Since RF-LISSOM models neurons at an abstract level, it allows cortical function to be studied without specifying a particular biochemical implementation. The same processes could be performed by a number of different mechanisms in different species, in different brain areas, at different stages of development, or at different time scales. Once the behavior is clear from computational simulations, candidates for its implementation can be proposed and tested. This section will relate the results from chapter 5 to experimental evidence, in an attempt to constrain the possible candidates for biological mechanisms underlying the TAE.
Given a network of interconnected neurons, adaptation may conceivably occur either in the connections or nonspecifically across the neurons themselves. It is sometimes hard to make a distinction between these alternatives, but there are cases when they can clearly be differentiated. For instance, if only the connections are changed, being able to stimulate a neuron through a different unadapted pathway can demonstrate that the neuron itself is unchanged. If the entire neuron itself changes, then no matter what mechanism is used to stimulate it, it will show the effects of adaptation.
The TAE seen in RF-LISSOM results from changes in the connection weights, while the discredited theory of neural fatigue (chapter 2) postulated changes occurring within the neuron itself. However, echoes of the fatigue theory persist, even from researchers who have accepted the lateral inhibition theory of the TAE (e.g. Gelbtuch et al. 1986; Kurtenbach and Magnussen 1981; Masini et al. 1990; Tolhurst and Thompson 1975). These researchers describe the TAE as arising from ``the prolonged effects of inhibition'' on a neuron. They appear to interpret these effects as changes that occur within the neuron, perhaps a buildup of some intracellular inhibitory messenger, or a change in the properties of ion channels in the cell membrane. These changes would be activated by lateral inhibition, but would remain in force for a short time following it. If this were true, the TAE would be resulting from exactly the same biochemical processes that presumably mediate the tilt illusion (see section 6.4.1). The only difference should be that the aftereffect eventually decreases with time, while the illusion would persist.
However, several of these same researchers then go on to present evidence that a number of psychoactive substances modify one effect but not the other (Gelbtuch et al., 1986; Masini et al., 1990). This prompts them to propose explanations of this apparent paradox that tend to be rather complex and speculative. This thesis suggests a much simpler interpretation which is also supported by clear physiological evidence. When an aftereffect occurs in the model, it is always a result of changes in the connection strength between neurons, not a nonspecific change in the neuron itself (cf. Barlow 1990). The model does not contain any representation of the state of the neuron, whose response changes only when its inputs or connection weights change.
Under these assumptions, there is no difficulty in explaining the differences between the effects of various drugs on the TAE and TI. Both effects would arise from lateral inhibitory interactions, accounting for the substantial similarities seen between them (see section 6.4.1). But there would be distinct differences in the biochemical mechanisms for the effects -- the TI requires only that the lateral inhibitory connections be functional, while the TAE requires that their strength be modifiable. Many substances have been shown to affect plasticity without otherwise altering function (Daw, 1995, ch.12). Similarly, since the inhibitory connections are polysynaptic, other substances could interfere with the effect of lateral inhibition on the target cell without disrupting adaptation occurring earlier in the pathway.
Furthermore, Vidyasagar (1990) has demonstrated that at least some types of orientation adaptation do not appear to be a result of changes within a single cell. Vidyasagar activated and inhibited single cells directly (using electrical and/or chemical stimulation), and was unable to find any adaptation effects in their responses. However, there was clear adaptation evident in the contrast-sensitivity threshold for the same cells when they were activated by a visual pattern that also activated other nearby cells. These results suggest that the effects occur somewhere along the connections between neurons (as in RF-LISSOM), rather than as a non-specific change within the individual neurons themselves.
If the afferent weights are modifiable in RF-LISSOM, the layout of the orientation map itself can undergo substantial reorganization. Areas representing the orientation used during adaptation increase in size, while those representing other orientations decrease. Such changes are known to occur in response to ordinary visual experience during development (Movshon and van Sluyters, 1981). In the adult, however, they are thought to require cortical lesions or very long-term changes in visual input (Gilbert et al. 1996; Kapadia et al. 1994; Sugita 1996; see also Miikkulainen et al. 1997; Sirosh et al. 1996). On the other hand, substantial plasticity has been demonstrated for neurons in the adult visual cortex in vitro (Artola and Singer, 1987; Hirsch and Gilbert, 1993; Kirkwood and Bear, 1994). It has been proposed that such plasticity is controlled by a plasticity gate ordinarily held closed by the inhibitory connections from other active neurons (Kirkwood and Bear, 1994; von der Malsburg, 1987). It is not yet firmly established what circumstances cause such a gate to open.
If afferent plasticity is possible over periods less than one hour, it may be responsible for the saturation of the tilt aftereffect found by Greenlee and Magnussen (1987). The results computed in chapter 5 for the RF-LISSOM model assume that the neurons in the model encode a fixed orientation. After a marathon adaptation session with plastic afferent connections, this assumption would become invalid: the neurons in the map would develop substantially different orientation preferences. It is possible that higher levels in the cortex may begin to rearrange in the same way, resulting in a perceived orientation based upon the new map instead. Such higher-level adaptation would counteract the effects of adaptation in V1, because it would change the interpretation of activity on the map. The result could be that the perceived TAE levels off at a maximum, i.e. that it saturates.
A psychophysical test might be conducted to determine if hierarchical reorganization is occurring in this way. Adaptation to a grating of a particular orientation, spatial frequency, and contrast increases the ability to detect that similar stimuli actually differ very slightly from it along any of those dimensions (Albrecht et al., 1984; Greenlee and Heitger, 1987). The decrease in the incremental threshold for detection of difference is ordinarily considered to be just another way of expressing what occurs in the TAE, and is presumed to result from the same mechanism. If it does, then it may provide a way to detect the phenomena causing the TAE even when the changes in perceived orientation have reached saturation. If reorganization is occurring, the lower level would continue becoming more sensitive to neighboring orientations, but the higher level would begin to cancel out the changes in the orientation map in order to restore veridical perception. It is not clear how the higher-level system would gauge the veridicality of the orientations in the map; it might compare responses in different parts of the map (likely receiving different levels of adaptation) and make appropriate corrections at local areas to ensure the map is consistent. If a process of this nature is occurring, it could be detected by testing if improved incremental sensitivity continues increasing past where the perceived orientation changes have saturated. If it does, then the saturation effect may be due to this reorganization at higher levels.
Alternatively, saturation may result from limits on the plasticity of the inhibitory connections, as proposed in the next section. Whether or not afferent and lateral excitatory connections are plastic in ordinary circumstances in the adult, the results from this thesis suggest that at least the inhibitory connections must retain some degree of plasticity. The next section will examine what type of inhibitory plasticity would be required to account for the evidence.
The steady decay of the tilt aftereffect in complete darkness may be a manifestation of differences between adult and developmental plasticity. For humans, it has been found that the TAE decays in darkness with approximately the same curve as when it increases in figure 5.10 (Greenlee and Magnussen, 1987; Magnussen and Johnsen, 1986). Other experiments, however, have found that small residual tilt aftereffects can be detected as long as two weeks after a four-minute adaptation (Wolfe and O'Connell, 1986). In any case, the decay does not appear to rely on visual input, since it has the same time course whether the subject is in complete darkness, or if test patterns are presented at intervals during decay (Magnussen and Johnsen, 1986).
In the RF-LISSOM model, decay will occur in the same way as adaptation occurs -- subsequent inputs will cause the organization to return to equilibrium as long as they include orientations different from the fixation stimulus (cf. Wolfe 1984). However, if no inputs are presented (or, equivalently, blank inputs are presented), no weight changes will occur, and the tilt aftereffects will remain indefinitely. Random spontaneous retinal activity present in darkness is not expected to be sufficient to cause a return to equilibrium, since it is unlikely to contain oriented components at the spatial scale of the adaptation stimulus.
One quite speculative explanation of decay consistent with the present RF-LISSOM model is that it results from the same process of higher-level reorganization proposed in section 6.2.2. Reorganization that occurs while the adaptation stimulus is being presented would result in saturation, while reorganization that occurs after the map in V1 has stopped being modified would result in a steady decay in the perceived orientation difference. Thus neither saturation nor decay would have been found in the experiments in chapter 5, as observed. From this perspective, there is no reason to suppose that the mechanisms of plasticity differ in the adult and the infant. However, this is unlikely to be the full explanation, since even single cells in V1 demonstrate decay of adaptation effects (Albrecht et al., 1984); though of course the single-cellular decay could be caused by feedback from higher levels as they reorganize.
Another less extravagant explanation may be that changes in synaptic effectiveness are merely a side-effect of limits on synaptic transmission at particular excitatory connections. This would act as a form of connection-specific fatigue (Geisler, 1997). During presentation of an adaptation pattern, the ability of the connection to carry action potentials would decrease, resulting in a direct TAE. As resources are replenished, the effects of adaptation would decrease, thus explaining why decay occurs. This mechanism does not readily account for the saturation effect, since it is not obvious why there should be a limit to the amount of depletion possible.
Finally, a more compelling explanation for decay and saturation might
be that adult and infant plasticity are two different (but possibly
related) cellular mechanisms. This explanation would not depend upon
reorganization of the orientation map in V1 or at higher levels. In
this view, the mechanism underlying the TAE in the adult may be a
separate fast, limited, and temporary version of the self-organizing
process that captures longer-term correlations. The connection
weights in this process would act as a small additive or
multiplicative term on top of a larger long-term weight. For example,
each inhibitory weight w could be represented as 
.The wo portion would be comparatively static, keeping its value
indefinitely in darkness and changing only with a long time constant,
or perhaps not at all in the absence of cortical or retinal trauma.
The 
term, on the other hand, would adapt and decay very
quickly, perhaps representing the short-term correlations between
image elements.
Having this set of temporary, highly-plastic, strength-limited weights might be a quite deliberate feature of the cortex. Such a mechanism has been proposed by von der Malsburg (1987) as an explanation of visual object segmentation. He proposed that temporary plasticity allows the cortex to group elements of a visual scene into coherent objects, each composed of neurons firing in synchrony. The synchronization would be achieved by rapidly modulating lateral connection strength to temporarily strengthen connections between active units and weaken other connections. The amount of strengthening possible over this time scale would be quite limited, which would result in eventual saturation of the effects. Similarly, changes would be expected to decay after the visual input is removed, so that subsequent inputs are not affected if they are sufficiently far removed in time. But over short time scales, the interactions between subsequent inputs (e.g., the tilt aftereffect) could actually be beneficial: they would facilitate the segmentation of other similar collections of features. Analogous synchronization and segmentation effects have been modeled in RF-LISSOM already (Choe and Miikkulainen, 1996; Miikkulainen et al., 1997).
Permanent changes in synaptic strength would require repeated presentation of inputs grouping on the short time scale, and the opening of some form of plasticity gate (Kirkwood and Bear, 1994; von der Malsburg, 1987). The long-term changes would thus represent long-term persistence of short-term correlations. The short-term and long-term processes might share some of the same biochemical pathways, or they might be entirely different processes that both implement the same function over different time scales. The TAE itself may be merely a minor consequence of this complex architecture for representing a wide range of correlations. The details of these mechanisms are abstracted in the current model, where only one type of reorganization mechanism is present. Future versions of RF-LISSOM may be extended to explore these issues in more detail.
The linkage explanation was disproved by the finding that indirect and direct effects are similar at all absolute orientations (Mitchell and Muir, 1976). The O'Toole and Wenderoth (1977) theory (i.e., inhibition at intermediate distances, but excitation at near and far distances) was abandoned by at least some of its original proponents when they found that the indirect effect arises significantly later than the direct effect (Wenderoth and Johnstone, 1988; Wenderoth et al., 1989). If both effects result from very similar processes of lateral interactions, differing only in sign, one would have expected them to have a fairly similar time course as well.
Spivey-Knowlton (1993) has proposed that Coltheart's explanation in terms of cross-neurons may represent a possible neural substrate for the virtual axis theory, as described in section 2.3.3. Spivey-Knowlton's formulation of the virtual axis theory helps make it less abstract and more testable, but it does not provide any functional justification for indirect effects. Nevertheless, the virtual axis theory appears to be the working hypothesis for the indirect effect at present, if only because of the lack of competing theories compatible with the lateral inhibition theory of direct effects.
This thesis demonstrates, however, that a possibly quite simple, local mechanism in V1 is sufficient to produce the indirect effect. If the total synaptic resources at each neuron are limited, for whatever reason, the strengthening of the lateral inhibitory connections between active neurons must also decrease the effectiveness of inactive connections to those neurons. Such a limit appears biologically plausible on the face of it, since a neuron has only a fixed surface area to which connections can made unless the neuron expands in size, and the neuron cannot become indefinitely large because the volume of the brain is fixed. Miller and MacKay (1994) note that there is widespread evidence of competition for a limited number of synaptic sites (Bourgeois et al. 1989; Hayes and Meyer 1988a,b; Murray et al. 1982; Pallas and Finlay 1991; Purves and Lichtman 1985; Purves 1988).
There is also extensive computational justification for synaptic resource conservation. One of the first computational models of Hebbian adaptation (Rochester et al., 1956) discovered that without such normalization, connection weights governed by a Hebbian rule will increase to infinity. Each time an input is presented, some connections will be strengthened, and the others will remain as they were. If each weight has a maximum strength, then each will eventually increase to its maximum value. Thus all connections will end up identical and will be unable to perform any useful function (Miller and MacKay, 1994).
To prevent such unwanted behavior in a model, von der Malsburg (1973) proposed keeping the total synaptic strength constant. Thus when a connection strengthens, the other connections must be weakened. Such normalization could be accomplished by subtracting the weight change equally from each of the other connections. Miller and MacKay (1994) showed that doing so would result in a set of strictly binary connections, each either at full strength or zero strength. Such subtractive normalization seems implausible given that a variety of lateral connection strengths are found in the cortex (Hirsch and Gilbert, 1991, 1993).
The multiplicative normalization used in RF-LISSOM (equation 3.4) results in each of the other connections being scaled down in proportion to its current strength. Multiplicative normalization preserves a variety of connection strengths. Other forms of normalization are possible, however, and the demonstration of indirect tilt effects with multiplicative normalization does not in itself rule out other possibilities for keeping the sum of connection strengths constant.
One must bear in mind that short-term strengthening might temporarily violate the above longer-term constraints. For instance, the total synaptic resources might not all be in use initially, so there could conceivably be a small delay before synaptic resource conservation would cause indirect effects. This delay could account for the findings that the indirect effect has a later onset than the direct effect (Wenderoth and Johnstone, 1988; Wenderoth et al., 1989). In contrast, the direct and indirect effects in RF-LISSOM always occur simultaneously, since normalization is enforced as soon as any weights change. (Note the small error bars for the model over the range 45° to 90° in figure 5.2, indicating that most runs showed similar indirect effects.)
Variations in the utilization of synaptic resources in different individuals and under different circumstances may help explain why the indirect TAE varies greatly in magnitude between different studies, between different individuals in the same study, and for the same individual over different trials. (Note the large error bars for the human subject over the range 45° to 90° in figure 5.2.) Since the synaptic modifications are apparently temporary in adults (i.e., since the TAE decays in darkness), at any point in time some synaptic resources may be unused. The equilibrium state of some individuals may represent nearly full utilization of resources, and they would show relatively large indirect effects in general. For any individual, adaptation resulting from recent visual experience might change the amount of undedicated resources, causing wide variations in the indirect TAE depending upon the circumstances. But regardless of the state of resource utilization, the direct effect should show a consistent magnitude due to simple Hebbian adaptation, as is seen in the model and in humans.
The RF-LISSOM account of indirect effects is also consistent with many other possible explanations of the late onset and variation of the indirect effect. If the TAE is occurring in the cortex as in RF-LISSOM, the process of synaptic resource conservation could be mediated by entirely different cellular mechanisms from that of the direct effect. These mechanisms could easily have different time courses, be influenced differently by various drugs, etc. The dissociation between the mechanisms is strongly supported by the experiments of Wenderoth and Johnstone (1988).
In the absence of evidence to the contrary, one would assume that these mechanisms are operating within each neuron in V1 or in the neuron's lateral connections. No higher-level process is needed to explain the differences found in the model. This contrasts strongly with the explanation from Wenderoth and Johnstone (1988), who argued that their evidence indicated that the indirect effect arises beyond V1. In summary, the indirect TAE explanation supported by RF-LISSOM is biologically plausible, computationally justified, and requires only local mechanisms.