Ординатура / Офтальмология / Английские материалы / Computational Maps in the Visual Cortex_Miikkulainen_2005

356 16 Discussion: Biological Assumptions and Predictions

through a variation of the mechanisms involved in retinal waves. A relatively large circular area could be activated, which could then break up into individual activity bubbles through mutual inhibition.

In preliminary experiments using LISSOM it turned out relatively easy to generate such multi-spot activity using short-range excitation and long-range inhibition, starting from an initial larger set of activated neurons. Biasing the patterns to produce vertically oriented sets of spots, with more on top than below, is slightly more difficult, but can be achieved using a gradient of activation threshold or excitation strength across the dimension representing vertical in the cortex. Such a gradient makes it more likely for bubbles to form in the upper portion of an activated region than in the lower. Such mechanisms might be implemented in the developing brainstem, giving it the capability to generate spatial patterns that lead to newborn face preferences.

The second assumption is that such patterns can be propagated to the higher levels of the visual system during development. As described in Section 2.3.4, PGO waves generated during REM sleep are a good candidate for this process. However, there are a large number of theories for other functions of REM sleep (Harnad, Pace-Schott, Blagrove, and Solms 2003; Horne 1988; Moorcroft 1995; Rechtschaffen 1998), and it is important to evaluate whether pattern generation is consistent with them.

The most prominent theory is that REM sleep helps consolidate long-term episodic memories: Such memories are believed to be stored temporarily in the hippocampus as they are acquired, then rehearsed repeatedly during REM sleep (Alvarez and Squire 1994; Qin, McNaughton, Skaggs, and Barnes 1997; Sejnowski 1995; Shastri 2002; Smith 1996; Wilson and McNaughton 1994). Rehearsal helps store the memories permanently in the cortex through long-term learning that interleaves and integrates the new memories with existing ones. In this way an organism can quickly acquire new memories, without interference from older ones, and then store them more permanently through long-term learning. Evidence for the memory consolidation theory comes from several types of experiments and observations (Smith 1996). First, damage to the human or animal hippocampus often results in retrograde amnesia, i.e. forgetting of recent, but not distant, memories (although other functions may be affected as well, such as probabilistic category learning and spatial representation and navigation; Fuhs, Redish, and Touretzky 1998; Hasselmo, Bodelon,´ and Wyble 2002; Hopkins, Myers, Shohamy, Grossman, and Gluck 2003; O’Keefe and Burgess 1996; Touretzky 2002). Second, REM sleep deprivation can act much like retrograde amnesia. If an animal is deprived of REM sleep soon after training it on a new task, it performs poorly on that task later; deprivation before the task or long after the task does not have as large an effect. Third, when animals are trained on new tasks or exposed to novel environments, they spend more time in REM sleep. The conclusion is that new episodic memories depend on the hippocampus and REM sleep until the memories are consolidated into the cortex.

However, over the past few years, alternative explanations for each of these phenomena have emerged. For instance, retrograde amnesia does not necessarily indicate that memory is being consolidated (Moscovitch and Nadel 1998; Nadel and

Moscovitch 1997). Such amnesia could result from an impaired process of storing memories permanently in the hippocampus just as well as it can from disrupted consolidation in the cortex. Similarly, depriving subjects of REM sleep causes significant stress and changes the behavior of the animal, which in turn can make learning more difficult even if memory is consolidated normally (Horne 1988; Rotenberg 1992). Finally, REM sleep may in fact increase after learning and in novel environments in order to counteract excessive learning (Jouvet 1998, 1999).

It is possible that it has been difficult to establish a clear role for REM sleep because it may serve a variety of functions. For instance, REM sleep might be a way for the nervous system to rehearse important sensory patterns, replaying them to strengthen connections and responses. This mechanism could be used both for rehearsing memories, as in memory consolidation, and for training the system with genetically controlled activity patterns, like the three-dot patterns in Part III. Such training could be useful for constructing the system initially, and it could be crucial for integrating environment-driven learning with the genetic biases. While it is not yet possible to refute or verify this hypothesis experimentally, internally generated activity patterns resembling PGO waves are known to exist during sleep even before waking experience (Marks et al. 1995). The crucial assumption of the HLISSOM model is that higher cortical areas can learn from such patterns just as they do from externally evoked activity.

The third assumption is that the patterns propagated as PGO waves have the shape that can drive self-organization of higher levels, such as the three-dot configuration that results in prenatal face preferences in HLISSOM. At this point, PGO waves and other types of spontaneous activity have not been studied as thoroughly as retinal waves. In particular, it is not yet known whether they consist of large, coherent patches of activity, and whether those patches are organized in configurations such as three-dot patterns. Recent advances in imaging equipment may make measurements of this type possible in the near future (Rector et al. 1997), allowing testing these assumptions directly.

As internally generated patterns are measured in more detail in the future, candidates other than PGO waves may emerge; it may also be possible to identify other areas and behaviors where prenatal self-organization might play a role. However, based on our current biological and computational knowledge, the PGO waves are an explanation at least for the newborn preferences for faces.

16.2.3 Evolving Complex Systems

The HLISSOM simulations show how pattern generation can be an effective way to develop a functional system. The underlying assumption of the whole approach is that at some point during vertebrate evolution, pattern generation proved to be a more effective way to construct advanced perceptual and cognitive abilities than direct hard wiring and general-purpose learning. It is important to understand why, both to gain insight into the biological observations, and potentially to generate better artificial learning systems.

358 16 Discussion: Biological Assumptions and Predictions

One important reason is that with pattern generation, the desired outcome can be encoded independently of the architecture that performs the task. For instance, it is possible to specify that neurons should respond to three-dot stimuli independently of the actual hardware that implements face processing. Using pattern generation, evolution could insert a measured amount of bias (Turney 1996) into the generalpurpose learning system without changing the architecture of the learning system itself. The system can then learn to become specific for faces, using mechanisms like those explored by Dailey and Cottrell (1999), even without specific genetic control. In short, the divide-and-conquer strategy of pattern generation would allow such an architecture to evolve and develop independently of the function, which may have been crucial for the rapid evolution and development of complex adaptive systems.

In terms of information processing, pattern generation combined with selforganization may represent a general way to solve difficult problems like face detection and recognition. Rather than meticulously specifying the final, desired individual, the specification need only encode a process for constructing an individual through interaction with its environment (Section 2.3.2; see Elman et al. 1996; Marcus 2003; Mareschal, Johnson, Sirois, Spratling, Thomas, and Westermann 2005a,b for related and alternative explanations). The result can combine the full complexity of the environment with a priori information about the desired function of the system. In the future, this approach could be used for engineering complex artificial systems for real-world tasks, e.g. handwriting recognition, speech recognition, and language processing. This idea is explored in more detail in Section 17.3.5.

16.3 Temporal Coding

Like self-organization depends on adapting lateral connections and development depends on internally generated patterns, perceptual grouping in LISSOM depends on temporal coding through synchronization. The main assumptions are that neural synchrony drives perceptual performance, low-level temporal codes can be understood at a higher level, and synchronization can be implemented together with self-organization in different layers of the visual cortex.

16.3.1 Synchrony as a Perceptual Representation

The assumption that synchronous neural activity represents coherent percepts originates from two kinds of experiments: Either input properties and neural synchrony are compared in animals (Eckhorn 1999; Eckhorn et al. 1988; Gray 1999; Gray et al. 1989; Gray and Singer 1987; Singer 1993, 1999; Singer and Gray 1995), or psychophysical performance and timing between input features are compared in humans (Fahle 1993; Lee and Blake 2001; Leonards and Singer 1998; Leonards et al. 1996; Usher and Donnelly 1998). In the first case, whether the animal perceived the input as coherent is not known; in the second, whether the neurons fired in synchrony has not been observed. However, to verify the assumption, it would be necessary to observe both phenomena at the same time and establish a link between them.

Such an animal study might indeed be possible. Over the last decade, considerable evidence has emerged suggesting that under certain conditions, neural activity of the animal is faithfully represented in its observable behavior. For example, microstimulation of neurons in the monkey middle temporal area (MT, the visual motion center in the brain) causes a significant change in motion detection tasks (Salzman, Britten, and Newsome 1990). Also, the spike count of a single neuron in MT accurately predicts the behavior of the monkey in such tasks (Britten, Shalden, Newsome, and Movshon 1992; Celebrini and Newsome 1994).

In these studies on monkey MT, periodically modulated synchronization (or coherent oscillations) was not observed (Bair, Zohary, and Newsome 2001). However, it should be possible to apply the same methods to areas where such oscillations have been found, such as areas V1 and V2 in cats (Eckhorn et al. 1988; Gray et al. 1989; Gray and Singer 1987; Singer 1993). The animal could be trained to respond to the stimuli and act out the decision it made about the stimuli. The coherence in input features, the synchrony in neural firing, and the perceptual experience (manifested as behavioral performance) could all be measured and compared to verify explicitly that correlated firing of neurons represents perceptually salient events.

In order to account for graded responses in behavior, like those in the PGLISSOM grouping experiments of Chapter 13, it must be possible to observe different degrees of synchrony in the neural activity. In PGLISSOM, such a gradation is measured as correlation coefficients between the MUA sequences. The two sequences can match to a degree, and that degree can vary over time; the correlation of the two sequences over time corresponds to the degree of synchrony. Similar methods could be used in the experiments outlined above for comparing neural activity and behavior.

However, with graded synchrony, it will be difficult to interpret synchrony in more complex representations, like those constructed using the transitive grouping rule (Geisler et al. 2001; Geisler and Super 2000). For example, if representations (A, B) are synchronized to degree x, (B, C) to y, and (A, C) to z, how strong is

the synchrony in this group, i.e. how strong is the sense of a coherent object? Should it be max(x, y, z), min(x, y, z), their average, or some other quantity? If z, y < z,

should B be be interpreted as part of the representation of the object or not? Although it is possible to adopt various rules in computational models, such questions can be answered conclusively only through biological measurements of synchrony and performance, as outlined above.

16.3.2 Interpretation of Temporal Codes

The PGLISSOM approach assumes that synchronized activity is the perceptual representation employed by the brain, for the reasons outlined above. However, there are other forms of temporal information that neural systems could utilize as well, including time to first spike, inter-spike intervals, phase difference of spikes relative to background oscillation, variation of response amplitude over time, and degree of resonance in frequency-tuned response (Bruns, Eckhorn, Jokeit, and Ebner 2000; Eckhorn, Gail, Bruns, Gabriel, Al-Shaikhli, and Saam 2004; Freeman and Burke 2003; Izhikevich 2001; Kozma, Alvarado, Rogers, Lau, and Freeman 2001; Maass

360 16 Discussion: Biological Assumptions and Predictions

1998; O’Keefe and Reece 1993; Oram, Wiener, Lestienne, and Richmond 1999). In a broader sense, the question is how the information in the spike sequence (or spike train) can be interpreted. Various techniques have been used in this task, including information theory, Bayesian inference, and other probabilistic methods (Aguera¨ y Arcas and Fairhall 2003; Baldi 1998; Rieke, Warland, de Ruyter van Steveninck, and Bialek 1997). These methods work in different cases and lead to different results; however, there is little direct neurobiological evidence on what kinds of codes might actually be used by the brain, and for what purpose.

It might be possible to observe various temporal codes using these techniques in PGLISSOM, and it might be possible to adjust the model to express some of them in particular. Their possible causes and roles can be relatively easily assessed because the entire state of the model is known at all times and can be easily altered. Such computational studies may turn valuable in testing hypotheses about temporal codes, as well as in designing methods for measuring them.

Assuming that synchronized activity is used at the primary visual cortex to represent objects, how can the higher levels of the visual system respond to them? Somehow, such activity would have to be recognized as a coherent pattern, distinguishing groups of neurons that fire at different synchronized phases. One possibility is that different high-level neurons detect coincident low-level firing for different objects, and produce spatially separate rate codes as a result (Abeles 1982; Marsalek, Koch, and Maunsell 1997). Mechanisms such as depressing synapses, which synchronize synaptic transmission even when action potentials are only partially synchronized (Senn, Segev, and Tsodyks 1998; Tsodyks, Pawelzik, and Markram 1998), may make such coincidence detection robust in practice.

However, coincidence detection requires that a different neuron represents each possible binding of input features into a coherent object, which is unlikely to be a general solution to the interpretation problem. The alternative is that the highlevel representations are distributed as well, each consisting of a collection of more abstract feature representations. These high-level patterns can then be synchronized together with their low-level constituents (von der Malsburg 1999).

Because high-level representations are difficult to identify and measure, it is difficult to distinguish between these alternatives experimentally. However, computational models can be used to study whether coincidence detection could be accurate or general enough, and what kind of connectivity would be required for synchronization at the high level. Such models might eventually lead to testable predictions about how the brain interprets temporal codes.

16.3.3 The Role of the Different Layers

The two-layer organization of PGLISSOM was developed because long-range lateral inhibition with short-range excitation was found computationally necessary for ordered self-organization (SMAP), and long-range inhibition and excitation for grouping (GMAP; Section 11.1). Such a design can also be interpreted in terms of the connectivity patterns in the cortex, leading to insights into their function.

As was discussed in Section 2.1.2, the visual cortex is often described in terms of six layers. These layers are connected in complex but systematic ways (Binzegger, Douglas, and Martin 2004; C¸ ur¨ukl¨u¨ and Lansner 2003; Douglas and Martin 2004; Robert 1999). Afferent excitatory connections to neurons in layer 4 are often accompanied by inhibitory connections to their surrounding neurons, established through inhibitory interneurons in layer 6 (Ahmed, Anderson, Martin, and Charmaine 1997; Ferster and Lindstrom¨ 1985; Grieve and Sillito 1995). The long-range inhibitory and short-range excitatory connections in SMAP can be interpreted as abstractions of this on-center off-surround effect, as well as the effect of direct inhibitory lateral connections of layers 3, 5, and 6 (Kisvarday,´ Kim, Eysel, and Bonhoeffer 1994; McDonald and Burkhalter 1993). On the other hand, the very long-range excitatory and inhibitory lateral connections in GMAP most naturally correspond to the long-range axonal projections in layer 2/3 (Gilbert and Wiesel 1989; Hirsch and Gilbert 1991; McGuire et al. 1991). As in the cortex, the inhibitory connections in the SMAP can be shorter than the connections in the GMAP. The third architectural component in PGLISSOM consists of the intracolumnar connections, corresponding to such known connections between layers 2/3, 4, 5 and 6 in the cortex (Callaway and Wiser 1996; Gilbert and Wiesel 1979).

Thus, the PGLISSOM architecture has a natural interpretation as a biological model. Consequently, PGLISSOM suggests that the specific anatomical arrangements of the visual cortex may be due to different functional requirements, as they are in PGLISSOM: The lower layers may contribute primarily to self-organization, and layer 2/3 mostly to perceptual grouping. As a matter of fact, layer 2/3 in the cortex contains fast-spiking cells known as chattering cells (Gray and McCormick 1996), postulated to contribute to coherent oscillations and suggesting that the longrange connections in layer 2/3 might play a central role in grouping (Grossberg 1999; Grossberg and Williamson 2001; Raizada and Grossberg 2001). Although the lateral excitatory and inhibitory connections appear to have opposite effects, they serve different purposes and operate through different mechanisms. While decorrelation takes place at the level of average activity, synchronization applies to temporal coding, and the system can therefore be both decorrelating and grouping at the same time. The PGLISSOM model further suggests that the lateral circuitry may adjust the balance of these two functions according to contrast (Section 16.1.4). With highcontrast inputs, which make grouping easier but strongly influence self-organization, the long-range interactions are mostly inhibitory; with low contrast these interactions are mostly excitatory, enhancing the grouping function.

In the future, the PGLISSOM model can be extended to model the biological circuitry in more detail, and some of its biological predictions can be verified, as will be discussed in Sections 16.4.8 and 17.1.3. In this way, models such as PGLISSOM can help explain the different functions found in the layered architecture of the visual cortex, and allow gaining insight into how the functional divisions may occur and how they interact.

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16.4 Predictions

The main prediction of the LISSOM model is that the self-organization, pattern generation, and synchronization mechanisms described in this book are responsible for much of the structure, development, and function of the visual cortex. Because the model matches biological data well, many of its assumptions (outlined above) can also be interpreted as predictions. They are computationally advantageous and sometimes even necessary, suggesting that they might apply to biology as well.

The main advantage of a computational model is that its processes and mechanisms are completely observable at all times. Such observations lead to specific predictions and suggestions for future biological and psychological experiments. A number of such predictions are reviewed in this chapter, referring back to the individual chapters where the underlying mechanisms are discussed in more detail. Predictions about cortical structure are reviewed first, followed by those about development, perceptual grouping, and visual coding. The focus is on experimental (biological or psychological) studies that could be performed in the near future. Future computational work is reviewed in Chapter 17.

16.4.1 Cortical Organization

The LISSOM simulations in Chapter 5 show how multiple input feature dimensions and patchy lateral connections can self-organize at the same time based on a single input-driven Hebbian learning process. The model can be used to make several predictions about how the cortical organization depends on visual inputs.

Hubel and Wiesel (1959; 1965; 1974; Section 2.1.2) originally observed that input features such as ocularity and orientation seemed to be hierarchically organized in V1: For each retinal location there were two areas with different ocular dominance, further divided into orientation-selective patches. Further measurements have shown that neurons have more complex spatiotemporal receptive fields, and the features depend on each other more than originally thought. In many cases the emergent organization is well approximated by a hierarchy (e.g. Weliky et al. 1996), but e.g. the orientation maps may differ depending on the spatial frequency used in measuring them (Basole, White, and Fitzpatrick 2003; Issa et al. 2001). Thus, the hierarchical organization should be considered primarily as a way to describe the complex properties of neurons rather than an underlying principle of cortical organization.

Self-organizing models such as LISSOM can be instrumental in understanding how such complex cortical organization emerges. The V1 organization is not built in, but is constructed in a self-organizing process based on properties of visual inputs. What structures develop depends on how much each feature varies and how large the map is. The feature with the highest variance is represented as large map areas with uniform values, such as ocular dominance stripes. If the map has enough units, these areas are further divided into subareas with uniform values for the feature with the next largest variance, such as orientation preference. Eventually the features vary too little or there are too few units to continue the hierarchy, and the remaining features

are represented simultaneously at the same level (Kohonen 1989; Miikkulainen 1993; Obermayer et al. 1990d).

How strongly expressed the hierarchy is depends on how different the variances of different features are (Section 5.5.3). An important prediction of self-organizing models is that different maps can be obtained by manipulating the variances. For example, if spatial frequency is artificially varied more and orientation less than in the normal visual environment, the visual cortex of a test animal should develop large spatial frequency stripes and orientation patches inside them. The model also predicts that in species with a larger V1, topographic organization would be visible for more visual features. However, as V1 gets larger to fit a wider variety of feature-selective cells, eventually it becomes infeasible to connect the entire map laterally, and the visual cortex is instead divided into several different visual areas (Section 15.6; Kaas 2000).

Such models also predict that the shapes of the observed structures, such as the periodicity of the preference patches, depend on correlations in the input patterns. For example, the stronger the correlations between the eyes, the narrower the ocular dominance stripes, and with perfect correlation they disappear entirely. Similar observations have already been made in cats, comparing normal and strabismic (uncorrelated) organizations (Section 5.1.2; Goodhill and Lowel¨ 1995; Lowel¨ 1994; Lowel¨ and Singer 1992).

It should be possible to verify these predictions in biological experiments where the input variances and correlations in the visual environment are systematically varied and the resulting organization observed through optical imaging. If confirmed, they would suggest that the cortical organization is indeed constructed in a selforganizing process driven by the properties of the visual input.

16.4.2 Patterns of Lateral Connections

The LISSOM model predicts that lateral connection patterns follow the activity correlations set up by the organization of receptive fields. If the major activity correlations are organized according to ocular dominance, as in a strabismic animal, the patterns follow the organization of ocular dominance (Section 5.4.3). If the ocular dominance is a less important feature, as in normal animals, the lateral connections follow the organization of the orientation and direction maps (Section 5.6).

In the orientation map, the lateral connection patterns are determined not only by the orientation preference, but also orientation selectivity, i.e. by how tuned the neuron is to orientation. Highly selective cells have lateral connections that connect primarily to other highly tuned cells with similar orientation preference. When the connection patterns are mapped back to visual space, they appear elongated along the direction of orientation preference. This prediction has already been verified experimentally (Bosking et al. 1997; Sincich and Blasdel 2001). Other related predictions have not yet been tested. For instance, less selective cells in the model have lateral connections that are unspecific to orientation. The connections also follow the local organization of the orientation map: At pinwheel centers for example, the lateral connection patterns are unspecific to orientation, and more or less isotropic.

364 16 Discussion: Biological Assumptions and Predictions

At discontinuities such as fractures, the patterns are elongated along the orientation preferences of the nearby cells. At saddles, they follow the orientations that make up the saddle, but also intermediate orientations that match the preferences in the middle of the saddle (Section 5.3.4).

Similarly, long-range connections for direction-selective cells in the LISSOM maps are specific for direction of motion, in addition to orientation. They extend along the preferred orientation, not direction, and avoid patches of orthogonal orientations and opposite directions. Preliminary experimental results in ferrets are consistent with this prediction (White, Bosking, Weliky, and Fitzpatrick 1996). Further, neurons at DR fractures connect with both directions and extend along their common orientation. At DR saddles, they connect with the directions of the saddle, and at DR pinwheels with all directions; these DR features can occur at a variety of OR map features. The ocular dominance preferences are overlaid with the OR and DR preferences: The neurons most selective for one eye prefer connections from that eye, but such preference is absolute only in strabismic animals.

As will be discussed in Section 17.2.1, the primary visual cortex also has an organization of spatial frequency and color (Issa et al. 1999, 2001; Landisman and Ts’o 2002a,b; Livingstone and Hubel 1984a). The lateral connections of cells with these feature preferences should be organized according to similar principles. The cells that are highly tuned to low spatial frequencies should preferentially connect to other cells with similar tuning. Color-selective cells typically occur near the center of ocular dominance columns in locations called blobs. The connections of cells at these locations should strongly prefer color-selective cells in other blobs.

A number of experiments can be performed on young animals to verify the above predictions. Two such experiments have previously shown that when kittens are deprived of visual input they develop shorter and less dense lateral connections in V1 (Callaway and Katz 1991), and that when they are made strabismic, these connections follow ocular dominance instead of orientation (Lowel¨ and Singer 1992). Similarly, one would expect that if an animal is brought up in a visual environment with only diffuse light spots and no edges or lines, the lateral connections would not be elongated along the orientation axes of cells, but would be more isotropic. Further, it should be possible to devise conditions such that these patterns follow the organization of spatial frequency. If the diffuse light spots have varying sizes, but not edges and boundaries, orientation preferences of cortical cells should be weak. However, because the stimuli vary in size, spatial frequency should become the prominent component in the cortical representation. The lateral connections should then follow mainly the organization of spatial frequency, rather than the organization of the orientation map.

In essence, any manipulation of visual inputs that substantially changes the organization of feature-selective cells should alter the patterns of lateral connections to match the new activity correlations in the cortex. Such experiments would provide further evidence for the hypothesis that the lateral connections develop synergetically with the afferent connections, based on activity correlations in the cortex.

16.4.3 Tilt Aftereffects

The LISSOM model of tilt aftereffects (Chapter 7) makes specific predictions about the activation and adaptation processes underlying the effect. Assuming suitable protocols can be developed for measuring the tilt aftereffect in animals, these predictions could be verified in future animal experiments.

The LISSOM model predicts that the tilt aftereffect depends crucially on adapting lateral inhibition. This prediction could be verified by blocking intracortical inhibition mediated by GABAB receptors with bicuculline (Sillito 1979) and that mediated by GABAA receptors with phaclofen (Pfleger and Bonds 1995). The observed effect would then be due to adapting afferent connections only. According to LISSOM, its sign should be reversed and its magnitude should be significantly weaker (Figure 7.7).

The activity patterns during the tilt aftereffect could also be observed using optical imaging, directly verifying the model’s predictions. Although the temporal resolution is currently not sufficient to measure such transient activity, certain key predictions should be testable already. For instance, if an indirect-effect test pattern is repeated regularly throughout adaptation, the LISSOM model predicts that the overall response to the test pattern will increase each time. Other models, such as fatigue or those relying on levels above V1 (described in Section 7.1.2), predict that the activity levels in V1 do not change or actually decrease instead.

If imaging techniques with sufficient temporal and spatial resolution become available in the future, plots like those in Section 7.4.2 could be computed for monkeys and compared with those of the model. After an orientation map is first measured on the animal, the response of the cortex would be measured for test patterns at orientations typical of direct and indirect effects. Next, the cortex would be adapted to a stimulus of a particular orientation. The test patterns would then be presented again, measuring the cortical response once more. When the earlier measurements are subtracted from the later measurements, there should be a net decrease in activity for orientation detectors near the orientation used during adaptation, a net increase in activity of those with more distant orientations, and no change for very distant orientations.

The required temporal resolution for such measurements is on the order of a few seconds to avoid significant adaptation to the test pattern, and the spatial resolution at the level of individual orientation patches, i.e. 0.1 mm. With such resolution, it should also be possible to calculate perceived orientations, as was done on the LISSOM model in Section 7.2.1. If those orientations were found to be within the range of the measured tilt aftereffect, the experiment would provide strong support for the lateral inhibition theory of direct and indirect tilt aftereffects.

16.4.4 Plasticity

If the same processes that self-organize the visual cortex during early life are assumed to operate in the adult, many observations of cortical plasticity, such as recovery after damage, can be explained computationally by the LISSOM model. The