3 citations · 3 across the 10 of their papers we have counts for
4 papers · 1 filter
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…
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…
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…
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…