144 citations · 1k across the 90 of their papers we have counts for
94 papers
Variational Bounds for Perceptron Learning from Structured Data
Francesco Camilli, Pierluigi Contucci, Federica Gerace +1
We introduce a variational approach to a finite-temperature continuous-spin perceptron trained on a Gaussian mixture. The model allows for a broad class of concave utilities and lo…
From entropic constraints to reinforced processes: a probabilistic origin of multiscale measures
Francesco Camilli, Pierluigi Contucci, Emanuele Mingione
We study multiscale measures, defined by a hierarchy of partial Gibbs equilibria, from variational and probabilistic perspectives. We first show that they are the unique solutions…
Testing Transformer Learnability on the Arithmetic Sequence of Rooted Trees
Alessandro Breccia, Federica Gerace, Marco Lippi +2
We study whether a transformer network can learn the deterministic sequence of trees generated by the iterated prime factorization of the natural numbers. Each integer is mapped in…
Statistical Properties of the Rooted-Tree Encoding of
Pierluigi Contucci, Claudio Giberti, Godwin Osabutey +1
We prime-encode the natural numbers via recursive factorisation, iterated to the exponents, generating a corpus of planar rooted trees equivalently represented as Dyck words. This…
Tree asymptotic densities in number theory
Roberto Conti, Pierluigi Contucci, Vitalii Iudelevich
We study the asymptotic distribution of integers sharing the same rooted-tree structure that encodes their complete prime factorization tower. For each tree we derive an explicit d…
A New Lens on the Sustainability of the AI Revolution
Pierluigi Contucci, Godwin Osabutey, Filippo Zimmaro
We introduce the Economic Productivity of Energy (EPE), GDP generated per unit of energy consumed, as a quantitative lens to assess the sustainability of the Artificial Intelligenc…