Related papers: Genus expansion for non-linear random matrix ensem…

This article studies the infinite-width limit of deep feedforward neural networks whose weights are dependent, and modelled via a mixture of Gaussian distributions. Each hidden node of the network is assigned a nonnegative random variable…

Inspired by the universal approximation theorem and widespread adoption of artificial neural network techniques in a diversity of fields, we propose feed-forward neural networks as a general purpose trial wave function for quantum Monte…

We give an expansion in $1/N$ and $\beta$ of the cumulants of power sums of the particles of the $\beta$-ensemble. This new expansion is obtained using the tridiagonal model of Dumitriu and Edelman. The coefficients of the expansion are…

We show that randomly choosing the matrices in a completely positive map from the unitary group gives a quantum expander. We consider Hermitian and non-Hermitian cases, and we provide asymptotically tight bounds in the Hermitian case on the…

Analysing statistical properties of neural networks is a central topic in statistics and machine learning. However, most results in the literature focus on the properties of the neural network minimizing the training error. The goal of this…

We show generalisation error bounds for deep learning with two main improvements over the state of the art. (1) Our bounds have no explicit dependence on the number of classes except for logarithmic factors. This holds even when formulating…

Using Stein's method techniques introduced by Chatterjee (2008) and further extended by Kasprzak and Peccati (2022) and by Lachi\`eze-Rey and Peccati (2017), we derive novel quantitative bounds on the convergence in distribution of…

Graph neural networks are widely used tools for graph prediction tasks. Motivated by their empirical performance, prior works have developed generalization bounds for graph neural networks, which scale with graph structures in terms of the…

In a neural network (NN), *weight matrices* linearly transform inputs into *preactivations* that are then transformed nonlinearly into *activations*. A typical NN interleaves multitudes of such linear and nonlinear transforms to express…

We consider words $G_{i_1} \cdots G_{i_m}$ involving i.i.d. complex Ginibre matrices, and study tracial expressions of their eigenvalues and singular values. We show that the limit distribution of the squared singular values of every word…

Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…

A primary advantage of neural networks lies in their feature learning characteristics, which is challenging to theoretically analyze due to the complexity of their training dynamics. We propose a new paradigm for studying feature learning…

The paper establishes generalization bounds for multitask deep neural networks using operator-theoretic techniques. The authors propose a tighter bound than those derived from conventional norm based methods by leveraging small condition…

Graph neural networks (GNNs) are a class of neural networks that allow to efficiently perform inference on data that is associated to a graph structure, such as, e.g., citation networks or knowledge graphs. While several variants of GNNs…

We study the gradients of a maxout network with respect to inputs and parameters and obtain bounds for the moments depending on the architecture and the parameter distribution. We observe that the distribution of the input-output Jacobian…

A major goal in genomics is to properly capture the complex dynamical behaviors of gene regulatory networks (GRNs). This includes inferring the complex interactions between genes, which can be used for a wide range of genomics analyses,…

The aim of this paper is to give a precise asymptotic description of some eigenvalue statistics stemming from random matrix theory. More precisely, we consider random determinants of the GUE, Laguerre, Uniform Gram and Jacobi beta ensembles…

We study convolutional neural networks with monomial activation functions. Specifically, we prove that their parameterization map is regular and is an isomorphism almost everywhere, up to rescaling the filters. By leveraging on tools from…

We propose a theoretical understanding of neural networks in terms of Wilsonian effective field theory. The correspondence relies on the fact that many asymptotic neural networks are drawn from Gaussian processes, the analog of…

Graphical models are frequently used to explore networks, such as genetic networks, among a set of variables. This is usually carried out via exploring the sparsity of the precision matrix of the variables under consideration. Penalized…