On the Inherent Regularization Effects of Noise Injection During Training
This provides a theoretical foundation for noise injection as a regularization technique, which is incremental but clarifies its effects in machine learning.
The paper theoretically analyzes how injecting Gaussian noise into training data acts as a weighted ridge regularization, improving generalization in random feature models, with numerical results confirming accuracy in moderate dimensions.
Randomly perturbing networks during the training process is a commonly used approach to improving generalization performance. In this paper, we present a theoretical study of one particular way of random perturbation, which corresponds to injecting artificial noise to the training data. We provide a precise asymptotic characterization of the training and generalization errors of such randomly perturbed learning problems on a random feature model. Our analysis shows that Gaussian noise injection in the training process is equivalent to introducing a weighted ridge regularization, when the number of noise injections tends to infinity. The explicit form of the regularization is also given. Numerical results corroborate our asymptotic predictions, showing that they are accurate even in moderate problem dimensions. Our theoretical predictions are based on a new correlated Gaussian equivalence conjecture that generalizes recent results in the study of random feature models.