5.5 Time course of the tilt aftereffect

  In addition to the angular changes in the TAE described in the previous sections, the magnitude of the TAE in humans increases regularly with adaptation time (Gibson and Radner, 1937). The equivalent of ``time'' in the RF-LISSOM model is an iteration, i.e. a single cycle of input presentation, activity propagation, settling, and weight modification. Figure 5.9 shows how the TAE varies for each angle as the number of adaptation iterations is increased.

 

Figure 5.9: Tilt aftereffect versus angle over the course of adaptation.

The same basic S-shaped curve is always evident, but its magnitude increases monotonically with adaptation. Since obtaining human data for even a single curve is extremely time consuming, equivalently comprehensive data for human subjects is unavailable. The plots are easily obtained for the model, however, which illustrates one reason why computational models are important -- they make it possible to obtain quite detailed data that can constitute predictions for later experimental work.

The experimental work that has been done so far on the time course of the TAE in humans (Gibson and Radner, 1937; Greenlee and Magnussen, 1987; Magnussen and Johnsen, 1986) corresponds to a single vertical slice through the direct TAE region in figure 5.9. It is measured by presenting an oriented adaptation figure for an extended period interrupted at intervals by the presentation of test and comparison lines. At each test presentation, the amount of the TAE present is measured using the standard techniques illustrated in figure 2.3. The duration of the test presentation is minimized so that it will not affect the magnitude of the TAE significantly.

When the time course of the direct TAE is measured in this way for human subjects, the increase is approximately logarithmic with time (Gibson and Radner, 1937), as is evident for the model in figure 5.9. The magnitude of the TAE eventually reaches saturation at a level that depends upon the experimental protocol used (Greenlee and Magnussen, 1987; Magnussen and Johnsen, 1986). Figure 5.10 compares the shape of the TAE versus time curve for human subjects and for the RF-LISSOM model.

 

Figure 5.10: Direct tilt aftereffect versus time.

The x axis for the RF-LISSOM and human data has different units, but the correspondence between the two curves might provide a rough way of quantifying the equivalent real time for an ``iteration'' of the model. The time course of the TAE in the RF-LISSOM model is similar to the human data, but the model does not show saturation effects over the adaptation amounts tested so far. This difference indicates that the biological implementation has additional constraints on the amount of learning that can be achieved over the time scale over which the tilt aftereffect is seen. This issue is explored further in the discussion in the next chapter, including possible ways that saturation might be incorporated into the RF-LISSOM model.