6.1 Psychophysical evidence relating to the TAE

Even though the RF-LISSOM model was not developed as an explanation for the tilt aftereffect, it exhibits tilt aftereffects that have nearly all of the features of those measured in humans. With the appropriate extensions, it is expected to account for all of the known data on the TAE. The features of the TAE which have already been demonstrated in the model include those in the following list. Except where noted, all of these features have been replicated by a number of researchers and are quite consistent across different studies, so any viable model of the tilt aftereffect would be expected to account for them.

Null at training angle:

Adaptation does not change the perceived orientation of the stimulus used during adaptation (figure 5.2; (Gibson and Radner, 1937).

Direct effect:

Similar orientations are misperceived by human subjects as having a larger difference than they actually do (Gibson and Radner, 1937), peaking between 5° and 20°, typically 10°- 13° ([p.216]howard:hso66; Campbell and Maffei 1971; Mitchell and Muir 1976). In RF-LISSOM, peaks at locations between 5° and 15° have been observed; 10° is typical (figure 5.2).

Null between direct and indirect effects:

Human aftereffects return to zero somewhere between 25° and 50° (Campbell and Maffei, 1971; Mitchell and Muir, 1976; Muir and Over, 1970). Zero-crossings between 30° and 60° have been observed in RF-LISSOM; 45° is typical (figure 5.2).

Indirect effect:

Distant orientations are misperceived as having a smaller difference than they actually do (Gibson and Radner, 1937), peaking somewhere between 60° and 85° (Campbell and Maffei, 1971; Mitchell and Muir, 1976; Muir and Over, 1970). In RF-LISSOM, indirect effect peaks between 45° and 75° have been observed; 60° is typical. These effects vary significantly between studies and different individuals, as described in section 6.2.4.

Time course:

The TAE magnitude increases at a diminishing rate with further adaptation (figure 5.10; Gibson and Radner 1937; Greenlee and Magnussen 1987; Magnussen and Johnsen 1986).

Orientation-independence:

The TAE versus angle curve is similar for all pairs of test and adaptation angles which differ by the same amount, regardless of the absolute orientation on the retina (Mitchell and Muir, 1976). Conflicting results were found by previous researchers, who could not demonstrate effects on oblique lines of adaptation to vertical lines. This discrepancy has been satisfactorily explained as a methodological problem of the earlier studies, and the assumption of orientation independence now seems well established.

Spatial localization:

The TAE is localized to the area of the retina which was trained (Gibson and Radner, 1937). Adaptation for a figure in one location has no measurable effect on test figures in other locations sufficiently distant. In the model, this occurs because weights are only adapted between active neurons, and a small stimulus activates only neurons in a small cortical area.

Several other aspects of the TAE will likely be exhibited by an RF-LISSOM model trained on more realistic input distributions. These simulations do not necessarily require any significant extensions to the model, but most will require larger cortex sizes and longer training times. When sufficient computing power is available and the model is extended as described, RF-LISSOM is expected to account for these experimental observations as well:

Higher variance at oblique orientations:

The TAE versus angle curve shows greater variance for oblique testing orientations (Mitchell and Muir, 1976), often sufficiently high to entirely mask the effect (Campbell and Maffei, 1971). The variance may result from the smaller number of detectors in the fovea subserving angles that are neither horizontal nor vertical (Bauer et al., 1991; Mansfield, 1974). Assuming the orientation is perceived with a mechanism similar to that in section 4.5, when fewer detectors are activated the response will vary more because the average is being computed from fewer neurons. An RF-LISSOM model trained on a non-uniform training distribution with a preponderance of horizontal and vertical lines develops more detectors for horizontal and vertical orientations. This type of adaptation has also been observed in kittens raised in deprived visual environments (Blakemore and van Sluyters, 1975). Such an anisotropic distribution is probably typical of the early visual experience of humans (Mansfield, 1974).

Frequency localization:

The TAE is selective for spatial frequency (Ware and Mitchell, 1974); adapting to a figure with narrow bars has no measurable effect upon a figure with wide bars, and vice versa. Spatial frequency selectivity has previously been demonstrated in the RF-LISSOM model (Miikkulainen et al., 1997; Sirosh et al., 1996). A unified orientation/spatial frequency RF-LISSOM model, obtained by training on oriented Gaussians of different sizes, would exhibit frequency localization for the same reason as for spatial localization. That is, only a small range of frequency detectors will be activated by a given stimulus, so only that range will show adaptation effects.

Movement direction specificity:

The TAE is selective for the direction of movement (Carney, 1982). Adapting on a pattern moving in one direction past a fixation point does not affect the orientation judgment of a pattern moving in the opposite direction. A unified orientation/movement direction RF-LISSOM model, obtained by training on oriented Gaussians moving in different directions, would exhibit this property as well. However, simulations have not yet been performed with moving stimuli for RF-LISSOM, and further work will be needed to determine how motion should be represented in the model.

Ocular transfer:

The TAE transfers completely from one eye to the other (Campbell and Maffei, 1971; Gibson and Radner, 1937); adapting one eye causes equal effects upon test lines in the same location in the visual field for either eye. A unified RF-LISSOM orientation/ocular dominance model could be obtained by training on oriented Gaussians at slightly offset positions in the two eyes. Such a model would exhibit ocular transfer if the neurons most selective for orientation were also binocular. If this does not turn out to be true for the model, it might be that the most plastic neurons in the cortex are also more likely to be binocular. The latter appears to be true for human cortex, with the input layer (layer IV) showing strong ocular dominance but lower adult plasticity, and the output layers (II, III, V, and VI) showing strong binocularity and high plasticity ([pp.139-140]daw:visdevel95; Shatz and Stryker 1978). Modeling such layer-dependent effects would require a significant extension to RF-LISSOM because currently all the neurons in each column are grouped together for simulation.

Large-scale combined simulations allowing the study of some of these features were proposed by Sirosh (1995), but they generally require greater cortex sizes and training times to represent multiple dimensions on the same map. Current computer resources are not sufficient, but with forthcoming advances in technology they should soon be more practical.

Besides the above, there are a small number of features of the TAE not yet demonstrated by the current model, and not expected to be found unless extensions are made:

Saturation:

The TAE saturates at approximately 4° (Campbell and Maffei, 1971; Greenlee and Magnussen, 1987; Magnussen and Johnsen, 1986; Mitchell and Muir, 1976) but in the RF-LISSOM model it will steadily increase up to at least 20° with sufficiently long adaptation times. Possible mechanisms for this limit to plasticity will be discussed further in section 6.2. It is a simple matter to artificially limit the plasticity allowed in the model, once it is known what the limiting factor should be.

Dark recovery:

After the adaptation stimulus is removed, TAE magnitude gradually reduces in strength, even in the absence of visual input. In contrast, the RF-LISSOM model will ordinarily remain static until further input is received. Explanations for dark recovery in humans will be discussed further in section 6.2.3; adults may have connections which change strength rapidly but temporarily.

There are also some small effects due to the absolute orientation of the head with respect to gravity; these are presumably due to the vestibular system, not to processing in V1 (Howard and Templeton, 1966; Wolfe and Held, 1982). Apart from such data not expected to apply to V1, there is no known psychophysical evidence against the RF-LISSOM explanation of tilt aftereffects. The following section will examine the types of cellular processes that may underlie the psychological effects above, if the TAE is occurring in humans in the same way it does in the model.