منابع مشابه
Another Critique of the Replica Trick
Kamenev and Mezard, and Yurkevich and Lerner, have recently shown how to reproduce the large-frequency asymptotics of the energy level correlations for disordered electron systems, by doing perturbation theory around the saddles of the compact nonlinear σ model derived from fermionic replicas. We present a critical review of their procedure and argue that its validity is limited to the perturba...
متن کاملValidation of the Replica Trick for Simple Models
We discuss replica analytic continuation using several simple models in order to prove mathematically the validity of replica analysis, which is used in a wide range of fields related to large scale complex systems. While replica analysis consists of two analytical techniques, the replica trick (or replica analytic continuation) and the thermodynamical limit (and/or order parameter expansion), ...
متن کاملNonlinear Sigma Model for Disordered Media: Replica Trick for Non-Perturbative Results and Interactions
In these lectures, given at the NATO ASI at Windsor (2001), applications of the replicas nonlinear sigma model to disordered systems are reviewed. A particular attention is given to two sets of issues. First, obtaining non-perturbative results in the replica limit is discussed, using as examples (i) an oscillatory behaviour of the two-level correlation function and (ii) long-tail asymptotes of ...
متن کاملReparameterization trick for discrete variables
Low-variance gradient estimation is crucial for learning directed graphical models parameterized by neural networks, where the reparameterization trick is widely used for those with continuous variables. While this technique gives low-variance gradient estimates, it has not been directly applicable to discrete variables, the sampling of which inherently requires discontinuous operations. We arg...
متن کاملThe Kernel Trick for Distances
A method is described which, like the kernel trick in support vector machines (SVMs), lets us generalize distance-based algorithms to operate in feature spaces, usually nonlinearly related to the input space. This is done by identifying a class of kernels which can be represented as norm-based distances in Hilbert spaces. It turns out that common kernel algorithms, such as SVMs and kernel PCA, ...
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ژورنال
عنوان ژورنال: Physical Review B
سال: 2014
ISSN: 1098-0121,1550-235X
DOI: 10.1103/physrevb.89.174401