Abstract
We derive Thouless-Anderson-Palmer (TAP) equations and order parameter equations for stochastic analog neural network models with fluctuating synaptic couplings. Such systems with finite number of neurons originally have no energy concept. Thus they defy the use of the replica method or the cavity method, which require the energy concept. However for some realizations of synaptic noise, the systems have the effective Hamiltonian and the cavity method becomes applicable to derive the TAP equations.
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References
Sherrington, D., Kirkpatrick, S.: Solvable Model of a Spin-Glass. Phys. Rev. Lett. 35, 1792–1796 (1975)
Amit, D.J., Geutfreund, H., Sompolinsky, H.: Storing Infinite Numbers of Patterns in a Spin-Glass Model of Neural Networks. Phys. Rev. Lett. 55, 1530–1533 (1985)
Mézard, M., Parisi, G., Virasoro, M.A.: Spin Glass Theory and Beyond. World Scientific, Singapore (1987)
Thouless, D.J., Anderson, P.W., Palmer, R.G.: Solution of ’solvable model of a spin glass’. Philos. Mag. 35, 593–601 (1977)
Morita, T., Horiguchi, T.: Exactly solvable model of a spin glass. Solid. State. Comm. 19, 833–835 (1976)
Shiino, M., Fukai, T.: Self-consistent signal-to-noise analysis and its application to analogue neural networks with asymmetric connections. J. Phys. A: Math. Gen. 25, L375-L381 (1992)
Shiino, M., Yamana, M.: Statistical mechanics of stochastic neural networks: Relationship between the self-consistent signal-to-noise analysis. Thouless-Anderson-Palmer equation, and replica symmetric calculation approaches. Phys. Rev. E. 69, 011904-1-13 (2004)
Ichiki, A., Shiino, M.: Thouless-Anderson-Palmer equation for analog neural network with temporally fluctuating white synaptic noise. J. Phys. A: Math. Theor. 40, 9201–9211 (2007)
Shiino, M., Fukai, T.: Self-consistent signal-to-noise analysis of the statistical behavior of analog neural networks and enhancement of the storage capacity. Phys. Rev. E. 48, 867–897 (1993)
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Ichiki, A., Shiino, M. (2008). Thouless-Anderson-Palmer Equation for Associative Memory Neural Network Models with Fluctuating Couplings. In: Ishikawa, M., Doya, K., Miyamoto, H., Yamakawa, T. (eds) Neural Information Processing. ICONIP 2007. Lecture Notes in Computer Science, vol 4984. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69158-7_11
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DOI: https://doi.org/10.1007/978-3-540-69158-7_11
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