arXiv:2608. 25807v1 Announce Type: new Abstract: Kolmogorov-Arnold Networks (KANs) replace fixed activations in deep architectures with learnable univariate edge functions, making the choice of edge parametrisation central.
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.
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.
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.
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.
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.
arXiv:2608. 14773v1 Announce Type: cross Abstract: The efficient-KAN literature---covering Chebyshev, wavelet, and radial-basis-function variants of the original Kolmogorov-Arnold Network---has been benchmarked almost entirely on clean data.
The paper studies Kolmogorov‑Arnold Networks (KANs), a neural architecture that treats activation functions as learnable components, offering improved interpretability for scientific applications. It investigates how KANs scale with dataset size on image classification tasks (MNIST, Fashion‑MNIST) and a magnetic‑parameter regression task, revealing a broken neural scaling law that transitions from a faster to a slower decay of test loss as data grows. The authors also analyze how the learned activation functions evolve from simple linear approximations to more complex, interpretable symbolic forms as more data is provided.
RecKAN introduces a learnable recursive polynomial basis for Kolmogorov–Arnold Networks, replacing fixed bases like B-splines or Chebyshev polynomials. The basis is defined by a second‑order polynomial recurrence whose five coefficients are jointly learned with the network, enabling it to encompass classical families such as Chebyshev, Fibonacci, Pell, and Jacobsthal. Experiments across image, text, biomedical time‑series classification, and forecasting tasks show RecKAN outperforming parameter‑matched KAN baselines and achieving state‑of‑the‑art results on several benchmarks.
arXiv:2608. 00859v1 Announce Type: new Abstract: Kolmogorov--Arnold Networks (KANs) replace scalar edge weights with learnable univariate functions parameterized by multiple basis coefficients.
Methods operating on Vision Transformer (ViT) feature spaces typically rely on Euclidean distance or cosine similarity. This assumes that every direction is equally meaningful, but there is no reason...
arXiv:2609.26067v1 Announce Type: new Abstract: Kolmogorov--Arnold Networks (KANs) replace scalar edge weights with learnable univariate functions, increasing flexibility but also parameter memory be...