Related papers: A statistical mechanics approach to the factorizat…
The chapter starts with a historical summary of first attempts to optimize the spin glass Hamiltonian, comparing it to recent results on searching largest cliques in random graphs. Exact algorithms to find ground states in generic spin…
As a problem in data science the inverse Ising (or Potts) problem is to infer the parameters of a Gibbs-Boltzmann distributions of an Ising (or Potts) model from samples drawn from that distribution. The algorithmic and computational…
We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…
Due to an extremely rugged structure of the free energy landscape, the determination of spin-glass ground states is among the hardest known optimization problems, found to be NP-hard in the most general case. Owing to the specific structure…
Ground-state properties of the two-dimensional $S=1/2$ random Heisenberg models are investigated by the exact-diagonalization method. The phase diagram of the bond-random model (the $\pm J$ model) is the same as that of the corresponding…
We propose a general framework for solving statistical mechanics of systems with finite size. The approach extends the celebrated variational mean-field approaches using autoregressive neural networks, which support direct sampling and…
We propose a new Ising spin glass model on $Z^d$ of Edwards-Anderson type, but with highly disordered coupling magnitudes, in which a greedy algorithm for producing ground states is exact. We find that the procedure for determining…
We investigate the sensitivity of the time evolution of a kinetic Ising model with Glauber dynamics against the initial conditions. To do so we apply the "damage spreading" method, i.e., we study the simultaneous evolution of two identical…
The Cotter-Holm Slice Model (CHSM) was introduced to study the behavior of whether and specifically the formulation of atmospheric fronts, whose prediction is fundamental in meteorology. Considered herein is the influence of stochastic…
Estimating the density of states of systems with rugged free energy landscapes is a notoriously difficult task of the utmost importance in many areas of physics ranging from spin glasses to biopolymers. Density of states estimation has also…
It is widely expected that systems which fully thermalize are chaotic in the sense of exhibiting random-matrix statistics of their energy level spacings, whereas integrable systems exhibit Poissonian statistics. In this paper, we…
We represent the Ising model of statistical physics by normal factor graphs in the primal and in the dual domains. By analogy with Kirchhoff's voltage and current laws, we show that in the primal normal factor graphs, the dependency among…
A disordered spin glass model where both static and dynamical properties depend on macroscopic magnetizations is presented. These magnetizations interact via random couplings and, therefore, the typical quenched realization of the system…
Statistical inference on the mean of a Poisson distribution is a fundamentally important problem with modern applications in, e.g., particle physics. The discreteness of the Poisson distribution makes this problem surprisingly challenging,…
We propose and study a novel stochastic inertial primal-dual approach to solve composite optimization problems. These latter problems arise naturally when learning with penalized regularization schemes. Our analysis provide convergence…
A generalised integer S Ising spin glass model is analysed using the replica formalism. The bilinear couplings are assumed to have a Gaussian distribution with ferromagnetic mean <J_ij> = Jo. Incorporation of a quadrupolar interaction term…
In this paper we describe a deep learning--based probabilistic algorithm for integer factorisation. We use Lawrence's extension of Fermat's factorisation algorithm to reduce the integer factorisation problem to a binary classification…
The notion of duality -- that a given physical system can have two different mathematical descriptions -- is a key idea in modern theoretical physics. Establishing a duality in lattice statistical mechanics models requires the construction…
We study the critical behavior of two-dimensional short-range quantum spin glasses by numerical simulations. Using a parallel tempering algorithm, we calculate the Binder cumulant for the Ising spin glass in a transverse magnetic field with…
This paper develops an inferential theory for state-varying factor models of large dimensions. Unlike constant factor models, loadings are general functions of some recurrent state process. We develop an estimator for the latent factors and…