7 citations · 10 across the 9 of their papers we have counts for
5 papers · 1 filter
Thermodynamics a la Souriau on Kähler Non Compact Symmetric Spaces for Cartan Neural Networks
Pietro G. Fré, Alexander S. Sorin, Mario Trigiante
In this paper, we clarify several issues concerning the abstract geometrical formulation of thermodynamics on non compact symmetric spaces that are the mathematical…
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…
The paint group Tits Satake theory of hyperbolic symmetric spaces: the distance function, paint invariants and discrete subgroups
Ugo Bruzzo, Pietro Fré, Mario Trigiante
The present paper, which is partially a review, but also contains several completely new results, aims at presenting, in a unified mathematical framework, a complex and articulated…