Related papers: Function Fitting Based on Kolmogorov-Arnold Theore…
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…
We propose a new method for feature learning and function estimation in supervised learning via regularised empirical risk minimisation. Our approach considers functions as expectations of Sobolev functions over all possible one-dimensional…
Kolmogorov-Arnold Networks (KANs), whose design is inspired-rather than dictated-by the Kolmogorov superposition theorem, have emerged as a structured alternative to MLPs. This review provides a systematic and comprehensive overview of the…
Kolmogorov-Arnold Networks (KANs) represent an innovation in neural network architectures, offering a compelling alternative to Multi-Layer Perceptrons (MLPs) in models such as Convolutional Neural Networks (CNNs), Recurrent Neural Networks…
We propose a novel adaptive learning algorithm based on iterative orthogonal projections in the Cartesian product of multiple reproducing kernel Hilbert spaces (RKHSs). The task is estimating/tracking nonlinear functions which are supposed…
In this paper, we introduce a new kernel function which differs from previous functions, and play an important role for generating a new design of primal-dual interior point algorithms for semidefinite linear complementarity problem. Its…
Kolmogorov-Arnold Networks (KANs) have recently shown promise for solving partial differential equations (PDEs). Yet their original formulation is computationally and memory intensive, motivating the introduction of Chebyshev Type-I-based…
Inspired by the Kolmogorov-Arnold superposition theorem, Kolmogorov-Arnold Networks (KANs) have recently emerged as an improved backbone for most deep learning frameworks, promising more adaptivity than their multilayer perceptron (MLP)…
Face Recognition (FR) has been the interest to several researchers over the past few decades due to its passive nature of biometric authentication. Despite high accuracy achieved by face recognition algorithms under controlled conditions,…
The emergence of Kolmogorov-Arnold Networks (KANs) has sparked significant interest and debate within the scientific community. This paper explores the application of KANs in the domain of computer vision (CV). We examine the convolutional…
The paper studies face spoofing, a.k.a. presentation attack detection (PAD) in the demanding scenarios of unknown types of attack. While earlier studies have revealed the benefits of ensemble methods, and in particular, a multiple kernel…
In this paper, we introduce a method for multivariate function approximation using function evaluations, Chebyshev polynomials, and tensor-based compression techniques via the Tucker format. We develop novel randomized techniques to…
The design of activation functions is a growing research area in the field of neural networks. In particular, instead of using fixed point-wise functions (e.g., the rectified linear unit), several authors have proposed ways of learning…
Rolling element bearings are critical components of rotating machinery, with their performance directly influencing the efficiency and reliability of industrial systems. At the same time, bearing faults are a leading cause of machinery…
This paper introduces the Hierarchical Kolmogorov-Arnold Network (HKAN), a novel network architecture that offers a competitive alternative to the recently proposed Kolmogorov-Arnold Network (KAN). Unlike KAN, which relies on…
Kernel methods in machine learning use a kernel function that takes two data points as input and returns their inner product after mapping them to a Hilbert space, implicitly and without actually computing the mapping. For many kernel…
Machine learning models can represent climate processes that are nonlocal in horizontal space, height, and time, often by combining information across these dimensions in highly nonlinear ways. While this can improve predictive skill, it…
In recommender systems, models mostly use a combination of embedding layers and multilayer feedforward neural networks. The high-dimensional sparse original features are downscaled in the embedding layer and then fed into the fully…
This paper investigates the usage of kernel functions at the different layers in a convolutional neural network. We carry out extensive studies of their impact on convolutional, pooling and fully-connected layers. We notice that the linear…
Despite the remarkable empirical performance of Transformers, their theoretical understanding remains elusive. Here, we consider a deep multi-head self-attention network, that is closely related to Transformers yet analytically tractable.…