Maei, H.; (2005) How can realistic networks process time-varying signals? Masters thesis , University of London.

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Abstract

The brain is easily able to process and categorise complex time-varying signals. For example, the two sentences "it is cold in London this time of year" and "it is hot in London this time of year" have different meanings, even though the words "hot" and "cold" appear about 3000 ms before the ends of the two sentences. A network that can perform this kind of processing must, therefore, have a long memory. In other words, the current state of the network must depend on events that happened many seconds ago. This is particularly difficult because neurons are dominated by relatively short time constants---10s to 100s of ms. Recently Jaeger and Haas 2004 (see also Jaeger 2001 ) and Maass et al. 2002, 2004 proposed that randomly connected networks could exhibit the long memories necessary for complex temporal processing. This is an attractive idea, both for its simplicity and because little fine tuning is required. However, a necessary condition for it to work is that the underlying network dynamics must be non-chaotic that is, it must exhibit negative Lyapunov exponents White et al., 2004, Bertschinger and Natschlager, 2004 . Real networks, though, tend to be chaotic Banerjee, 2001a,b , an observation that we have corroborated based on an extension of the analysis used by Bertschinger and Natschlager. Real networks also tend to be very noisy---they exhibit synaptic failures 10-90% of the time in the central nervous system Walmsley et al., 1987, Volgushev et al., 2004 . The question we ask here, then, is: given the chaotic dynamics and high noise intrinsic to biologically realistic networks, can randomly connected networks exhibit memories that are significantly longer than the time constants of their constituent neurons.

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