Related papers: Construction of the Kolmogorov-Arnold representati…

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…

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…

Kolmogorov's representation theorem provides a framework for decomposing any arbitrary real-valued, multivariate, and continuous function into a two-layer nested superposition of a finite number of functions. The functions at these two…

This work investigates Kolmogorov-Arnold network-based wavefunction ansatz as viable representations for quantum Monte Carlo simulations. Through systematic analysis of one-dimensional model systems, we evaluate their computational…

The Kolmogorov-Arnold representation theorem states that any continuous multivariable function can be exactly represented as a finite superposition of continuous single variable functions. Subsequent simplifications of this representation…

We propose a Kolmogorov-Arnold Representation-based Hamiltonian Neural Network (KAR-HNN) that replaces the Multilayer Perceptrons (MLPs) with univariate transformations. While Hamiltonian Neural Networks (HNNs) ensure energy conservation by…

The Kolmogorov-Arnold network (KAN) is a regression model that is based on a representation of an arbitrary continuous multivariate function by a composition of functions of a single variable. Experimentally-obtained datasets for regression…

This systematic review explores the theoretical foundations, evolution, applications, and future potential of Kolmogorov-Arnold Networks (KAN), a neural network model inspired by the Kolmogorov-Arnold representation theorem. KANs…

Kolmogorov-Arnold Networks (KANs) offer a theoretically grounded alternative to multi-layer perceptrons by representing multivariate functions as compositions of univariate basis functions. However, a critical limitation of KANs is the need…

With increasing penetration of distributed energy resources installed behind the meter, there is a growing need for adequate modelling of composite loads to enable accurate power system simulation analysis. Existing measurement based load…

Accurate approximation of complex nonlinear functions is a fundamental challenge across many scientific and engineering domains. Traditional neural network architectures, such as Multi-Layer Perceptrons (MLPs), often struggle to efficiently…

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 Convolutional Neural Networks (CNNs) have been the dominant and effective approach for general computer vision tasks. Recently, Kolmogorov-Arnold neural networks (KANs), based on the Kolmogorov-Arnold representation theorem, have shown…

The research undertakes a comprehensive comparative analysis of Kolmogorov-Arnold Networks (KAN) and Multi-Layer Perceptrons (MLP), highlighting their effectiveness in solving essential computational challenges like nonlinear function…

The present paper introduces concurrency-driven enhancements to the training algorithm for the Kolmogorov-Arnold networks (KANs) that is based on the Newton-Kaczmarz (NK) method. Prior research shows that KANs trained using the NK-based…

Inspired by the Kolmogorov-Arnold representation theorem, we propose Kolmogorov-Arnold Networks (KANs) as promising alternatives to Multi-Layer Perceptrons (MLPs). While MLPs have fixed activation functions on nodes ("neurons"), KANs have…

Kolmogorov and Arnold, in answering Hilbert's 13th problem (in the context of continuous functions), laid the foundations for the modern theory of Neural Networks (NNs). Their proof divides the representation of a multivariate function into…

Kolmogorov-Arnold Networks (KAN) is a groundbreaking model recently proposed by the MIT team, representing a revolutionary approach with the potential to be a game-changer in the field. This innovative concept has rapidly garnered worldwide…

This paper introduces a novel application of Kolmogorov-Arnold Networks (KANs) to time series forecasting, leveraging their adaptive activation functions for enhanced predictive modeling. Inspired by the Kolmogorov-Arnold representation…

Fuzzy Cognitive Maps constitute a neuro-symbolic paradigm for modeling complex dynamic systems, widely adopted for their inherent interpretability and recurrent inference capabilities. However, the standard FCM formulation, characterized by…