Figure 1.

Extending associative learning paradigm to GRNs

The sequence of behavioral changes is driven by particular combinations of stimuli in every phase of associative memory. The stimuli-response mapping is shown for each phase, and the relevant ones are marked with a green box. For example, during the pre-association phase (A), the relevant combinations are where either the individual stimuli or no stimuli are presented. (B) During the association phase, both stimuli are presented at the same time. The most important observation to be made here is the distinction between the stimuli-response mappings of the pre-association and the post-association phases (C). In particular, the salivation response to CS during post-association is altered compared with that in the pre-association phase. This is accomplished by the activation of memory during the association phase. In other words, the dog with a memory of the association between UCS and CS responds to the latter stimulus differently. This altered behavior is a result of memory, as shown by the equation at the bottom of (C). The underlying Boolean network model (D) shows the rules of behavior of the memory (M) and the response (R) nodes. The phenomenon of associative memory can also be understood in symbolic terms as follows. During the pre-association phase M is not activated as per the relevant stimuli-response combinations. Thus, if we set M = OFF in the rule for R, we get a rule that says that R can be triggered by UCS only (R←UCS). During the association phase, the joint presentation of the stimuli activates M. Finally, during the post-association phase, if we set M = ON in the rule for R, we get a rule that says R can be triggered by either UCS or CS in a symmetrical way (R←UCS OR CS). In other words, association casts UCS and CS as equivalent from the point of view of R.