A random shift of Gaussian inputs forces the first Hermite coefficient of any non-linear target to be large, yielding near-linear sample complexity independent of the target's information exponent, and a similar result holds for juntas.
The merged-staircase property: a necessary and nearly sufficient condition for sgd learning of sparse functions on two-layer neural networks
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Low-dimensional Functions are Efficiently Learnable under Randomly Biased Distributions
A random shift of Gaussian inputs forces the first Hermite coefficient of any non-linear target to be large, yielding near-linear sample complexity independent of the target's information exponent, and a similar result holds for juntas.