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cs.LG2022
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…
math.CT2022
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…
cs.LG2022
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…