Related papers: Input Convex Kolmogorov Arnold Networks
Traditional neural networks (multi-layer perceptrons) have become an important tool in data science due to their success across a wide range of tasks. However, their performance is sometimes unsatisfactory, and they often require a large…
Gradient flows are a powerful tool for optimizing functionals in general metric spaces, including the space of probabilities endowed with the Wasserstein metric. A typical approach to solving this optimization problem relies on its…
We study feedforward neural networks with inputs from a topological space (TFNNs). We prove a universal approximation theorem for shallow TFNNs, which demonstrates their capacity to approximate any continuous function defined on this…
Kolmogorov-Arnold Networks (KANs) have inspired numerous works exploring their applications across a wide range of scientific problems, with the potential to replace Multilayer Perceptrons (MLPs). While many KANs are designed using basis…
Recent advancements in neural network design have given rise to the development of Kolmogorov-Arnold Networks (KANs), which enhance speed, interpretability, and precision. This paper presents the Fractional Kolmogorov-Arnold Network (fKAN),…
Currently, increasingly deeper neural networks have been applied to improve their accuracy. In contrast, We propose a novel wider Convolutional Neural Networks (CNN) architecture, motivated by the Multi-column Deep Neural Networks and the…
Graph Neural Networks (GNNs) have shown strong performance on graph-structured data, but their reliance on graph connectivity often limits scalability and efficiency. Kolmogorov-Arnold Networks (KANs), a recent architecture with learnable…
In the realm of deep learning, the Kolmogorov-Arnold Network (KAN) has emerged as a potential alternative to multilayer projections (MLPs). However, its applicability to vision tasks has not been extensively validated. In our study, we…
Kolmogorov-Arnold Networks (KANs) offer a promising framework for approximating complex nonlinear functions, yet the original B-spline formulation suffers from significant computational overhead due to De Boor algorithm. While recent…
Kolmogorov-Arnold Networks (KAN) offer universal function approximation using univariate spline compositions without nonlinear activations. In this work, we integrate Error-Correcting Output Codes (ECOC) into the KAN framework to transform…
In this paper, we introduce FC-KAN, a Kolmogorov-Arnold Network (KAN) that leverages combinations of popular mathematical functions such as B-splines, wavelets, and radial basis functions on low-dimensional data through element-wise…
Recent works have introduced input-convex neural networks (ICNNs) as learning models with advantageous training, inference, and generalization properties linked to their convex structure. In this paper, we propose a novel feature-convex…
We propose PO-CKAN, a physics-informed deep operator framework based on Chunkwise Rational Kolmogorov--Arnold Networks (KANs), for approximating the solution operators of partial differential equations. This framework leverages a Deep…
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…
We introduce a new class of neural networks designed to be convex functions of their inputs, leveraging the principle that any convex function can be represented as the supremum of the affine functions it dominates. These neural networks,…
In this work, we explore the use of a novel neural network architecture, the Kolmogorov-Arnold Networks (KANs) as feature extractors for sensor-based (specifically IMU) Human Activity Recognition (HAR). Where conventional networks perform a…
XNet is a single-layer neural network architecture that leverages Cauchy integral-based activation functions for high-order function approximation. Through theoretical analysis, we show that the Cauchy activation functions used in XNet can…
Input-convex neural networks (ICNNs) are widely used for log-concave density estimation, convex-potential normalizing flows, optimal transport, and transport-map inversion for high-dimensional Bayesian posteriors. These tasks share a…
This paper proposes an input convex neural network (ICNN)-Assisted optimal power flow (OPF) in distribution networks. Instead of relying purely on optimization or machine learning, the ICNN-Assisted OPF is a combination of optimization and…
This paper proposes a new family of algorithms for training neural networks (NNs). These are based on recent developments in the field of non-convex optimization, going under the general name of successive convex approximation (SCA)…