Related papers: Geometric Kolmogorov--Arnold Network (GeoKAN)

Massive number of applications involve data with underlying relationships embedded in non-Euclidean space. Graph neural networks (GNNs) are utilized to extract features by capturing the dependencies within graphs. Despite groundbreaking…

Recent work has established an alternative to traditional multi-layer perceptron neural networks in the form of Kolmogorov-Arnold Networks (KAN). The general KAN framework uses learnable activation functions on the edges of the…

In traditional neural network architectures, a multilayer perceptron (MLP) is typically employed as a classification block following the feature extraction stage. However, the Kolmogorov-Arnold Network (KAN) presents a promising alternative…

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) have attracted attention recently as an alternative to multilayer perceptrons (MLPs) for scientific machine learning. However, KANs can be expensive to train, even for relatively small networks. Inspired by…

Recent advancements in Lyapunov-based Deep Neural Networks (Lb-DNNs) have demonstrated improved performance over shallow NNs and traditional adaptive control for nonlinear systems with uncertain dynamics. Existing Lb-DNNs rely on…

Kolmogorov-Arnold Networks (KANs) have recently emerged as a flexible and parameter-efficient alternative to conventional neural networks. Unlike standard architectures that use fixed node-based activations, KANs place learnable functions…

Uncovering the underlying dynamics from observed data is a critical task in various scientific fields. Recent advances have shown that combining deep learning techniques with linear multistep methods (LMMs) can be highly effective for this…

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…

Artificial Neural Networks (ANNs) have significantly advanced various fields by effectively recognizing patterns and solving complex problems. Despite these advancements, their interpretability remains a critical challenge, especially in…

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)…

The growing need for accurate and efficient 3D identification of tumors, particularly in liver segmentation, has spurred considerable research into deep learning models. While many existing architectures offer strong performance, they often…

This paper proposes a novel approach for designing Single-Parameterized Kolmogorov-Arnold Networks (SKAN) by utilizing a Single-Parameterized Function (SFunc) constructed from trigonometric functions. Three new SKAN variants are developed:…

Recurrent Neural Networks (RNNs) have revolutionized many areas of machine learning, particularly in natural language and data sequence processing. Long Short-Term Memory (LSTM) has demonstrated its ability to capture long-term dependencies…

We introduce a novel symbolic regression framework, namely KAN-SR, built on Kolmogorov Arnold Networks (KANs) which follows a divide-and-conquer approach. Symbolic regression searches for mathematical equations that best fit a given dataset…

This paper introduces Kolmogorov-Arnold Networks (KAN) as an enhancement to the traditional linear probing method in transfer learning. Linear probing, often applied to the final layer of pre-trained models, is limited by its inability to…

Partial differential equations (PDEs) form a central component of scientific computing. Among recent advances in deep learning, evolutionary neural networks have been developed to successively capture the temporal dynamics of time-dependent…

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…

Physics-Informed Neural Networks (PINNs) have become a popular and powerful framework for solving partial differential equations (PDEs), leveraging neural networks to approximate solutions while embedding PDE constraints, boundary…

Physics-Informed Neural Networks (PINNs) have emerged as a promising method for solving partial differential equations (PDEs) in scientific computing. While PINNs typically use multilayer perceptrons (MLPs) as their underlying architecture,…