Related papers: Kolmogorov-Arnold Wavefunctions
This short paper is a fast proof-of-concept that the 3-order B-splines used in Kolmogorov-Arnold Networks (KANs) can be well approximated by Gaussian radial basis functions. Doing so leads to FastKAN, a much faster implementation of KAN…
Kolmogorov-Arnold Networks (KAN) models were recently proposed and claimed to provide improved parameter scaling and interpretability compared to conventional multilayer perceptron (MLP) models. Inspired by the KAN architecture, we propose…
The curse of dimensionality poses a significant challenge to modern multilayer perceptron-based architectures, often causing performance stagnation and scalability issues. Addressing this limitation typically requires vast amounts of data.…
The complexity of many-body quantum wave functions is a central aspect of several fields of physics and chemistry where non-perturbative interactions are prominent. Artificial neural networks (ANNs) have proven to be a flexible tool to…
The construction of trial wave functions based on neural networks combined with the variational Monte Carlo method is discussed. The mathematical formulation for representing quantum states as artificial neural networks is introduced. The…
Kolmogorov-Arnold Networks (KANs) replace scalar weights with per-edge vectors of basis coefficients, thereby increasing expressivity and accuracy while also resulting in a multiplicative increase in parameters and memory. We propose…
The application of machine learning methodologies for predicting properties within materials science has garnered significant attention. Among recent advancements, Kolmogorov-Arnold Networks (KANs) have emerged as a promising alternative to…
The Kolmogorov-Arnold Network (KAN) has emerged as a promising neural network architecture for small-scale AI+Science applications. However, it suffers from inflexibility in modeling ridge functions, which is widely used in representing the…
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) have been recently proposed as a machine learning framework that is more interpretable and controllable than the multi-layer perceptron. Various network architectures have been proposed within the KAN…
We investigate the integration of Kolmogorov-Arnold Networks (KANs) into hard-constrained recurrent physics-informed architectures (HRPINN) to evaluate the fidelity of learned residual manifolds in oscillatory systems. Motivated by the…
Kolmogorov-Arnold Networks (KANs) shift neural computation from linear layers to learnable nonlinear edge functions, but implementing these nonlinearities efficiently in hardware remains an open challenge. Here we introduce a physical…
In this paper, we introduce the KANtrol framework, which utilizes Kolmogorov-Arnold Networks (KANs) to solve optimal control problems involving continuous time variables. We explain how Gaussian quadrature can be employed to approximate the…
We reformulate the projected imaginary-time evolution of Full Configuration Interaction Quantum Monte Carlo in terms of a Lagrangian minimization. This naturally leads to the admission of polynomial complex wavefunction parameterizations,…
We present a novel approach for verifying properties of Kolmogorov-Arnold Networks (KANs), a class of neural networks characterized by nonlinear, univariate activation functions typically implemented as piecewise polynomial splines or…
The Kolmogorov-Arnold representation is a proven adequate replacement of a continuous multivariate function by an hierarchical structure of multiple functions of one variable. The proven existence of such representation inspired many…
Kolmogorov-Arnold Networks (KANs) have recently emerged as a powerful architecture for various machine learning applications. However, their unique structure raises significant concerns regarding their computational overhead. Existing…
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…
Inspired by the Kolmogorov-Arnold representation theorem and Kurkova's principle of using approximate representations, we propose the Kurkova-Kolmogorov-Arnold Network (KKAN), a new two-block architecture that combines robust multi-layer…
We discuss differences and similarities between variational Monte Carlo approaches that use conventional and artificial neural network parameterizations of the ground-state wave function for systems of fermions. We focus on a relatively…