Theory of Recurrent Neural Network with Common Synaptic Inputs

Details Theory of Recurrent Neural Network with Common Synaptic Inputs Theory of Recurrent Neural Network with Common Synaptic Inputs

2005-10-07

arxiv.org/abs/cond-mat/0510169v1

Journal of the Physical Society of Japan, vol.74, no.11, Nov. 2005, pp.2961-2965

Physics

Condensed Matter

Disordered Systems and Neural Networks

12 pages

Scientific paper

10.1143/JPSJ.74.2961

We discuss the effects of common synaptic inputs in a recurrent neural network. Because of the effects of these common synaptic inputs, the correlation between neural inputs cannot be ignored, and thus the network exhibits sample dependence. Networks of this type do not have well-defined thermodynamic limits, and self-averaging breaks down. We therefore need to develop a suitable theory without relying on these common properties. While the effects of the common synaptic inputs have been analyzed in layered neural networks, it was apparently difficult to analyze these effects in recurrent neural networks due to feedback connections. We investigated a sequential associative memory model as an example of recurrent networks and succeeded in deriving a macroscopic dynamical description as a recurrence relation form of a probability density function.

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