3 citations · 6 across the 7 of their papers we have counts for
8 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…
Dependent Optics
Pietro Vertechi
A wide variety of bidirectional data accessors, ranging from mixed optics to functor lenses, can be formalized within a unique framework-dependent optics. Starting from two indexed…
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…