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A formalism capable of handling the first step of hierarchical replica symmetry breaking in finite-connectivity models is introduced. The emerging order parameter is claimed to be a probability distribution over the space of field…
We introduce a methodology for generating benchmark problem sets for Ising machines---devices designed to solve discrete optimization problems cast as Ising models. In our approach, linear systems of equations are cast as Ising cost…
The state space of finite square and cubic Ising spin glass models is analysed in terms of the global and the local density of states. Systems with uniform and gaussian probability distribution of interactions are compared. Different…
We propose a general learning algorithm for solving optimization problems, based on a simple strategy of trial and adaptation. The algorithm maintains a probability distribution of possible solutions (configurations), which is updated…
A weak law of large numbers is established for a sequence of systems of N classical point particles with logarithmic pair potential in $\bbR^n$, or $\bbS^n$, $n\in \bbN$, which are distributed according to the configurational microcanonical…
Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…
I propose a new method to study computationally difficult problems. I consider a new system, larger than the one I want to simulate. The original system is recovered by imposing constraints on the large system. I simulate the large system…
This paper develops a method to carry out the large-$N$ asymptotic analysis of a class of $N$-dimensional integrals arising in the context of the so-called quantum separation of variables method. We push further ideas developed in the…
Here we first discuss briefly the quantum annealing technique. We then study the quantum annealing of Sherrington-Kirkpatrick spin glass model with the tuning of both transverse and longitudinal fields. Both the fields are time-dependent…
We show that a large collection of statistical mechanical systems with quadratically represented Hamiltonians on the complete graph can be extended to infinite exchangeable processes. This extends a known result for the ferromagnetic…
We study the problem of testing and recovering $k$-clique Ferromagnetic mean shift in the planted Sherrington-Kirkpatrick model (i.e., a type of spin glass model) with $n$ spins. The planted SK model -- a stylized mixture of an uncountable…
In order to overcome the limitations of small system sizes in spin-glass simulations, we investigate the one-dimensional Ising spin chain with power-law interactions. The model has the advantage over traditional higher-dimensional…
We investigate the computational hardness of spin-glass instances on a square lattice, generated via a recently introduced tunable and scalable approach for planting solutions. The method relies on partitioning the problem graph into…
We consider the task of learning Ising models when the signs of different random variables are flipped independently with possibly unequal, unknown probabilities. In this paper, we focus on the problem of robust estimation of…
We present a methodology for generating Ising Hamiltonians of tunable complexity and with a priori known ground states based on a decomposition of the model graph into edge-disjoint subgraphs. The idea is illustrated with a spin-glass model…
Typical properties of computing circuits composed of noisy logical gates are studied using the statistical physics methodology. A growth model that gives rise to typical random Boolean functions is mapped onto a layered Ising spin system,…
Identifying small subsets of features that are relevant for prediction and/or classification tasks is a central problem in machine learning and statistics. The feature selection task is especially important, and computationally difficult,…
Comparisons of different treatments or production processes are the goals of a significant fraction of applied research. Unsurprisingly, two-sample problems play a main role in Statistics through natural questions such as `Is the the new…
The Sherrington--Kirkpatrick model of spin glasses, the Hopfield model of neural networks and the Ising spin glass are all models of binary data belonging to the one-parameter exponential family with quadratic sufficient statistic. Under…
Ising machines are hardware solvers which aim to find the absolute or approximate ground states of the Ising model. The Ising model is of fundamental computational interest because it is possible to formulate any problem in the complexity…