Related papers: Wahkon: A Statistically Principled Deep RKHS Super…

The aim of this study is to present a good modernistic strategy for solving some well-known classes of Lane-Emden type singular differential equations. The proposed approach is based on the reproducing kernel Hilbert space (RKHS) and…

We study the computation complexity of deep ReLU (Rectified Linear Unit) neural networks for the approximation of functions from the H\"older-Zygmund space of mixed smoothness defined on the $d$-dimensional unit cube when the dimension $d$…

This paper presents a new neural architecture that combines a modulated Hebbian network (MOHN) with DQN, which we call modulated Hebbian plus Q network architecture (MOHQA). The hypothesis is that such a combination allows MOHQA to solve…

Superposition refers to encoding representations of multiple features within a single neuron, which is common in deep neural networks. This property allows neurons to combine and represent multiple features, enabling the model to capture…

We present a fully constructive analysis of deep ReLU neural networks for classification and function approximation tasks. First, we prove that any dataset with $N$ distinct points in $\mathbb{R}^d$ and $M$ output classes can be exactly…

We focus on the problem of finding a non-linear classification function that lies in a Reproducing Kernel Hilbert Space (RKHS) both from the primal point of view (finding a perfect separator when one exists) and the dual point of view…

In this paper, we introduce Wav-KAN, an innovative neural network architecture that leverages the Wavelet Kolmogorov-Arnold Networks (Wav-KAN) framework to enhance interpretability and performance. Traditional multilayer perceptrons (MLPs)…

Feedforward multilayer networks trained by supervised learning have recently demonstrated state of the art performance on image labeling problems such as boundary prediction and scene parsing. As even very low error rates can limit…

This paper studies convergence of empirical risks in reproducing kernel Hilbert spaces (RKHS). A conventional assumption in the existing research is that empirical training data do not contain any noise but this may not be satisfied in some…

Random backpropagation (RBP) is a variant of the backpropagation algorithm for training neural networks, where the transpose of the forward matrices are replaced by fixed random matrices in the calculation of the weight updates. It is…

Deep neural networks are workhorse models in machine learning with multiple layers of non-linear functions composed in series. Their loss function is highly non-convex, yet empirically even gradient descent minimisation is sufficient to…

Multi-dimensional Hawkes process (MHP) is a class of self and mutually exciting point processes that find wide range of applications -- from prediction of earthquakes to modelling of order books in high frequency trading. This paper makes…

Deep Neural Networks (DNNs) are powerful algorithms that have been proven capable of extracting non-Gaussian information from weak lensing (WL) data sets. Understanding which features in the data determine the output of these nested,…

The need for scalable and expressive models in machine learning is paramount, particularly in applications requiring both structural depth and flexibility. Traditional deep learning methods, such as multilayer perceptrons (MLP), offer depth…

The notion of reproducing kernel Hilbert space (RKHS) has emerged in system identification during the past decade. In the resulting framework, the impulse response estimation problem is formulated as a regularized optimization defined on an…

Despite the remarkable success of deep learning in pattern recognition, deep network models face the problem of training a large number of parameters. In this paper, we propose and evaluate a novel multi-path wavelet neural network…

Reproducing kernel Hilbert $C^*$-module (RKHM) is a generalization of reproducing kernel Hilbert space (RKHS) by means of $C^*$-algebra, and the Perron-Frobenius operator is a linear operator related to the composition of functions.…

Recently, deep-networks-based hashing (deep hashing) has become a leading approach for large-scale image retrieval. It aims to learn a compact bitwise representation for images via deep networks, so that similar images are mapped to nearby…

This paper presents a general vector-valued reproducing kernel Hilbert spaces (RKHS) framework for the problem of learning an unknown functional dependency between a structured input space and a structured output space. Our formulation…

We show that several machine learning estimators, including square-root LASSO (Least Absolute Shrinkage and Selection) and regularized logistic regression can be represented as solutions to distributionally robust optimization (DRO)…