相关论文: Uncertainty Quantification for Scientific Machine …
A new Kolmogorov-Arnold network (KAN) is proposed to approximate potentially irregular functions in high dimensions. We provide error bounds for this approximation, assuming that the Kolmogorov-Arnold expansion functions are sufficiently…
Understanding and modeling nonlinear dynamical systems is a fundamental challenge across science and engineering. Deep learning has shown remarkable potential for capturing complex system behavior, yet achieving models that are both…
Zero-inflated datasets, which have an excess of zero outputs, are commonly encountered in problems such as climate or rare event modelling. Conventional machine learning approaches tend to overestimate the non-zeros leading to poor…
Tabular data analysis presents unique challenges that arise from heterogeneous feature types, missing values, and complex feature interactions. While traditional machine learning methods like gradient boosting often outperform deep…
Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…
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…
This paper presents a novel machine-learning framework for reconstructing low-order gust-encounter flow field and lift coefficients from sparse, noisy surface pressure measurements. Our study thoroughly investigates the time-varying…
We study posterior contraction rates for sparse Bayesian Kolmogorov-Arnold networks (KANs) over anisotropic Besov spaces, providing a statistical foundation of KANs from a Bayesian point of view. We show that sparse Bayesian KANs equipped…
While most modern machine learning methods offer speed and accuracy, few promise interpretability or explainability -- two key features necessary for highly sensitive industries, like medicine, finance, and engineering. Using eight datasets…
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),…
Kolmogorov Arnold Networks (KANs) are neural architectures inspired by the Kolmogorov Arnold representation theorem that leverage B Spline parameterizations for flexible, locally adaptive function approximation. Although KANs can capture…
The Gaussian process (GP) is a powerful tool for nonparametric modeling, but its sensitivity to outliers limits its applicability to data distributions with heavy-tails. Studentt processes offer a robust alternative for heavy tail modeling,…
Kolmogorov-Arnold Networks (KANs) introduce a paradigm of neural modeling that implements learnable functions on the edges of the networks, diverging from the traditional node-centric activations in neural networks. This work assesses the…
Effective molecular representation learning is crucial for advancing molecular property prediction and drug design. Mainstream molecular representation learning approaches are based on Graph Neural Networks (GNNs). However, these approaches…
We propose a Stein variational gradient descent method to concurrently sparsify, train, and provide uncertainty quantification of a complexly parameterized model such as a neural network. It employs a graph reconciliation and condensation…
We introduce Graph Kolmogorov-Arnold Networks (GKAN), an innovative neural network architecture that extends the principles of the recently proposed Kolmogorov-Arnold Networks (KAN) to graph-structured data. By adopting the unique…
It has been observed that even a small amount of noise introduced into the dataset can significantly degrade the performance of KAN. In this brief note, we aim to quantitatively evaluate the performance when noise is added to the dataset.…
Kolmogorov-Arnold Networks (KANs) have very recently been introduced into the world of machine learning, quickly capturing the attention of the entire community. However, KANs have mostly been tested for approximating complex functions or…
Machine learning applications require fast and reliable per-sample uncertainty estimation. A common approach is to use predictive distributions from Bayesian or approximation methods and additively decompose uncertainty into aleatoric…
Kolmogorov-Arnold Networks (KANs) are a recent neural network architecture offering an alternative to Multilayer Perceptrons (MLPs) with improved explainability and expressibility. However, KANs are significantly slower than MLPs due to the…