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State-of-the-art results on image recognition tasks are achieved usingover-parameterized learning algorithms that (nearly) perfectly fit the trainingset and are known to fit well even random labels. This tendency to memorize thelabels of the training data is not explained by existing theoretical analyses.Memorization of the training data also presents significant privacy risks whenthe training data contains sensitive personal information and thus it isimportant to understand whether such memorization is necessary for accuratelearning.  We provide the first conceptual explanation and a theoretical model for thisphenomenon. Specifically, we demonstrate that for natural data distributionsmemorization of labels is necessary for achieving close-to-optimalgeneralization error. Crucially, even labels of outliers and noisy labels needto be memorized. The model is motivated and supported by the results of severalrecent empirical works. In our model, data is sampled from a mixture ofsubpopulations and our results show that memorization is necessary whenever thedistribution of subpopulation frequencies is long-tailed. Image and text datais known to be long-tailed and therefore our results establish a formal linkbetween these empirical phenomena. Our results allow to quantify the cost oflimiting memorization in learning and explain the disparate effects thatprivacy and model compression have on different subgroups.

Does Learning Require Memorization? A Short Tale about a Long Tail