This paper develops approximate message passing algorithms to optimize multi-species
spherical spin glasses. We first show how to efficiently achieve the algorithmic threshold …

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 dense, associative neural-networks trained by a teacher (ie, with supervision)
and we investigate their computational capabilities analytically, via statistical-mechanics …

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 give simple criteria to identify the exponential order of magnitude of the absolute value of
the determinant for wide classes of random matrix models, not requiring the assumption of …

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 …

This paper characterizes the annealed complexity of bipartite spherical spin glasses, both
pure and mixed. This means we give exact variational formulas for the asymptotics of the …

In a companion paper we developed the generalized TAP approach for general
multispecies spherical mixed p-spin models. In this paper we use it to compute the limit of …

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 consider critical points of the spherical pure p-spin spin glass model with Hamiltonian
HN σ= 1 N p− 1/2∑ i 1,…, ip= 1 NJ i 1,…, ip σ i 1… σ ip⁠, where σ= σ 1,…, σ N∈ SN− 1≔ …