8 papers
Persistent Homology and Equivariance in Data Analysis: A Topological Introduction
Patrizio Frosini, Ulderico Fugacci, Nicola Quercioli +1
This new book is intended as a first elementary introduction to Topological Data Analysis for mathematics students seeking a rigorous account of the foundations of persistent homol…
The Convex Matching Distance in Multiparameter Persistence
Francesco Conti, Patrizio Frosini, Ulderico Fugacci +4
We introduce the convex matching distance, a novel metric for comparing functions with values in the real plane. This metric measures the maximal bottleneck distance between the pe…
An Algebraic Representation Theorem for Linear GENEOs in Geometric Machine Learning
Francesco Conti, Patrizio Frosini, Nicola Quercioli
Geometric and Topological Deep Learning are rapidly growing research areas that enhance machine learning through the use of geometric and topological structures. Within this framew…
Reconstruction of SINR Maps from Sparse Measurements using Group Equivariant Non-Expansive Operators
Lorenzo Mario Amorosa, Francesco Conti, Nicola Quercioli +4
As sixth generation (6G) wireless networks evolve, accurate signal-to-interference-noise ratio (SINR) maps are becoming increasingly critical for effective resource management and…
GENEOnet: Statistical analysis supporting explainability and trustworthiness
Giovanni Bocchi, Patrizio Frosini, Alessandra Micheletti +5
Group Equivariant Non-Expansive Operators (GENEOs) have emerged as mathematical tools for constructing networks for Machine Learning and Artificial Intelligence. Recent findings su…
Mathematical Foundation of Interpretable Equivariant Surrogate Models
Jacopo Joy Colombini, Filippo Bonchi, Francesco Giannini +3
This paper introduces a rigorous mathematical framework for neural network explainability, and more broadly for the explainability of equivariant operators called Group Equivariant…