3 citations · 3 across the 2 of their papers we have counts for
5 papers
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…
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…