For two-layer KANs trained with gradient descent under logistic loss and NTK-separable assumption, polylogarithmic width suffices for 1/T optimization and 1/n generalization rates, while differential privacy requires the same width and yields √d/(nε) utility.
Combining (37) and the above equality and dividing byηyield g,Θ ∗ −Θ + ≥ 1 2η ∥Θ+ −Θ ∗∥2 2 +∥Θ−Θ +∥2 2 − ∥Θ−Θ ∗∥2 2
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Optimization, Generalization and Differential Privacy Bounds for Gradient Descent on Kolmogorov-Arnold Networks
For two-layer KANs trained with gradient descent under logistic loss and NTK-separable assumption, polylogarithmic width suffices for 1/T optimization and 1/n generalization rates, while differential privacy requires the same width and yields √d/(nε) utility.