Evaluations of Machine Learning Privacy Defenses are Misleading

Empirical defenses for machine learning privacy forgo the provable guarantees of differential privacy in the hope of achieving higher utility while resisting realistic adversaries. We identify severe pitfalls in existing empirical privacy evaluations (based on membership inference attacks) that result in misleading conclusions. In particular, we show that prior evaluations fail to characterize the privacy leakage of the most vulnerable samples, use weak attacks, and avoid comparisons with practical differential privacy baselines. In 5 case studies of empirical privacy defenses, we find that prior evaluations underestimate privacy leakage by an order of magnitude. Under our stronger evaluation, none of the empirical defenses we study are competitive with a properly tuned, high-utility DP-SGD baseline (with vacuous provable guarantees).

Strong inductive biases provably prevent harmless interpolation

Classical wisdom suggests that estimators should avoid fitting noise to achieve good generalization. In contrast, modern overparameterized models can yield small test error despite interpolating noise -- a phenomenon often called "benign overfitting" or "harmless interpolation". This paper argues that the degree to which interpolation is harmless hinges upon the strength of an estimator's inductive bias, i.e., how heavily the estimator favors solutions with a certain structure: while strong inductive biases prevent harmless interpolation, weak inductive biases can even require fitting noise to generalize well. Our main theoretical result establishes tight non-asymptotic bounds for high-dimensional kernel regression that reflect this phenomenon for convolutional kernels, where the filter size regulates the strength of the inductive bias. We further provide empirical evidence of the same behavior for deep neural networks with varying filter sizes and rotational invariance.

Interpolation can hurt robust generalization even when there is no noise

Numerous recent works show that overparameterization implicitly reduces variance for min-norm interpolators and max-margin classifiers. These findings suggest that ridge regularization has vanishing benefits in high dimensions. We challenge this narrative by showing that, even in the absence of noise, avoiding interpolation through ridge regularization can significantly improve generalization. We prove this phenomenon for the robust risk of both linear regression and classification and hence provide the first theoretical result on robust overfitting.