Figure 3.

Cognitive systems. A schematic of an analysis approach for cognitive systems: what to analyse (Marr's three levels of analysis) and how to analyse (proposed tools of analysis spanning across the levels). Any tool can in principle be used to study any level (figure 2). Here is an example of how to relate dynamical systems tools with the three levels, in the context of the problem of associative learning (§3f). At the computational level, the associative learning problem may be specified as ‘associate two stimuli, natural and neutral, of which the natural stimulus evokes a response while the neutral one does not. In dynamical systems (DS) language, this may be translated as ‘a system with two attractors, each associated with a stimulus, corresponding to low-response and high-response’ (please see figure 6 for details). At the algorithmic level of analysis, the problem may be solved as ‘every time both stimuli are supplied, let the ability of the natural stimulus to evoke a response also strengthen the ability of the neutral stimulus to evoke the response such that over time the two stimuli become equivalent’. In DS terms, this may be translated as ‘let the internal state associated with the natural stimulus steer that associated with the neutral stimulus to the high-response attractor’. Finally, at the implementation level, the problem becomes ‘design a network with three nodes consisting of two stimuli and one response, where there is a connection between each stimulus and the response, such that the strength of the connection between the neutral stimulus and the response increases over time with the joint application of the two stimuli’. In DS terms, this is equivalent to ‘design a 3-variable (two weights and one response) coupled DS with a positive feedback loop such that the weight-state of the natural stimulus steers the weight-state of the neutral stimulus from the low-response basin of attraction through the basin-boundary to the high-response basin of attraction’. (Online version in colour.)