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Exactly solvable neural network models with asymmetric weights are rare, and exact solutions are available only in some mean-field approaches. In this article we find exact analytical solutions of an asymmetric spin-glass-like model of…

Max-Linear Bayesian Networks (MLBNs) provide a powerful framework for causal inference in extreme-value settings; we consider MLBNs with noise parameters with a given topology in terms of the max-plus algebra by taking its logarithm. Then,…

In physics, complex systems are often simplified into minimal, solvable models that retain only the core principles. In machine learning, layerwise linear models (e.g., linear neural networks) act as simplified representations of neural…

We consider the neural ODE perspective of supervised learning and study the impact of the final time $T$ (which may indicate the depth of a corresponding ResNet) in training. For the classical $L^2$--regularized empirical risk minimization…

Within the framework of statistical learning theory we analyze in detail the so-called elastic-net regularization scheme proposed by Zou and Hastie for the selection of groups of correlated variables. To investigate on the statistical…

This paper presents meta-sparsity, a framework for learning model sparsity, basically learning the parameter that controls the degree of sparsity, that allows deep neural networks (DNNs) to inherently generate optimal sparse shared…

There have been many attempts to identify high-dimensional network features via multivariate approaches. Specifically, when the number of voxels or nodes, denoted as p, are substantially larger than the number of images, denoted as n, it…

We study stochastic processes that generate non-growing complex networks without self-loops and multiple edges (simple graphs). The work concentrates on understanding and formulation of constraints which keep the rewiring stochastic…

In all but the most trivial optimization problems, the structure of the solutions exhibit complex interdependencies between the input parameters. Decades of research with stochastic search techniques has shown the benefit of explicitly…

Network analysis has played a key role in knowledge discovery and data mining. In many real-world applications in recent years, we are interested in mining multilayer networks, where we have a number of edge sets called layers, which encode…

We consider stochastic systems of interacting particles or agents, with dynamics determined by an interaction kernel which only depends on pairwise distances. We study the problem of inferring this interaction kernel from observations of…

When modeling network data using a latent position model, it is typical to assume that the nodes' positions are independently and identically distributed. However, this assumption implies the average node degree grows linearly with the…

We establish criteria under which stochastic networks in a Markovian environment stabilize, thus confirming Conjecture 7.2 from Levine-Greco [GL23]. The networks evolve on finite connected graphs $G=(V,E)$, and their dynamics are encoded by…

Recently there has been a great deal of interest surrounding the calibration of quantum sensors using machine learning techniques. In this work, we explore the use of regression to infer a machine-learned point estimate of an unknown…

Long Short-Term Memory (LSTM) neural network models have become the cornerstone for sequential data modeling in numerous applications, ranging from natural language processing to time series forecasting. Despite their success, the problem…

Due to the non-convex nature of training Deep Neural Network (DNN) models, their effectiveness relies on the use of non-convex optimization heuristics. Traditional methods for training DNNs often require costly empirical methods to produce…

State-space models (SSMs) offer a powerful framework for dynamical system analysis, wherein the temporal dynamics of the system are assumed to be captured through the evolution of the latent states, which govern the values of the…

Large language models (LLMs) have advanced rapidly, emerging as versatile tools across fields thanks to their exceptional language understanding, generation, and reasoning capabilities. However, performing LLM inference at the network edge…

Graphs are fundamental mathematical structures used in various fields to model statistical and physical relationships between data, signals, and processes. In some applications, such as data processing in graphs that represent physical…

We consider the problem of learning a graph modeling the statistical relations of the $d$ variables from a dataset with $n$ samples $X \in \mathbb{R}^{n \times d}$. Standard approaches amount to searching for a precision matrix $\Theta$…