Related papers: Multi-Kernel Fusion for RBF Neural Networks

Kernel methods, particularly kernel ridge regression (KRR), are time-proven, powerful nonparametric regression techniques known for their rich capacity, analytical simplicity, and computational tractability. The analysis of their predictive…

Deep learning methods have predominantly been applied to large artificial neural networks. Despite their state-of-the-art performance, these large networks typically do not generalize well to datasets with limited sample sizes. In this…

The success of kernel-based learning methods depend on the choice of kernel. Recently, kernel learning methods have been proposed that use data to select the most appropriate kernel, usually by combining a set of base kernels. We introduce…

This paper developed a systematic strategy establishing RBF on the wavelet analysis, which includes continuous and discrete RBF orthonormal wavelet transforms respectively in terms of singular fundamental solutions and nonsingular general…

Neural networks are generally built by interleaving (adaptable) linear layers with (fixed) nonlinear activation functions. To increase their flexibility, several authors have proposed methods for adapting the activation functions…

Binarized neural networks, or BNNs, show great promise in edge-side applications with resource limited hardware, but raise the concerns of reduced accuracy. Motivated by the complex neural networks, in this paper we introduce complex…

Neural networks are rapidly gaining popularity in scientific research, but training the models is often very time-consuming. Particularly when the training data samples are large high-dimensional arrays, efficient training methodologies…

Binary neural networks (BNNs), where both weights and activations are binarized into 1 bit, have been widely studied in recent years due to its great benefit of highly accelerated computation and substantially reduced memory footprint that…

Modern wireless communication networks, particularly cellular networks utilize multiple antennas to improve the capacity and signal coverage. In these systems, typically an active transceiver is connected to each antenna. However, this…

Ridgeless regression has garnered attention among researchers, particularly in light of the ``Benign Overfitting'' phenomenon, where models interpolating noisy samples demonstrate robust generalization. However, kernel ridgeless regression…

Thanks to their easy implementation via Radial Basis Functions (RBFs), meshfree kernel methods have been proved to be an effective tool for e.g. scattered data interpolation, PDE collocation, classification and regression tasks. Their…

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…

The Radiative Transfer Equations (RTEs) exhibit high dimensionality and multiscale characteristics, rendering conventional numerical methods computationally intensive. Existing deep learning methods perform well in low-dimensional or linear…

Regularization techniques are widely used to improve the generality, robustness, and efficiency of deep convolutional neural networks (DCNNs). In this paper, we propose a novel approach of regulating DCNN convolutional kernels by a…

Random Fourier Features (RFF) demonstrate wellappreciated performance in kernel approximation for largescale situations but restrict kernels to be stationary and positive definite. And for non-stationary kernels, the corresponding RFF could…

We propose a differential radial basis function (RBF) network termed RBF-DiffNet -- whose hidden layer blocks are partial differential equations (PDEs) linear in terms of the RBF -- to make the baseline RBF network robust to noise in…

The architecture of a neural network and the selection of its activation function are both fundamental to its performance. Equally vital is ensuring these two elements are well-matched, as their alignment is key to achieving effective…

Convolutional neural networks (CNNs) are able to attain better visual recognition performance than fully connected neural networks despite having much fewer parameters due to their parameter sharing principle. Modern architectures usually…

Neural networks have been successfully employed in various domains such as classification, regression and clustering, etc. Generally, the back propagation (BP) based iterative approaches are used to train the neural networks, however, it…

We propose the framework of dual convexified convolutional neural networks (DCCNNs). In this framework, we first introduce a primal learning problem motivated by convexified convolutional neural networks (CCNNs), and then construct the dual…