3 citations · 6 across the 7 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…
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…