HyCNNs are a new architecture that learns convex functions with exponentially fewer parameters than ICNNs and outperforms them in convex regression and high-dimensional optimal transport on synthetic and single-cell RNA data.
P1-KAN: an effective Kolmogorov-Arnold network with application to hydraulic valley optimization
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abstract
A new Kolmogorov-Arnold network (KAN) is proposed to approximate potentially irregular functions in high dimensions. We provide error bounds for this approximation, assuming that the Kolmogorov-Arnold expansion functions are sufficiently smooth. When the function is only continuous, we also provide universal approximation theorems. We show that it outperforms multilayer perceptrons in terms of accuracy and convergence speed. We also compare it with several proposed KAN networks: it outperforms all networks for irregular functions and achieves similar accuracy to the original spline-based KAN network for smooth functions. Finally, we compare some of the KAN networks in optimizing a French hydraulic valley.
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cs.LG 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Hyper Input Convex Neural Networks for Shape Constrained Learning and Optimal Transport
HyCNNs are a new architecture that learns convex functions with exponentially fewer parameters than ICNNs and outperforms them in convex regression and high-dimensional optimal transport on synthetic and single-cell RNA data.