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Diego Alberici

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Publications associées (6)

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We study the solution of the two-temperature Fokker-Planck equation and rigorously analyse its convergence towards an explicit non-equilibrium stationary measure for long time and two widely separated time scales. The exponential rates of convergence are e ...

Cham2024

Deep Boltzmann Machines: Rigorous Results at Arbitrary Depth

Emanuele Mingione, Diego Alberici

A class of deep Boltzmann machines is considered in the simplified framework of a quenched system with Gaussian noise and independent entries. The quenched pressure of a K-layers spin glass model is studied allowing interactions only among consecutive laye ...

2021

The Solution of the Deep Boltzmann Machine on the Nishimori Line

Emanuele Mingione, Diego Alberici

The deep Boltzmann machine on the Nishimori line with a finite number of layers is exactly solved by a theorem that expresses its pressure through a finite dimensional variational problem of min-max type. In the absence of magnetic fields the order paramet ...

SPRINGER2021

The Multi-species Mean-Field Spin-Glass on the Nishimori Line

Emanuele Mingione, Diego Alberici

In this paper we study a multi-species disordered model on the Nishimori line. The typical properties of this line, a set of identities and inequalities among correlation functions, allow us to prove the replica symmetry i.e. the concentration of the order ...

SPRINGER2021

A Statistical Physics approach to a multi-channel Wigner spiked model

Emanuele Mingione, Diego Alberici

In this letter we present a finite temperature approach to a high-dimensional inference problem, the Wigner spiked model, with group-dependent signal-to-noise ratios. For two classes of convex and non-convex network architectures the error in the reconstru ...

IOP Publishing Ltd2021

Annealing and Replica-Symmetry in Deep Boltzmann Machines

Emanuele Mingione, Diego Alberici

In this paper we study the properties of the quenched pressure of a multi-layer spin-glass model (a deep Boltzmann Machine in artificial intelligence jargon) whose pairwise interactions are allowed between spins lying in adjacent layers and not inside the ...

SPRINGER2020