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A surprising phenomenon in modern machine learning is the ability of a highlyoverparameterized model to generalize well (small error on the test data) evenwhen it is trained to memorize the training data (zero error on the trainingdata). This has led to an arms race towards increasingly overparameterizedmodels (c.f., deep learning). In this paper, we study an underexplored hiddencost of overparameterization: the fact that overparameterized models may bemore vulnerable to privacy attacks, in particular the membership inferenceattack that predicts the (potentially sensitive) examples used to train amodel. We significantly extend the relatively few empirical results on thisproblem by theoretically proving for an overparameterized linear regressionmodel in the Gaussian data setting that membership inference vulnerabilityincreases with the number of parameters. Moreover, a range of empirical studiesindicates that more complex, nonlinear models exhibit the same behavior.Finally, we extend our analysis towards ridge-regularized linear regression andshow in the Gaussian data setting that increased regularization also increasesmembership inference vulnerability in the overparameterized regime.

Parameters or Privacy: A Provable Tradeoff Between Overparameterization and Membership Inference