3 citations · 3 across the 10 of their papers we have counts for
14 papers
Equivariant optimisation for the gravitational -body problem: a computational factory of symmetric orbits
Vivina Barutello, Mattia G. Bergomi, Gian Marco Canneori +4
In this paper we present \texttt{SymOrb.jl}, a software which combines group representation theory and variational methods to provide numerical solutions of singular dynamical syst…
Persistence-based operators in machine learning
Mattia G. Bergomi, Massimo Ferri, Alessandro Mella +1
Artificial neural networks can learn complex, salient data features to achieve a given task. On the opposite end of the spectrum, mathematically grounded methods such as topologica…
Neural network layers as parametric spans
Mattia G. Bergomi, Pietro Vertechi
Properties such as composability and automatic differentiation made artificial neural networks a pervasive tool in applications. Tackling more challenging problems caused neural ne…
Machines of finite depth: towards a formalization of neural networks
Pietro Vertechi, Mattia G. Bergomi
We provide a unifying framework where artificial neural networks and their architectures can be formally described as particular cases of a general mathematical construction--machi…
Steady and ranging sets in graph persistence
Mattia G. Bergomi, Massimo Ferri, Antonella Tavaglione
Topological data analysis can provide insight on the structure of weighted graphs and digraphs. However, some properties underlying a given (di)graph are hardly mappable to simplic…
Parametric machines: a fresh approach to architecture search
Pietro Vertechi, Mattia G. Bergomi
Using tools from topology and functional analysis, we provide a framework where artificial neural networks, and their architectures, can be formally described. We define the notion…
Rank-based persistence
Mattia G. Bergomi, Pietro Vertechi
Persistence has proved to be a valuable tool to analyze real world data robustly. Several approaches to persistence have been attempted over time, some topological in flavor, based…
Beyond topological persistence: Starting from networks
Mattia G. Bergomi, Massimo Ferri, Pietro Vertechi +1
Persistent homology enables fast and computable comparison of topological objects. However, it is naturally limited to the analysis of topological spaces. We extend the theory of p…
Towards a topological-geometrical theory of group equivariant non-expansive operators for data analysis and machine learning
Mattia G. Bergomi, Patrizio Frosini, Daniela Giorgi +1
The aim of this paper is to provide a general mathematical framework for group equivariance in the machine learning context. The framework builds on a synergy between persistent ho…
idtracker.ai: Tracking all individuals in large collectives of unmarked animals
Francisco Romero-Ferrero, Mattia G. Bergomi, Robert Hinz +2
Our understanding of collective animal behavior is limited by our ability to track each of the individuals. We describe an algorithm and software, idtracker.ai, that extracts from…
Topological Graph Persistence
Mattia G. Bergomi, Massimo Ferri, Lorenzo Zuffi
Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dim…
Towards a topological fingerprint of music
Mattia G. Bergomi, Adriano Baraté, Barbara Di Fabio
Can music be represented as a meaningful geometric and topological object? In this paper, we propose a strategy to describe some music features as a polyhedral surface obtained by…
A mathematical model for voice leading and its complexity
Mattia G. Bergomi, Riccardo D. Jadanza, Alessandro Portaluri
We give a formal definition of the musical concept of voice leading in mathematical terms, based on the idea of partial permutations of certain ordered multisets. Then we associate…
Modes in modern music from a topological viewpoint
Mattia G. Bergomi, Alessandro Portaluri
The aim of this paper is twofold: on one side we review the classical concept of musical mode from the viewpoint of modern music, reading it as a superimposition of a base-chord (s…