5 papers
An Analytical Theory of Auxiliary Learning
Federico Milanesio, Alessandro Ingrosso, Matteo Osella
Auxiliary learning is an optimization paradigm in which a neural network's performance on a target task is improved by jointly training it on additional tasks. However, the mechani…
The Advantage of Fine-Grained Training
Davide Pirovano, Federico Milanesio, Michele Caselle +2
In classification problems, models are trained to predict a class label based on the input data features. However, class labels are organized hierarchically in many datasets. While…
Tessellation Groups, Harmonic Analysis on Non-compact Symmetric Spaces and the Heat Kernel in view of Cartan Convolutional Neural Networks
Pietro Fré, Federico Milanesio, Marcelo Oyarzo +2
In this paper, we continue the development of the Cartan neural networks programme, launched with three previous publications, by focusing on some mathematical foundational aspects…
Navigation through Non-Compact Symmetric Spaces: a mathematical perspective on Cartan Neural Networks
Pietro Giuseppe Fré, Federico Milanesio, Guido Sanguinetti +1
Recent work has identified non-compact symmetric spaces U/H as a promising class of homogeneous manifolds to develop a geometrically consistent theory of neural networks. An initia…
Cartan Networks: Group theoretical Hyperbolic Deep Learning
Federico Milanesio, Matteo Santoro, Pietro G. Fré +1
Hyperbolic deep learning leverages the metric properties of hyperbolic spaces to develop efficient and informative embeddings of hierarchical data. Here, we focus on the solvable g…