Kolmogorov-Arnold Networks (KANs) replace fixed activations in deep architectures with learnable univariate edge functions, making the choice of edge parametrisation central. Existing variants rely on...
Monotonicity has been a long-running architectural inductive bias for neural networks, motivated by tabular, scientific, and economic settings where outputs are known to respond monotonically to certain inputs. Existing approaches are MLP- or flow-based and lack per-edge functional transparency; the only Kolmogorov--Arnold Network (KAN) variant with monotonicity, MonoKAN, enforces the constraint only on a restricted parameter subset and requires a projection-style training procedure.
The paper investigates Kolmogorov‑Arnold networks (KANs) and their approximation properties. It shows that while KANs can achieve dimension‑independent approximation exponents for targets with smooth univariate edge functions, this advantage is tied to the target structure rather than the architecture itself. Empirical tests reveal that KANs outperform MLPs only when each nonlinear component depends on a single input coordinate; otherwise, MLPs can be more efficient, especially under tight parameter budgets or for interacting targets.
By Yunhao Ni, Yuxin Guo, Jie Luo, Wenjun Wu, Lei Huang
arXiv:2607. 15525v1 Announce Type: cross Abstract: Kolmogorov--Arnold Networks (KANs) replace fixed node activations with learned one-dimensional edge functions, offering an explicit interface for interpretation and a possible alternative to transformer feed-forward networks.
By Felippe Alves, Renato Vicente
arXiv:2606. 17886v1 Announce Type: new Abstract: Monotonicity has been a long-running architectural inductive bias for neural networks, motivated by tabular, scientific, and economic settings where outputs are known to respond monotonically to certain inputs.
By Mikhail Krasnov, Carolina Fortuna, Bla\v{z} Bertalani\v{c}
arXiv:2608. 00737v1 Announce Type: new Abstract: Hard-constrained recurrent physics-informed networks (HRPINNs) embed known dynamics inside a recurrent numerical integrator and restrict a neural branch to learning only the residual dynamics that the first-principles model does not capture.
By Enzo Nicolas Spotorno, Josafat Leal Filho