Minimum norm interpolation by perceptra: Explicit regularization and implicit bias
This work addresses the problem of understanding interpolation mechanisms in neural networks for researchers in machine learning theory, but it is incremental as it builds on existing concepts of implicit bias and regularization.
The paper analyzes how shallow ReLU networks achieve interpolation, showing that empirical risk minimizers converge to a minimum norm interpolant under specific scaling of weight decay regularization as network width and data points increase, and numerically studies the implicit bias of optimization algorithms toward such interpolants.
We investigate how shallow ReLU networks interpolate between known regions. Our analysis shows that empirical risk minimizers converge to a minimum norm interpolant as the number of data points and parameters tends to infinity when a weight decay regularizer is penalized with a coefficient which vanishes at a precise rate as the network width and the number of data points grow. With and without explicit regularization, we numerically study the implicit bias of common optimization algorithms towards known minimum norm interpolants.