Statistical Mechanics · Neural Networks · Interpretability

eXplainable
Artificial Intelligence
Laboratory

Bridging the gap between statistical physics and deep learning. We develop theoretical frameworks to understand, interpret, and explain the emergent behavior of neural networks through the lens of spin-glass theory and statistical mechanics.

Z = ∫ exp(−βH[J]) dJ · P(ξ|x) · ⟨σᵢσⱼ⟩
01

Research Areas

Jᵢⱼ

Hebbian Learning Theory

Developing supervised and unsupervised Hebbian learning protocols for Hopfield networks and their generalizations, with analytical characterization via statistical mechanics.

⟨·⟩

Replica Method

Exploiting the replica trick to analyze the computational capabilities of neural networks, characterizing phase transitions and storage capacity in associative memories.

RBM

Boltzmann Machines

Statistical mechanics framework for Restricted Boltzmann Machines, investigating generative capabilities, hyper-parameter tuning, and replica-symmetry breaking phenomena.

💤

Dreaming Neural Networks

Studying sleep-like mechanisms in artificial neural networks to optimize storage capacity and improve generalization from small datasets—toward Sustainable AI.

Pᴺ⁻¹

Dense Associative Memories

Investigating dense neural networks with higher-order interactions, achieving sub-threshold pattern recognition and enhanced storage scaling with network size.

∇ℒ

Interpretable AI

Building bridges between cost functions in statistical mechanics and loss functions in machine learning, toward transparent and explainable neural architectures.

02

Research Team

MA

Miriam Aquaro

PhD · Co-Founder

Formazione: Sapienza Università di Roma

Restricted Boltzmann Machines, Hopfield networks, dreaming mechanisms, replica theory, Hebbian learning

FA

Francesco Alemanno

PhD · Co-Founder

Formazione: Università del Salento

Spin glasses, dense associative neural networks, supervised learning, Guerra's interpolation techniques

03

Selected Publications

2025

Learning in Associative Networks through Pavlovian Dynamics

D. Lotito, M. Aquaro, C. Marullo

arXiv:2405.03823

2023

Hebbian Dreaming for Small Datasets

M. Aquaro, F. Alemanno, I. Kanter, F. Durante, A. Barra, E. Agliari

SSRN Preprint

2022

Supervised Hebbian Learning

F. Alemanno, M. Aquaro, I. Kanter, A. Barra, E. Agliari

Neural Networks, 2022

2020

Neural Networks with a Redundant Representation: Detecting the Undetectable

E. Agliari, F. Alemanno, A. Barra, M. Centonze, A. Fachechi

Physical Review Letters 124, 028301

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Contact

Get in Touch

We welcome collaborations with researchers in statistical physics, machine learning, and related fields. We are always open to discussing new ideas at the intersection of spin-glass theory and neural networks.

eXAI Lab
Italy
[ eXAI Lab ] Italy