Strong topological trivialization of multi-species spherical spin glasses
We study the landscapes of multi-species spherical spin glasses. Our results determine the
phase boundary for annealed trivialization of the number of critical points, and establish its …
phase boundary for annealed trivialization of the number of critical points, and establish its …
Nonconvex interactions in mean-field spin glasses
JC Mourrat - Probability and Mathematical Physics, 2021 - msp.org
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 …
structure, and show that the conjectured limit is an upper bound. The conjectured limit is …
On the free energy of vector spin glasses with non-convex interactions
HB Chen, JC Mourrat - arXiv preprint arXiv:2311.08980, 2023 - arxiv.org
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 …
variational problem involving an explicit functional. Models with non-convex interactions are …
Free energy in multi-species mixed p-spin spherical models
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 …
with mixed p-spin interactions. The upper bound involves a Guerra-style interpolation and …
Algorithmic threshold for multi-species spherical spin glasses
We study efficient optimization of the Hamiltonians of multi-species spherical spin glasses.
Our results characterize the maximum value attained by algorithms that are suitably …
Our results characterize the maximum value attained by algorithms that are suitably …
The solution of the deep Boltzmann machine on the Nishimori line
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 …
solved by a theorem that expresses its pressure through a finite dimensional variational …
Complexity of bipartite spherical spin glasses
B McKenna - Annales de l'Institut Henri Poincare (B) Probabilites …, 2024 - projecteuclid.org
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 …
pure and mixed. This means we give exact variational formulas for the asymptotics of the …
TAP approach for multispecies spherical spin glasses II: The free energy of the pure models
E Subag - The Annals of Probability, 2023 - projecteuclid.org
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 …
multispecies spherical mixed p-spin models. In this paper we use it to compute the limit of …
Spherical spin glass model with external field
J Baik, E Collins-Woodfin, P Le Doussal… - Journal of Statistical …, 2021 - Springer
We analyze the free energy and the overlaps in the 2-spin spherical Sherrington Kirkpatrick
spin glass model with an external field for the purpose of understanding the transition …
spin glass model with an external field for the purpose of understanding the transition …
The ground state energy and concentration of complexity in spherical bipartite models
P Kivimae - Communications in Mathematical Physics, 2023 - Springer
We establish an asymptotic formula for the ground-state energy of the spherical pure (p, q)-
spin glass model for p, q≥ 96. We achieve this through understanding the concentration of …
spin glass model for p, q≥ 96. We achieve this through understanding the concentration of …