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Effects of synaptic noise on the retrieval process of associative memoryneural networks are studied from the viewpoint of neurobiological andbiophysical understanding of information processing in the brain. Weinvestigate the statistical mechanical properties of stochastic analog neuralnetworks with temporally fluctuating synaptic noise, which is assumed to bewhite 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 oforder parameter equations, requires no energy concept and thus becomesavailable in studying networks without energy functions. Applying the SCSNA tostochastic network requires the knowledge of the Thouless-Anderson-Palmer (TAP)equation which defines the deterministic networks equivalent to the originalstochastic ones. The study of the TAP equation which is of particular interestfor the case without energy concept is very few, while it is closely related tothe SCSNA in the case with energy concept. This paper aims to derive the TAPequation for networks with synaptic noise together with a set of orderparameter equations by a hybrid use of the cavity method and the SCSNA.

Thouless-Anderson-Palmer equation for analog neural network with temporally fluctuating white synaptic noise