Statistical physics of spin glasses and information processing : an introduction

By 西森秀稔. 2001

998 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/a383be0e428c9a2b1cae3abd4a54670f2cc813dc

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Citations in the corpus

Heavy-Tailed Universality Predicts Trends in Test Accuracies for Very Large Pre-Trained Deep Neural Networks (2019, background): “HT-MU applies to the analysis of complicated systems, including many physical systems, traditional NNs [23, 24], and even models of the dynamics of actual spiking neurons.”
Ergodicity breaking in a model showing many-body localization (2012, background): “MBL also presents the terms in which a quantum glass can be defined and from there it is only a small leap to conjecturing that MBL is a natural ingredient for hard computational quantum problems [4, 5] (as Ising spin glasses are a natural scenario to discuss the Physics of hard combinatorial optimi”
Symmetry enriched phases of quantum circuits (2021, background): “Similarly, the onset of an EA order parameter in a spin glass signals the emergence of an error correcting code, allowing to encode information in random broken symmetry spin configurations [42, 43].”
Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications (2011, background): “Indeed, when the parameters θ are the actual ones from which the graph was generated, the system satisfies the so-called Nishimori condition, and a very general result is that there is no static spin glass phase on the Nishimori line [29, 36].”
Matrix-Calibration-Based Cascaded Channel Estimation for Reconfigurable Intelligent Surface Assisted Multiuser MIMO (2019, methodology): “• Based on the replica method from statistical physics [24], we analyze the asymptotic performance of the posterior mean estimators in the large-system limit.”
Machine learning and the physical sciences (2019, methodology): “For learning details of the replica method and its use in computer science, information theory and machine learning we would recommend the book of Nishimori (Nishimori, 2001).”
Bayes-Optimal Joint Channel-and-Data Estimation for Massive MIMO With Low-Precision ADCs (2015, methodology): “This technique, called the replica method, is from the field of statistical physics [40], which is not mathematically rigorous.”
Implicit Self-Regularization in Deep Neural Networks: Evidence from Random Matrix Theory and Implications for Learning (2018, unknown): “This is likewise similar in spirit to how certain spin glass models are Bayes optimal in that their optimal state lies on the Nishimori Line [105].”
Statistical physics of inference: thresholds and algorithms (2015, background): “With similar arguments one can derive equality of the distribution (over realizations of the sampling) of overlap P (q) between two configurations randomly sampled from the posterior and the distribution of the magnetization P (m), which is overlap between the planted configuration and a random samp”
A statistical-mechanics approach to large-system analysis of CDMA multiuser detectors (2002, background): “(47) and then (45) immediately follows by considering a series of analytic functions converging to [35].”
Perspectives of quantum annealing: methods and implementations (2019, background): “58 801 [29] Young A P (ed) 1998 Spin Glasses and Random Fields (Singapore: World Scientific) [30] Nishimori H 2001 Statistical Physics of Spin Glasses and Information Processing: An Introduction (Oxford, United Kingdom: Oxford University Press) [31] Mézard M, Parisi G and Virasoro M A 1987 Spin Glas”
Fundamental limits of detection in the spiked Wigner model (2018, background): “The latter is a very important property of the planted model Pλ, which is usually named after Nishimori (2001) in spin-glass theory.”
A CDMA multiuser detection algorithm on the basis of belief propagation (2003, methodology): “It should be noted that the expression obtained for the density evolution directly links the proposed algorithm to the replica analysis of the equilibrium state presented in [5] since equations (19) and (20) can be regarded as the naive iteration dynamics of the saddle point equations provided by th”