The results presented above suggest that the same self-organizing principles that result in sparse coding and reduce redundant activation may also be operating over short time intervals in the adult, with quantifiable psychological consequences such as the TAE. This finding demonstrates a potentially important computational link between development, structure, and function.
Even though the RF-LISSOM model was not originally developed as an explanation for the tilt aftereffect, it exhibits tilt aftereffects that have nearly all of the features of those measured in humans. The effect of varying angular separation between the test and adaptation lines is similar to human data at all orientations, the time course is approximately logarithmic in each, and the TAE is localized to the retinal location which experienced the stimulus. With minor extensions, the model should account for other features of the TAE, such as higher variance at oblique orientations, frequency localization, movement direction specificity, and ocular transfer. For a discussion of the match between the model and data for humans from a variety of experiments, see Bednar (1997).
The only prominent features of the TAE that do not directly follow from the model are saturation of the effect for long adaptations, and recovery of accurate perception even in complete darkness (Greenlee and Magnussen, 1987; Magnussen and Johnsen, 1986). These two features suggest that the inhibitory weights modified during tilt adaptation could actually be a set of small, temporary weights adding to or multiplying more permanent connections. Such a mechanism was proposed by von der Malsburg (1987) as an explanation of visual object segmentation; this idea was implemented for the RF-LISSOM model by Choe and Miikkulainen (1996) and Miikkulainen et al. (1997). The TAE may be merely a minor consequence of this multi-level architecture for representing correlations over a wide range of time scales.
A main contribution of the RF-LISSOM model of the TAE is its novel explanation of the indirect effect. Proponents of the lateral inhibitory theory of direct effects have generally ignored indirect effects, or postulated that they occur only at higher cortical levels (Wenderoth and Johnstone, 1988), partly because it has not been clear how they could arise through inhibition in V1. RF-LISSOM demonstrate that a quite simple, local mechanism in V1 is sufficient to produce indirect effects. If the total synaptic resources at each neuron are limited, strengthening the lateral inhibitory connections between active neurons weakens their inactive inhibitory connections. There is widespread biological evidence of competition for a limited number of synaptic sites (Bourgeois, Jastreboff, and Rakic, 1989; Hayes and Meyer, 1988; Murray, Sharma, and Edwards, 1982; Pallas and Finlay, 1991; Purves, 1988). There is also extensive computational justification for synaptic resource conservation, beginning with one of the first computational models of Hebbian adaptation (Rochester, Holland, Haibt, and Duda, 1956). Without such normalization, connection weights governed by a Hebbian rule will increase indefinitely, or else each would reach a maximum strength (Miller and MacKay, 1994). Neither outcome would appear biologically or computationally plausible, so the assumption of some form of normalization is well-motivated (Sirosh, 1995).
Through mechanisms similar to those causing the TAE, the RF-LISSOM model should also be able to explain simultaneous tilt illusions between spatially separated stimuli. Such an explanation was originally proposed by Carpenter and Blakemore (1973). However, it will be necessary to train the system with inputs that have longer-range correlations between similar orientations, such as sinusoidal gratings (representing objects with parallel lines). With such patterns, long-range connections develop between widely separated orientation detectors, in addition to the relatively local connections now present. Trained with such patterns, RF-LISSOM should be able to account for tilt illusions as well as tilt aftereffects. Although such experiments require even larger cortex and retina sizes, they should become practical in the near future.
In addition, many similar phenomena such as aftereffects of curvature, motion, spatial frequency, size, position, and color have been documented in humans (Barlow, 1990). Since specific detectors for most of these features have been found in the cortex, RF-LISSOM should be able to account for them by the same process of decorrelation mediated by self-organizing lateral connections.