# PRIN Grant Prot. 20229T9EAT (2023-2025) “Statistical Mechanics of Learning Machines: from algorithmic and information-theoretical limits to new biologically inspired paradigms"

ABSTRACT

The increasing availability of massive data sets with ever-increasing volume variety

and velocity has signed the direction of the recent ultimate technological progress

where Machine Learning (ML) has emerged as the key paradigm of modern artificial

intelligence systems. However despite the many impressive achievements of ML there

are serious gaps in our theoretical understanding of learning systems: deep learning

architectures are largely overparametrized yet they are able to easily fit the training

data with very greedy algorithms and at the same time they generalize well. This project

will be structured in three main objectives: 1) assess the information-theoretical limit of

learning: given certain models for the learning machine and the environment how much

information (in terms of amount of data) is necessary for the machine to produce a

faithful representation and correct predictions about the environment regardless of any

computational barrier 2) assess the actual limit of algorithms: the eventual information

codified in the dataset has to be efficiently retrieved. It is important to understand

whether existing algorithms are able to extract this information and how they use it to

build a representation of the environment with the machine parameters. 3) propose new

biologically and human intelligence inspired learning approaches: intended as new

learning machine new dynamics of learning and algorithms and new paradigms for

data driven artificial intelligence which are less task-specific more efficient and

parsimonious with data. Following this route the project intends to develop a

mathematically grounded understanding of ML merging ideas from statistical inference

statistical mechanics and information theory. At the same time it aims at proposing

new biologically and human intelligence inspired learning paradigms models and

algorithms.