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摘要翻译：
从神经生物学和生物物理学的角度研究了突触噪声对联想记忆神经网络提取过程的影响。我们研究了具有时间波动突触噪声（假定为白噪声）的随机模拟神经网络的统计力学性质。一般来说，这种网络不使用复制方法，因为它们没有能量概念。自洽信噪比分析(SCSNA)是一种替代复制品法推导序参量方程的方法，它不需要能量概念，因而可用于研究无能量函数的网络。将SCSNA应用于随机网络需要了解Thouless-Anderson-Palmer(TAP)方程，该方程定义了与原始随机网络等价的确定性网络。对于无能量概念情况下特别感兴趣的TAP方程的研究很少，而在有能量概念情况下与SCSNA密切相关。本文将空腔法和SCSNA相结合，导出了具有突触噪声的网络的抽头方程和一组序参量方程。
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英文标题：
《Thouless-Anderson-Palmer equation for analog neural network with
temporally fluctuating white synaptic noise》
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作者：
Akihisa Ichiki and Masatoshi Shiino
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：Disordered Systems and Neural Networks 无序系统与神经网络
分类描述：Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼镜和旋转眼镜；随机、非周期和准周期系统的性质；无序介质中的传输；本地化；由缺陷和无序介导的现象；神经网络
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一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
Effects of synaptic noise on the retrieval process of associative memory neural networks are studied from the viewpoint of neurobiological and biophysical understanding of information processing in the brain. We investigate the statistical mechanical properties of stochastic analog neural networks with temporally fluctuating synaptic noise, which is assumed to be white noise. Such networks, in general, defy the use of the replica method, since they have no energy concept. The self-consistent signal-to-noise analysis (SCSNA), which is an alternative to the replica method for deriving a set of order parameter equations, requires no energy concept and thus becomes available in studying networks without energy functions. Applying the SCSNA to stochastic network requires the knowledge of the Thouless-Anderson-Palmer (TAP) equation which defines the deterministic networks equivalent to the original stochastic ones. The study of the TAP equation which is of particular interest for the case without energy concept is very few, while it is closely related to the SCSNA in the case with energy concept. This paper aims to derive the TAP equation for networks with synaptic noise together with a set of order parameter equations by a hybrid use of the cavity method and the SCSNA.
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PDF链接：
https://arxiv.org/pdf/706.2048
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