The limit free energy of spin-glass models with convex interactions can be represented as a
variational problem involving an explicit functional. Models with non-convex interactions are …

In neural network's literature, Hebbian learning traditionally refers to the procedure by which
the Hopfield model and its generalizations store archetypes (ie, definite patterns that are …

We propose a conjecture for the limit free energy of mean-field spin glasses with a bipartite
structure, and show that the conjectured limit is an upper bound. The conjectured limit is …

We consider the high-dimensional inference problem where the signal is a low-rank matrix
which is corrupted by an additive Gaussian noise. Given a probabilistic model for the low …

We prove a Parisi formula for the limiting free energy of multi-species spherical spin glasses
with mixed p-spin interactions. The upper bound involves a Guerra-style interpolation and …

We study a multi-species spin glass system where the density of each species is kept fixed
at increasing volumes. The model reduces to the Sherrington–Kirkpatrick one for the single …

The standard Hopfield model for associative neural networks accounts for biological
Hebbian learning and acts as the harmonic oscillator for pattern recognition, however its …

Restricted Boltzmann machines are described by the Gibbs measure of a bipartite spin
glass, which in turn can be seen as a generalized Hopfield network. This equivalence allows …

We study generalized restricted Boltzmann machines with generic priors for units and
weights, interpolating between Boolean and Gaussian variables. We present a complete …

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 …