arXiv subjects

Fabrizio Durante

Publications and source records attributed to Fabrizio Durante.

10 recordsLinked to original sources

arXiv2026

Do Hopfield Networks Dream of Stored Patterns? A Statistical-Mechanical Theory of Dreaming in Multidirectional Associative Memories

We introduce the Dreaming $L$-directional Associative Memory (DLAM), a multi-layer Hebbian architecture in which off-line dreaming and supervised heteroassociative coupling coexist within a single energy function, placing our approach within the framework of energy-based models (EBMs). The replica-symmetric free energy, derived via the Guerra interpolation scheme, yields self-consistency equations governing the order parameters across the control-parameter space. The effective local field decomposes into signal, intra-layer dreaming noise, and inter-layer noise. Dreaming improves retrieval by differentially attenuating high-eigenvalue interference modes of the empirical correlation matrix, suppressing inter-pattern crosstalk while preserving the signal. Dreaming and inter-layer coupling prove synergistic, opening retrieval regions unreachable by either mechanism alone, as confirmed by Monte Carlo simulations for $L=3$. Their interplay is most pronounced on pattern disentanglement: given a mixture state as input, the network splits the constituent patterns one-per-layer, recovering each modality-specific pattern from a common cue that simultaneously blends noisy evidence from all sensory channels. Phase diagrams are planar projections of the hyperspace $(α,β,ρ,t)$-where $α$ is the storage load, $β$ the fast-noise inverse temperature, $ρ$ the dataset entropy, and $t$ the sleeping time. In the $(ρ,t)$-plane, the diagrams reveal a data-computation trade-off: off-line consolidation substitutes for additional training data, extending to heteroassociative architectures a phenomenon previously established for autoassociative networks. Enriching the standard Hopfield model with heteroassociativity and dreaming gives rise to EBMs capable of complex tasks beyond classical pattern recognition, contributing to a modern theory of neural information processing.

cond-mat.dis-nn↗

arXiv2026

A Federated Many-to-One Hopfield model for associative Neural Networks

Federated learning enables collaborative training without sharing raw data, but struggles under client heterogeneity and streaming distribution shifts, where drift and novel data can impair convergence and cause forgetting. We propose a federated associative-memory framework that learns shared archetypes in heterogeneous, continual settings, where client data are independent but not necessarily balanced. Each client encodes its experience as a low-rank Hebbian operator, sent to a central server for aggregation and factorization into global archetypes. This approach preserves privacy, avoids centralized replay buffers, and is robust to small, noisy, or evolving datasets. We cast aggregation as a low-rank-plus-noise spectral inference problem, deriving theoretical thresholds for detectability and retrieval robustness. An entropy-based controller balances stability and plasticity in streaming regimes. Experiments with heterogeneous clients, drift, and novelty show improved global archetype reconstruction and associative retrieval, supporting the spectral view of federated consolidation.

cond-mat.dis-nn↗

arXiv2025

Extreme semilinear copulas

We study the extreme points (in the Krein-Milman sense) of the class of semilinear copulas and provide their characterization. Related results into the more general setting of conjunctive aggregation functions (i.e, semi--copulas and quasi--copulas) are also presented.

math.PR↗

arXiv2024

CAP: Detecting Unauthorized Data Usage in Generative Models via Prompt Generation

To achieve accurate and unbiased predictions, Machine Learning (ML) models rely on large, heterogeneous, and high-quality datasets. However, this could raise ethical and legal concerns regarding copyright and authorization aspects, especially when information is gathered from the Internet. With the rise of generative models, being able to track data has become of particular importance, especially since they may (un)intentionally replicate copyrighted contents. Therefore, this work proposes Copyright Audit via Prompts generation (CAP), a framework for automatically testing whether an ML model has been trained with unauthorized data. Specifically, we devise an approach to generate suitable keys inducing the model to reveal copyrighted contents. To prove its effectiveness, we conducted an extensive evaluation campaign on measurements collected in four IoT scenarios. The obtained results showcase the effectiveness of CAP, when used against both realistic and synthetic datasets.

cs.LG↗

arXiv2024

Hebbian Learning from First Principles

Recently, the original storage prescription for the Hopfield model of neural networks -- as well as for its dense generalizations -- has been turned into a genuine Hebbian learning rule by postulating the expression of its Hamiltonian for both the supervised and unsupervised protocols. In these notes, first, we obtain these explicit expressions by relying upon maximum entropy extremization à la Jaynes. Beyond providing a formal derivation of these recipes for Hebbian learning, this construction also highlights how Lagrangian constraints within entropy extremization force network's outcomes on neural correlations: these try to mimic the empirical counterparts hidden in the datasets provided to the network for its training and, the denser the network, the longer the correlations that it is able to capture. Next, we prove that, in the big data limit, whatever the presence of a teacher (or its lacking), not only these Hebbian learning rules converge to the original storage prescription of the Hopfield model but also their related free energies (and, thus, the statistical mechanical picture provided by Amit, Gutfreund and Sompolinsky is fully recovered). As a sideline, we show mathematical equivalence among standard Cost functions (Hamiltonian), preferred in Statistical Mechanical jargon, and quadratic Loss Functions, preferred in Machine Learning terminology. Remarks on the exponential Hopfield model (as the limit of dense networks with diverging density) and semi-supervised protocols are also provided.

cond-mat.dis-nn↗

arXiv2022

Recurrent neural networks that generalize from examples and optimize by dreaming

The gap between the huge volumes of data needed to train artificial neural networks and the relatively small amount of data needed by their biological counterparts is a central puzzle in machine learning. Here, inspired by biological information-processing, we introduce a generalized Hopfield network where pairwise couplings between neurons are built according to Hebb's prescription for on-line learning and allow also for (suitably stylized) off-line sleeping mechanisms. Moreover, in order to retain a learning framework, here the patterns are not assumed to be available, instead, we let the network experience solely a dataset made of a sample of noisy examples for each pattern. We analyze the model by statistical-mechanics tools and we obtain a quantitative picture of its capabilities as functions of its control parameters: the resulting network is an associative memory for pattern recognition that learns from examples on-line, generalizes and optimizes its storage capacity by off-line sleeping. Remarkably, the sleeping mechanisms always significantly reduce (up to $\approx 90\%$) the dataset size required to correctly generalize, further, there are memory loads that are prohibitive to Hebbian networks without sleeping (no matter the size and quality of the provided examples), but that are easily handled by the present "rested" neural networks.

cond-mat.dis-nn↗

arXiv2022

A Multivariate Dependence Analysis for Electricity Prices, Demand and Renewable Energy Sources

This paper examines the dependence between electricity prices, demand, and renewable energy sources by means of a multivariate copula model {while studying Germany, the widest studied market in Europe}. The inter-dependencies are investigated in-depth and monitored over time, with particular emphasis on the tail behavior. To this end, suitable tail dependence measures are introduced to take into account a multivariate extreme scenario appropriately identified {through the} Kendall's distribution function. The empirical evidence demonstrates a strong association between electricity prices, renewable energy sources, and demand within a day and over the studied years. Hence, this analysis provides guidance for further and different incentives for promoting green energy generation while considering the time-varying dependencies of the involved variables

stat.AP↗

arXiv2021

Dissimilarity functions for rank-invariant hierarchical clustering of continuous variables

A theoretical framework is presented for a (copula-based) notion of dissimilarity between continuous random vectors and its main properties are studied. The proposed dissimilarity assigns the smallest value to a pair of random vectors that are comonotonic. Various properties of this dissimilarity are studied, with special attention to those that are prone to the hierarchical agglomerative methods, such as reducibility. Some insights are provided for the use of such a measure in clustering algorithms and a simulation study is presented. Real case studies illustrate the main features of the whole methodology.

stat.ME↗

arXiv2020

Distortion Representations of Multivariate Distributions

The univariate distorted distribution were introduced in risk theory to represent changes (distortions) in the expected distributions of some risks. Later they were also applied to represent distributions of order statistics, coherent systems, proportional hazard rate (PHR) and proportional reversed hazard rate (PRHR) models, etc. In this paper we extend this concept to the multivariate setup. We show that, in some cases, they are a valid alternative to the copula representations especially when the marginal distributions may not be easily handled. Several relevant examples illustrate the applications of such representations in statistical modeling. They include the study of paired (dependent) ordered data, joint residual lifetimes, order statistics and coherent systems.

math.ST↗

arXiv2007

Copulas: compatibility and Fréchet classes

We determine under which conditions three bivariate copulas are compatible, viz. they are the bivariate marginals of the same trivariate copula, and, then, construct the class of these copulas. In particular, the upper and lower bounds for this class of trivariate copulas are determined.

math.ST↗