Tuning Frequency Bias in Neural Network Training with Nonuniform DataDownload PDF

Published: 01 Feb 2023, Last Modified: 25 Feb 2023ICLR 2023 posterReaders: Everyone
Keywords: frequency bias, neural networks, training, nonuniform, Sobolev norms, Neural Tangent Kernel
Abstract: Small generalization errors of over-parameterized neural networks (NNs) can be partially explained by the frequency biasing phenomenon, where gradient-based algorithms minimize the low-frequency misfit before reducing the high-frequency residuals. Using the Neural Tangent Kernel (NTK), one can provide a theoretically rigorous analysis for training where data are drawn from constant or piecewise-constant probability densities. Since most training data sets are not drawn from such distributions, we use the NTK model and a data-dependent quadrature rule to theoretically quantify the frequency biasing of NN training given fully nonuniform data. By replacing the loss function with a carefully selected Sobolev norm, we can further amplify, dampen, counterbalance, or reverse the intrinsic frequency biasing in NN training.
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