神经网络的 Thouless - Anderson - Palmer 方程。

Thouless-anderson-palmer equations for neural networks.

作者信息

Shamir M, Sompolinsky H

机构信息

Racah Institute of Physics and Center for Neural Computation, The Hebrew University, Jerusalem 91904, Israel.

出版信息

Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Feb;61(2):1839-44. doi: 10.1103/physreve.61.1839.

DOI:10.1103/physreve.61.1839

PMID:11046469

Abstract

Previous derivation of the Thouless-Anderson-Palmer (TAP) equations for the Hopfield model by the cavity method yielded results that were inconsistent with those of the perturbation theory as well as the results derived by the replica theory of the model. Here we present a derivation of the TAP equation for the Hopfield model by the cavity method and show that it agrees with the form derived by perturbation theory. We also use the cavity method to derive TAP equations for the pseudoinverse neural network model. These equations are consistent with the results of the replica theory of these models.

摘要

先前通过腔方法对霍普菲尔德模型推导的 Thouless-Anderson-Palmer（TAP）方程所得到的结果，与微扰理论的结果以及该模型的副本理论推导的结果不一致。在此，我们通过腔方法给出霍普菲尔德模型的 TAP 方程的推导，并表明它与微扰理论推导的形式一致。我们还使用腔方法推导了伪逆神经网络模型的 TAP 方程。这些方程与这些模型的副本理论结果一致。