Related papers: Kernel Dependence Network
We study the sample complexity of learning neural networks, by providing new bounds on their Rademacher complexity assuming norm constraints on the parameter matrix of each layer. Compared to previous work, these complexity bounds have…
As deep neural networks grow in size, from thousands to millions to billions of weights, the performance of those networks becomes limited by our ability to accurately train them. A common naive question arises: if we have a system with…
Metric learning for classification has been intensively studied over the last decade. The idea is to learn a metric space induced from a normed vector space on which data from different classes are well separated. Different measures of the…
Motivated by the growing interest in representation learning approaches that uncover the latent structure of high-dimensional data, this work proposes new algorithms for reconstruction-based manifold learning within Reproducing-Kernel…
This paper proposes a novel approach to train deep neural networks by unlocking the layer-wise dependency of backpropagation training. The approach employs additional modules called local critic networks besides the main network model to be…
Hypernetworks, or hypernets for short, are neural networks that generate weights for another neural network, known as the target network. They have emerged as a powerful deep learning technique that allows for greater flexibility,…
In this article, we develop a kernel-based framework for constructing dynamic, pathdependent trading strategies under a mean-variance optimisation criterion. Building on the theoretical results of (Muca Cirone and Salvi, 2025), we…
Deep neural networks have revolutionized machine learning, yet their training dynamics remain theoretically unclear-we develop a continuous-time, matrix-valued stochastic differential equation (SDE) framework that rigorously connects the…
Kernels are powerful and versatile tools in machine learning and statistics. Although the notion of universal kernels and characteristic kernels has been studied, kernel selection still greatly influences the empirical performance. While…
Spectral analysis is a powerful tool, decomposing any function into simpler parts. In machine learning, Mercer's theorem generalizes this idea, providing for any kernel and input distribution a natural basis of functions of increasing…
Network classification aims to group networks (or graphs) into distinct categories based on their structure. We study the connection between classification of a network and of its constituent nodes, and whether nodes from networks in…
We analyze recurrent neural networks with diagonal hidden-to-hidden weight matrices, trained with gradient descent in the supervised learning setting, and prove that gradient descent can achieve optimality \emph{without} massive…
Artificial neural networks typically have a fixed, non-linear activation function at each neuron. We have designed a novel form of piecewise linear activation function that is learned independently for each neuron using gradient descent.…
Multi-label classification is a challenging task in pattern recognition. Many deep learning methods have been proposed and largely enhanced classification performance. However, most of the existing sophisticated methods ignore context in…
We present a novel approach for computing a variant of eigenvector centrality for multilayer networks with inter-layer constraints on node importance. Specifically, we consider a multilayer network defined by multiple edge-weighted,…
The kernel exponential family is a rich class of distributions, which can be fit efficiently and with statistical guarantees by score matching. Being required to choose a priori a simple kernel such as the Gaussian, however, limits its…
Neural networks have achieved remarkable empirical performance, while the current theoretical analysis is not adequate for understanding their success, e.g., the Neural Tangent Kernel approach fails to capture their key feature learning…
We propose a novel class of separable multilayer network models to capture cross-layer dependencies in multilayer networks, enabling the analysis of how interactions in one or more layers may influence interactions in other layers. Our…
The development of machine learning interatomic potentials has immensely contributed to the accuracy of simulations of molecules and crystals. However, creating interatomic potentials for magnetic systems that account for both magnetic…
In recent years neural networks have achieved impressive results on many technological and scientific tasks. Yet, the mechanism through which these models automatically select features, or patterns in data, for prediction remains unclear.…