Related papers: Geometric Kolmogorov-Arnold Superposition Theorem
A wide range of deep learning-based machine learning techniques are extensively applied to the design of high-entropy alloys (HEAs), yielding numerous valuable insights. Kolmogorov-Arnold Networks (KAN) is a recently developed architecture…
Kolmogorov-Arnold Networks (KANs) relocate learnable nonlinearities from nodes to edges, demonstrating remarkable capabilities in scientific machine learning and interpretable modeling. However, current KAN implementations suffer from…
The field of scientific machine learning, which originally utilized multilayer perceptrons (MLPs), is increasingly adopting Kolmogorov-Arnold Networks (KANs) for data encoding. This shift is driven by the limitations of MLPs, including poor…
Kolmogorov-Arnold Networks (KANs) are a recently introduced neural architecture that replace fixed nonlinearities with trainable activation functions, offering enhanced flexibility and interpretability. While KANs have been applied…
While accurate, black-box system identification models lack interpretability of the underlying system dynamics. This paper proposes State-Space Kolmogorov-Arnold Networks (SS-KAN) to address this challenge by integrating Kolmogorov-Arnold…
There is a longstanding debate whether the Kolmogorov-Arnold representation theorem can explain the use of more than one hidden layer in neural networks. The Kolmogorov-Arnold representation decomposes a multivariate function into an…
We explore the integration of Kolmogorov Networks (KANs) into molecular dynamics (MD) simulations to improve interatomic potentials. We propose that widely used potentials, such as the Lennard-Jones (LJ) potential, the embedded atom model…
Kolmogorov-Arnold Networks (KAN) \cite{liu2024kan} were very recently proposed as a potential alternative to the prevalent architectural backbone of many deep learning models, the multi-layer perceptron (MLP). KANs have seen success in…
Traditional constitutive models rely on hand-crafted parametric forms with limited expressivity and generalizability, while neural network-based models can capture complex material behavior but often lack interpretability. To balance these…
Time series classification is a relevant step supporting decision-making processes in various domains, and deep neural models have shown promising performance in this respect. Despite significant advancements in deep learning, the…
We propose a new approach for approximating functions in $C([0,1]^d)$ via Kolmogorov superposition theorem (KST) based on the linear spline interpolation of the outer function in the Kolmogorov representation. We improve the results in…
Kolmogorov-Arnold Networks (KANs) have recently demonstrated promising potential in scientific machine learning, partly due to their capacity for grid adaptation during training. However, existing adaptation strategies rely solely on input…
Function approximation is a critical task in various fields. However, existing neural network approaches struggle with locally complex or discontinuous functions due to their reliance on a single global model covering the entire problem…
Weight-space models learn directly from the parameters of neural networks, enabling tasks such as predicting their accuracy on new datasets. Naive methods -- like applying MLPs to flattened parameters -- perform poorly, making the design of…
Recently, Kolmogorov-Arnold Networks (KANs) have been proposed as an alternative to multilayer perceptrons, suggesting advantages in performance and interpretability. We study a typical binary event classification task in high-energy…
Traditional neural networks struggle to capture the spectral structure of complex signals. Fourier neural networks (FNNs) attempt to address this by embedding Fourier series components, yet many real-world signals are almost-periodic with…
There is increasing interest in solving partial differential equations (PDEs) by casting them as machine learning problems. Recently, there has been a spike in exploring Kolmogorov-Arnold Networks (KANs) as an alternative to traditional…
We propose a novel approach that enhances multivariate function approximation using learnable path signatures and Kolmogorov-Arnold networks (KANs). We enhance the learning capabilities of these networks by weighting the values obtained by…
We introduce the Kolmogorov-Arnold Network for Dynamics (KANDy) as a zero-depth, wide neural architecture capable of discovering governing equations in chaotic and complex dynamical systems. Building on the foundation of Kolmogorov-Arnold…
Small-angle scattering (SAS) techniques are indispensable tools for probing the structure of soft materials. However, traditional analytical models often face limitations in structural inversion for complex systems, primarily due to the…