In overparametrized 2-layer networks, non-smooth activations provably yield large NTK minimum eigenvalues, while smooth activations can have zero or exponentially small eigenvalues on low-dimensional data, predicting slow training.
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Effect of Activation Functions on the Training of Overparametrized Neural Nets
In overparametrized 2-layer networks, non-smooth activations provably yield large NTK minimum eigenvalues, while smooth activations can have zero or exponentially small eigenvalues on low-dimensional data, predicting slow training.