An attentional preactivation model of spatial memory distortions

In this final section, I will advance an attentional theory of distortional effects that can explain many of the phenomena we have observed so far. Based on earlier neural network models of prefrontal cortex (e.g., Camperi & Wang, 1998), this atten-tional account was developed in our laboratory by Julia Trommershäuser (2001).

Her model assumes that when landmarks and targets are presented at the beginning of a trial, a visual representation of these stimuli is formed that will have reached working memory by the beginning of the masking interval. Because succes-sive transformations of this representation proceed through neuronal maps with ever-increasing visual fields (i.e., from early visual high-resolution areas to low-resolution population-coded maps in the frontal lobe), random noise is added to the signal, in-troducing some spatial uncertainty. Finally, however, visual stimuli are represented in topographical fashion in dorsolateral prefrontal cortex. During the course of a typical trial, the memory representation of the landmarks will continue to receive visual input whereas input from the target is disrupted at the beginning of the masking interval.

107 The crucial assumption of the model is that neuronal maps in visual short-term memory are structured by attentional preactivation of certain points and lines. The pattern of preactivation defines the spatial reference system currently active in mem-ory and depends mainly on the visual stimulation. Note that this is in line with Psotka's (1978) results showing that participants might preferentially select virtual lines when asked to arbitrarily place a single dot into a surrounding shape, giving some independent validation to our concept of attentional preactivation. Note also that Psotka's patterns are generally consistent with the distortional fields observed in our stimulus configurations. For a two-landmark display, attentional preactivation might involve the landmarks, the connecting line, the midpoint, and the perpendicular line through the midpoint. Thus, spatial reference systems are assumed to be sented in spatial memory in much the same way that illusory contours are repre-sented in early visual representations. We do not assume that all these lines are be-ing attended all of the time, which would imply very demandbe-ing attention-splittbe-ing abilities of the memory system. Rather, it suffices to assume that attention will visit virtual lines with higher probability than other regions.

In Trommershäuser's model, the pattern of preactivation is jointly determined by intrinsic reference systems (stimulus centered), extrinsic reference systems (pos-sibly independent of stimulus properties), and strategical employment of attention.

During the masking interval, the memory trace of the target is superimposed on the pattern of preactivation, which continues to receive visual input from the still visible landmarks. Target location is retrieved from the map by localizing the maximum increase in activation beyond preactivation, i.e., the point where the difference distribution of the final and preactivation patterns is maximal.

If the visual signal and the pattern of preactivation were strictly additive, the difference distribution would be spatially unbiased, and the target could be repro-duced veridically, albeit with some spatial uncertainty. However, the model assumes that the firing rates are not strictly additive but subject to saturation because there is an upper limit to the overall firing rate. If preactivation is already high, additional acti-vation from the target stimulus is very restricted, whereas with low preactiacti-vation the additional activation has a larger impact (Byrne, 1999). It turns out that with neural saturation, the difference distribution is skewed away from preactivated regions.

The model is implemented in an artificial neuronal network with an input layer and a memory layer. For simplicity, the input layer is modelled as a sheet of

inde-pendent neurons that are directly activated by the visual stimuli, e.g. constituting a veridical map of two landmarks. Each neuron in the input layer is connected to a range of neurons in the memory layer, with the weights of these connections follow-ing a Gaussian distribution decreasfollow-ing with distance from the actual target location.³ The input layer therefore simply projects a fuzzy image of the stimuli onto the mem-ory layer, which is added to the memmem-ory layer's preactivation pattern according to a saturation function. A target location is retrieved from the memory layer by finding the neuron with maximum increase in activity exceeding the preactivation level. The model makes use of five free parameters, four less than Huttenlocher et al.'s (1991) prototype model.

Trommershäuser (2001) found that the model is able to predict the pattern of distortions obtained in the two-landmark displays very well, correctly accounting for spatial memory distortions away from the landmarks and from the midpoint between the landmarks. The amount of distortion depends on the amount of attention payed to the landmarks: with higher preactivation of a landmark, the spatial bias around it be-comes stronger, which was confirmed in an additional experiment. Importantly, the model also accounts for the pattern of variable error, predicting markedly reduced variances at preactivated locations, including landmarks and midpoint.

The model can also explain other aspects of the data. For example, it predicts that distortion will increase with mask duration when spatial information in the mem-ory layer decays or dissipates, leading to more noise in the representation, broader distributions of target and preactivated regions, and therefore stronger skewing of the target's difference distribution. Of course, it also predicts that distortional fields will closely follow intrinsic frames of reference. Because the distortional effects are strictly local, the model predicts that the combined fields of single landmarks will be locally additive, i.e., form a partition of the visual field.

Currently, the model still has some shortcomings. First, it is not able to account for the complex patterns of spatial distortions obtained with single landmarks (see, e.g., Experiments 3 and 4). Second, it is not yet clear how the subtle interactions of extrinsic and intrinsic reference systems observed in Experiments 7 to

3 The network was actually trained to acquire this pattern of connections from an initial random pattern. A Kohonen algorithm (von der Malsburg, 1974; Kohonen, 1982; see Rojas,1993, for an introduction) was used that allowed the network to find the optimal weights by self-organization based only on interactions between neighbouring cells. Kohonen-type networks are generally regarded as biologically plausible models of neural map formation.

109 9 might be built into the model except by using elaborate ad hoc patterns of preactivation.