as a strong limitation in the context of statistics andmachine learning. In this study, we redeem this line of work in the case ofgeneralized linear classification, a.k.a. the perceptron model, with randomlabels. We argue that there is a large universality class of high-dimensionalinput data for which we obtain the same minimum training loss as for Gaussiandata with corresponding data covariance. In the limit of vanishingregularization, we further demonstrate that the training loss is independent ofthe data covariance. On the theoretical side, we prove this universality for anarbitrary mixture of homogeneous Gaussian clouds. Empirically, we show that theuniversality holds also for a broad range of real datasets.

Gaussian Universality of Perceptrons with Random Labels