Topic
Cavity method
About: Cavity method is a research topic. Over the lifetime, 312 publications have been published within this topic receiving 9915 citations.
Papers published on a yearly basis
Papers
Book•
27 Mar 2009
TL;DR: The approach focuses on large random instances, adopting a common probabilistic formulation in terms of graphical models, and presents message passing algorithms like belief propagation and survey propagation, and their use in decoding and constraint satisfaction solving.
Abstract: This book presents a unified approach to a rich and rapidly evolving research domain at the interface between statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. It is accessible to graduate students and researchers without a specific training in any of these fields. The selected topics include spin glasses, error correcting codes, satisfiability, and are central to each field. The approach focuses on large random instances, adopting a common probabilistic formulation in terms of graphical models. It presents message passing algorithms like belief propagation and survey propagation, and their use in decoding and constraint satisfaction solving. It also explains analysis techniques like density evolution and the cavity method, and uses them to study phase transitions.
2,032 citations
TL;DR: This paper uses the cavity method of statistical physics to obtain an asymptotically exact analysis of the phase diagram of the stochastic block model, a commonly used generative model for social and biological networks, and develops a belief propagation algorithm for inferring functional groups or communities from the topology of the network.
Abstract: In this paper we extend our previous work on the stochastic block model, a commonly used generative model for social and biological networks, and the problem of inferring functional groups or communities from the topology of the network. We use the cavity method of statistical physics to obtain an asymptotically exact analysis of the phase diagram. We describe in detail properties of the detectability/undetectability phase transition and the easy/hard phase transition for the community detection problem. Our analysis translates naturally into a belief propagation algorithm for inferring the group memberships of the nodes in an optimal way, i.e., that maximizes the overlap with the underlying group memberships, and learning the underlying parameters of the block model. Finally, we apply the algorithm to two examples of real-world networks and discuss its performance.
1,155 citations
TL;DR: In this paper, a general non-perturbative solution of the Bethe lattice spin glass problem at a level of approximation which is equivalent to a one step replica symmetry breaking solution was proposed.
Abstract: So far the problem of a spin glass on a Bethe lattice has been solved only at the replica symmetric level, which is wrong in the spin glass phase. Because of some technical difficulties, attempts at deriving a replica symmetry breaking solution have been confined to some perturbative regimes, high connectivity lattices or temperature close to the critical temperature. Using the cavity method, we propose a general non perturbative solution of the Bethe lattice spin glass problem at a level of approximation which is equivalent to a one step replica symmetry breaking solution. The results compare well with numerical simulations. The method can be used for many finite connectivity problems appearing in combinatorial optimization.
1,054 citations
TL;DR: In this paper, the authors studied the problem of satisfiability of randomly chosen clauses, each with K Boolean variables, using the cavity method at zero temperature, and showed the existence of an intermediate phase in the satisfiable region.
Abstract: We study the problem of satisfiability of randomly chosen clauses, each with K Boolean variables. Using the cavity method at zero temperature, we find the phase diagram for the K=3 case. We show the existence of an intermediate phase in the satisfiable region, where the proliferation of metastable states is at the origin of the slowdown of search algorithms. The fundamental order parameter introduced in the cavity method, which consists of surveys of local magnetic fields in the various possible states of the system, can be computed for one given sample. These surveys can be used to invent new types of algorithms for solving hard combinatorial optimizations problems. One such algorithm is shown here for the K=3 satisfiability problem, with very good performances.
555 citations
TL;DR: In this article, the authors use the cavity method in the case of spin glass on a lattice with a local tree-like structure, which is the proper generalization of the usual Bethe lattice to frustrated problems.
Abstract: In this note we explain the use of the cavity method directly at zero temperature, in the case of the spin glass on a lattice with a local tree like structure, which is the proper generalization of the usual Bethe lattice to frustrated problems. The computation is done explicitly in the formalism equivalent to “one step replica symmetry breaking;” we compute the energy of the global ground state, as well as the complexity of equilibrium states at a given energy. Full results are presented for a Bethe lattice with connectivity equal to three. The main assumptions underlying the one step cavity approach, namely the existence of many local ground states, are explicitely stated and discussed: some of the main obstacles towards a rigorous study of the problem with the cavity method are outlined.
490 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 12 |
| 2020 | 10 |
| 2019 | 21 |
| 2018 | 16 |
| 2017 | 11 |
| 2016 | 13 |