Compositionally sparse functions given by finite computation trees admit deep KAN representations with dimension-independent layer-wise Lipschitz product bounds P(KAN) <= max(C*,1)^L_f where L_f scales linearly with tree size N.
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Layer-wise Lipschitz-Product Control for Deep Kolmogorov--Arnold Network Representations of Compositionally Structured Functions
Compositionally sparse functions given by finite computation trees admit deep KAN representations with dimension-independent layer-wise Lipschitz product bounds P(KAN) <= max(C*,1)^L_f where L_f scales linearly with tree size N.