Departments of Physiology and Otolaryngology, W.M. Keck Center for Integrative Neuroscience, Sloan-Swartz Center for Theoretical Neurobiology at UCSF, University of California, San Francisco, CA 941430444, USA
Address correspondence to: Kenneth Miller, Department of Physiology, University of California at San Francisco, 513 Parnassus, San Francisco, CA 941430444, USA. Email: ken{at}phy.ucsf.edu.
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Abstract |
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Introduction |
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To understand the computations being performed by cortex, we need to understand the nature of the processing undertaken by each layer. The natural starting place in thinking about sensory processing is layer 4, the primary layer in which sensory input first arrives. Here I outline a picture of the processing taking place in cortical layer 4 in cat primary visual cortex (V1) that has been emerging from both experimental and theoretical work in recent years. This picture is intriguingly similar to that emerging from studies of layer 4 of rodent primary somatosensory cortex (S1), as reviewed elsewhere (Miller et al., 2001; Pinto et al., 2002; Swadlow, 2002). As befits the position of layer 4 as the recipient of feedforward input, this picture suggests that the response tuning of layer 4 cells is largely determined by feedforward input, including feedforward inhibition (inhibition from interneurons driven by the thalamus) as well as feedforward excitation (from the thalamus). The inhibition dominates, so that a cell can only be excited by stimuli that cause the effects of feedforward excitation and inhibition to be separated in time; concurrent engagement of the two yields a net inhibiton. Neurons providing feedforward inhibition follow the tuning of the thalamic inputs, thereby sculpting the responses of excitatory cells to have tighter tuning than the thalamic inputs. Both the feedforward excitation and inhibition that a cell receives are evoked locally, from cells preferring nearby orientations. While the feedforward input establishes initial response tuning, local recurrent excitation and neuronal non-linearities (e.g. spike threshold) enhance responses evoked by preferred versus non-preferred stimuli.
In this article I review the evidence leading to this picture, along with countervailing evidence that renders it still controversial.
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The Problem Posed by the Thalamic Input |
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Opponent Inhibition Provides a Solution to the Problem Posed by the Thalamic Input |
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The model of Troyer et al. (Troyer et al., 1998) was inspired by intracellular recordings demonstrating (i) that the inhibition and the excitation that a simple cell receives have similar orientation tuning, with both being maximal at the preferred orientation (Ferster, 1986
; Martinez et al., 1998
; Anderson et al., 2000a
), but (ii) that inhibition and excitation are evoked by stimuli of opposite light/dark polarity at any given point in the receptive field (Ferster, 1988
; Hirsch et al., 1998
) [but see (Borg-Graham et al., 1998
)], i.e. in an ON-subregion, light evokes excitation and dark evokes inhibition, while in an OFF-subregion dark evokes excitation and light evokes inhibition. This can be summarized by saying that the receptive field of the inhibition received by a simple cell is antiphase to the receptive field of the excitation the cell receives. This is also described by saying that the inhibition a cell receives is spatially opponent to the excitation it receives. These findings inspired a circuit model (Troyer et al., 1998
) in which inhibitory cells tend to project to cells of similar preferred orientation but roughly opposite phase, while excitatory cells tend to project to cells of similar preferred orientation and phase (Fig. 3
). A key feature is that the feedforward (LGN-driven) antiphase inhibition is stronger than the feedforward LGN excitation; this is consistent with the experimental fact that an electrical shock to LGN, which indiscriminately activates both feedforward excitation and feedforward inhibition, yields strong inhibition in cortex (Ferster and Jagadeesh, 1992
).
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The model circuit also includes recurrent excitation among cells of similar orientation and phase preference, i.e. among cells with similar preferred stimuli. This serves to amplify responses to effective stimuli without altering tuning.
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Opponent Inhibition Can Explain a Range of Other Response Properties |
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The model circuit can also explain a number of contrast-dependent non-linearities (Kayser et al., 2001; Lauritzen et al., 2001
) that had previously been proposed to require normalizing inhibition derived equally from cells of all stimulus preferences [the normalization model (Carandini et al., 1999
)]. The normalization model begins with the idea that the input to simple cells derives from a linear filtering of the stimulus. This accords with the many response properties of simple cells that appear linear (up to rectification). For example, a linear model predicts that orientation tuning curves simply scale with contrast, i.e. that orientation tuning is contrast-invariant. However, some properties of simple cell responses are non-linear, and the normalization model posits that an additional cortical circuit a normalizing circuit is needed to correct the linear input and explain these response properties. These non-linear response properties include: an advance with increasing contrast in the phase of response to sinusoidal gratings (a linear model would show the same phase of response at all contrasts); an emergence with increasing contrast of responses to higher temporal frequencies that evoke little or no response at low contrast (in a linear model, temporal frequency curves would simply scale with contrast); saturation of cortical responses at contrasts lower than those at which the LGN inputs saturate; and cross-orientation inhibition, the reduction of response to a preferred-orientation stimulus by simultaneous presentation of an orthogonal stimulus which by itself evokes no response (in a linear model, responses to the two stimuli would add).
We propose a different viewpoint from that of the normalization model. It is not the case that a simple cell receives linear input that must be corrected to account for non-linearities. Rather, a simple cell receives non-linear input and processes it through non-linear machinery, and what is needed is an explanation of how the responses of the simple cell nonetheless come to appear linear. The most obvious non-linearity in the input to a simple cell is caused by the rectification of LGN responses the fact that LGN responses cannot be decreased below zero. We saw above that this rectification can cause a stimulus orthogonal to a cells preferred orientation to evoke a strong LGN input to the cell. There are a multitude of other non-linearities in the circuit, including frequency-dependent synaptic depression in LGN and cortical synapses, spike-rate adaptation currents in cortical cells, stimulus-induced conductance changes in cortical cells, and the cortical spike threshold. We argue that the approximately linear response of simple cells is achieved, in spite of these non-linearities, by the dominant opponent inhibition, which filters out the input caused by LGN rectification while leaving the linear component of LGN input [a similar explanation of simple cell linearity, but using phase-non-specific feedforward inhibition rather than antiphase feedforward inhibition, is found in the model of Wielaard et al. (Wielaard et al., 2001)]. The remaining non-linearities in the input and the circuit can explain the non-linear aspects of simple cell response no separate normalizing circuit is needed, instead the non-linearities are present from the outset. We showed that our model circuit can indeed explain all of the non-linear response properties described above (Kayser et al., 2001
; Lauritzen et al., 2001
).
In sum, this simple model circuit promises to provide a unified account of classical receptive field properties of simple cells, although many response properties such as direction selectivity, end stopping and beyond-the-classical-receptive-field effects remain to be addressed.
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Experimental Results that Functionally Characterize Inhibitory Neurons |
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In a recent study using intracellular recording in vivo, roughly ten inhibitory neurons were recorded in layer 4 of cat V1, and these were found to be of two types: simple cells showing good orientation tuning (studied with moving bars at one contrast), and complex cells cells responding either to light or dark throughout their receptive field showing roughly equal responses to all orientations (Hirsch et al., 2000). This raises the possibility that the tuning attributed in the antiphase model to simple inhibitory cells response to all orientations, though tuned for the preferred might actually be achieved by the combination of two inhibitory populations. The simple cells would provide opponent inhibition, but would not respond to orientations far from the preferred. The complex cells would provide the broadly tuned inhibition that prevents simple cells, both excitatory and inhibitory, from responding to orientations far from the preferred.
Numerous studies of suspected inhibitory neurons (SINs) in rodent and rabbit cortex also suggest that layer 4 neurons receive strong and broadly tuned feedforward inhibition (Miller et al., 2001; Pinto et al., 2002; Swadlow, 2002).
In slice recordings from layer 4 of rodent somatosensory cortex, two biophysical types of interneurons were found: fastspiking (FS) neurons receive strong feedforward input from thalamus, while low-threshold-spiking (LTS) neurons receive no feedforward input and so provide only feedback inhibition (Gibson et al., 1999) [however, Porter et al. found that both types of interneurons can provide feedforward inhibition (Porter et al., 2001
)]. Furthermore there is extensive gap-junction coupling within each type, but not between the two types. It is tempting to guess that these two biophysical types correspond to the two functional types, simple and complex, found in layer 4 of V1, but this appears not to be the case (J.A. Hirsch, private communication.) Our model interneurons had parameters corresponding to FS neurons, and lacked gap-junction coupling. The roles of LTS interneurons, of purely feedback inhibition and of gap-junction coupling in layer 4 functional responses remain to be explored. The high rate of gap-junction coupling suggests that these cells should have rather non-specific functional responses, consistent with the complex inhibitory cells seen in layer 4 (though not the simple inhibitory cells) and consistent with properties reported for SINs.
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Experimental Results that Suggest Feedforward Processing in Layer 4 |
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Ferster et al. attempted to directly compare the orientation tuning of the thalamic input to that induced by the full cortical circuit (Ferster et al., 1996). To achieve this, they compared the tuning of the voltage responses of simple cells in two conditions: the normal condition, with the full cortical circuit intact; and after cortical cooling, which blocked cortical spiking, leaving transmission along and vesicle release from thalamic axons intact (though slowed and diminished). By eliminating cortical spiking, the cooling should allow isolation of the voltage responses induced by the thalamic input alone. The temporal modulations of voltage in simple cells induced by high-contrast drifting sinusoidal gratings, though smaller in the cooled condition, showed identical orientation tuning in the control and cooled conditions, suggesting that the tuning of the full cortical circuit followed that of the thalamic inputs. This result is accounted for by the model of Troyer et al. (Troyer et al., 1998
): the voltage modulations follow the LGN inputs, while the inhibition and threshold sharpen spiking tuning relative to voltage tuning [a sharpening observed experimentally (Carandini and Ferster, 2000
; Volgushev et al., 2000
)]. Note that the tuning of the voltage modulations induced by the thalamic inputs should depend on the stimulus; sinusoidal gratings of higher spatial frequencies should evoke narrower thalamic orientation tuning than gratings of lower spatial frequencies (Troyer et al., 1998
) [and indeed, the voltage modulations induced by the full circuit show narrower orientation tuning with increasing grating spatial frequency (Lampl et al., 2001
)]. Thus, a match of thalamic and full-circuit tuning for a particular choice of stimulus suggests that the full-circuit tuning follows the thalamic more generally.
The cooling did not entirely eradicate cortical spiking; cells in layer 6, farthest from the cooling plate, showed perhaps 15% of their normal spiking responses. Fersters group therefore assayed the same question by an independent technique, using a shock to the cortex to induce hyperpolarization and thus suppress cortical spiking for a period of >100 ms, and examining the tuning of voltage responses to flashed gratings during the period of suppression (Chung and Ferster, 1998). Again, voltage responses showed the same orientation tuning in control and suppressed conditions. This experiment showed that transient responses, like the steady-state responses observed in the cooling experiment, appear to be largely determined by feedforward processing.
An argument against a feedforward computation of orientation tuning has been that orientation tuning width is narrower than would be expected from a semi-linear prediction based on the arrangement of the cells ON and OFF subregions (Gardner et al., 1999). (We use semi-linear to refer to a prediction that may take into account rectification of neuronal responses.) However, the antiphase model predicts that inhibition and threshold sharpen spiking tuning relative to voltage tuning; it is voltage tuning that would be expected to follow a semi-linear prediction. Fersters group tested this by mapping the cells receptive field intracellularly with flashed spots, and found that the orientation tuning of the voltage response to a drifting sinusoidal luminance grating could be well predicted from the receptive field map (Lampl et al., 2001
). For two cases in which two spatial frequencies were tested on the same cell, both the broader voltage tuning for the lower-frequency grating and the narrower voltage tuning for the higher-frequency grating were correctly predicted. However, the semi-linear prediction tended to predict a greater response orthogonal to the preferred orientation than is actually observed, in agreement with earlier results (Volgushev et al., 1996
).
Finally, Fersters group examined the intracellular basis of contrast-invariant orientation tuning (Anderson et al., 2000b). They examined two aspects of the voltage response to drifting sinusoidal gratings of various orientations and contrasts: the amplitude of the temporal modulation of voltage induced by the grating (voltage modulation); and the mean depolarization induced by the stimulus (voltage mean). They found that the voltage modulation and the voltage mean each showed similar orientation tuning that simply scaled with changes in stimulus contrast. In combination with their previous finding that the orientation tuning of the voltage modulation at high contrast followed the tuning of the thalamic inputs (Ferster et al., 1996
), this suggests that the voltage orientation tuning across contrasts follows the tuning of the thalamic inputs.
These results, while not a necessary consequence of the antiphase inhibition model, are consistent with it. The model predicts that the voltage modulation will have orientation tuning that scales with contrast, as observed, but is more agnostic about the tuning of the voltage mean. The model predicts that the mean LGN input to a simple cell should be untuned for orientation, because a grating stimulus raises LGN firing rates by an amount that depends on contrast but is independent of orientation. If not opposed by inhibition, this would lead to a mean voltage response that is depolarizing at all orientations. However, the dominant feedforward inhibition in the model adds to the direct LGN input to produce a total mean feedforward input that is inhibitory, meaning that it has a subthreshold reversal potential. In response to a null stimulus (a stimulus oriented orthogonal to the preferred), one should see only this mean feedforward input (because cortical cells are not driven to spike, so there is no local feedback input, only feedforward input). The voltage response induced by this input depends on the location of its reversal potential relative to rest. Empirically, little voltage change was observed in response to a null stimulus, suggesting that the mean feedforward input has a reversal potential near rest. Since rest is near the inhibitory reversal potential, this is consistent with this mean input being inhibition dominated. In sum, the lack of a voltage response to a null-oriented stimulus, despite the increase in LGN firing rates evoked by that stimulus, suggests the presence of dominant feedforward inhibition, as we have posited. However, a further complication is that short-term synaptic depression of thalamocortical synapses can eliminate a significant fraction of the feedforward mean input at the temporal frequencies studied, but at higher temporal frequencies (e.g. 8 Hz) the inhibitory mean should be strongly present, and so should be visible as a conductance change in response to a null stimulus even if no voltage change is apparent (Krukowski, 2000); this remains to be tested. Although the mean feedforward input is predicted to be untuned for orientation, at least two effects could lead the mean voltage response to have orientation tuning like that of the voltage modulation. First, voltage can modulate up much further than it can modulate down, because the excitatory reversal potential is much further from rest than is the inhibitory reversal potential; as a result, voltage modulation will induce a mean depolarization with an orientation tuning identical to that of the modulation. Second, spiking tuning follows (but is narrower than) the tuning of the voltage modulations, and recurrent excitatory connections will contribute a mean depolarization whenever spiking occurs.
Anderson et al. also found that voltage noise the trial-by-trial fluctuations about the average stimulus-induced voltage response for a given stimulus was critical to turning the contrast-invariant voltage tuning that they observed into contrastinvariant spiking tuning (Anderson et al., 2000b). A simple picture of this effect (Hansel and van Vreeswijk, 2002
; Miller and Troyer, 2002
) is given by assuming that the average spiking rate R is some instantaneous function R(V) of the average voltage V. In the absence of noise, this function would be linear above some threshold voltage and zero below the threshold. Such a linear-threshold function would convert the contrast-invariant voltage tuning into spiking tuning that broadens with contrast, because at higher contrasts more orientations would produce suprathreshold voltages. Noise smooths this linear threshold function, because a subthreshold average voltage will sometimes fluctuate above threshold. In particular, noise converts the linear threshold function into a power law R
Vn over some range of voltages, and a power law converts contrast-invariant voltage tuning into contrast-invariant spiking tuning, with tuning sharpened by a factor of
n. (Contrast-invariant voltage tuning means that the voltage response factors into a function of orientation
times a function of contrast C, V = f1(
)f2(C). Raising this to a power n preserves the factoring, R = Vn = [f1(
)]n[f2(C)]n, and thus preserves contrast invariance. Orientation tuning curves are reasonably described by Gaussians, and raising a Gaussian to a power n reduces the standard deviation of the Gaussian by a factor
n). Our model of contrast-invariant orientation tuning did not rely on such noise smoothing except at very low contrasts (Troyer et al., 2002
), and so needs some revision in light of Anderson et al.s finding that the full range of contrasts lies in the noise-smoothed regime. However, the noise smoothing achieves contrast-invariant tuning only if the voltage shows contrastinvariant tuning, and as discussed above this in turn requires dominant feedforward inhibition to suppress mean voltage responses to non-preferred orientations. Thus we expect the basic ideas of our model, including the role of dominant feedforward inhibition, to remain intact (also supported by preliminary results: S.E. Palmer and K.D. Miller, unpublished).
The results presented thus far have focused on orientation tuning. Another property of simple cells in layer 4 is direction selectivity: preference for stimulus movement in one of the two opposite directions orthogonal to the preferred orientation. Physiological evidence is suggestive that this property might also be understood in layer 4 from the structure of the feedforward input received by a cell along with the effects of the spike threshold nonlinearity. Voltage responses to moving stimuli can be predicted as a simple linear sum of inputs; stimuli moving in the two directions can be decomposed into a sum of stationary stimuli, and the voltage responses to the moving stimuli can correspondingly be predicted from a sum of the voltage responses to stationary stimuli (Jagadeesh et al., 1997). Further-more, the voltage responses could be understood as arising from sums of only two input components, with properties that closely resemble those of two temporal types of LGN inputs: non-lagged cells and lagged cells (Jagadeesh et al., 1997
). Just as adjacent rows of ON-and OFF-center inputs can explain a simple cells spatial response profile, an appropriate spatial mix of lagged and non-lagged input can produce cells whose space-time receptive fields show preference for one direction. Studies of temporal response profiles of simple cell receptive fields found timing corresponding to lagged-type input only in cells of layer 4B (Saul and Humphrey, 1992
), and correspondingly cells in layer 4B show the strongest direction preference in their linear space-time receptive fields (Murthy et al., 1998
). Strobe-rearing greatly reduces direction selectivity in cat V1 cells (Humphrey and Saul, 1998
), and correspondingly eliminates the convergence of non-lagged-like and lagged-like temporal responses in individual simple cells (Humphrey et al., 1998
). Studies of adaptation suggest that direction-selective simple cells receive inhibition from other simple cells preferring the same direction but with different space-time phases (Saul, 1999
), which suggests a generalization to space-time receptive fields of the spatial antiphase inhibition posited thus far.
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Experimental Results that Argue for Other Contributions to Orientation Tuning |
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Studies of the dynamics of orientation tuning in response to flashed stimuli have also been argued to support a role for feedback, but at least some of these results may instead be compatible with the results of feedforward inhibition. A recent intracellular study divided the orientation tuning curve of voltage responses into a tuned component and an untuned component, where the latter is a constant voltage response across orientations. The study found no statistically significant changes with time after stimulus onset in the width of the tuned component, but in many cells the untuned component grew more negative over time (Gillespie et al., 2001). This increasing negativity of the untuned component is expected if feedforward inhibition follows feedforward excitation. The overall voltage tuning curve tuned plus untuned component would narrow with time, as reported for some cells in another study (Volgushev et al., 1995
). An extracellular study in monkey reported that perhaps half of cells studied showed changes in the tuned response component with post-stimulus time, but these effects were not seen in thalamic-recipient portions of layer 4 (Ringach et al., 1997
). This study used stimuli several times larger than the classical receptive field, so surround suppression effects may have played a role.
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Alternative Models |
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McLaughlin et al. (McLaughlin et al., 2000) and Wielaard et al. (Wielaard et al., 2001
) have proposed a model of responses in layer 4C
of monkey V1. This model also relies on strong feedforward inhibition to cancel the non-linear component of the LGN input, but it assumes the inhibition has no phase specificity, coming equally from cells of all preferred phases. This is motivated in part by experiments reporting transient phase-non-specific inhibitory responses to flashed stimuli (Borg-Graham et al., 1998
), in contrast to the phase-specific opponent arrangement seen by others (Ferster, 1988
; Hirsch et al., 1998
). Phase-non-specific feedforward inhibition can also solve the problem posed by the thalamic inputs, by setting a contrast-dependent threshold for response a high-contrast stimulus orthogonal to the preferred would evoke stronger inhibition than a low-contrast preferred stimulus, allowing the cell to respond to the latter and not the former. However, the model of McLaughlin et al. and Wielaard et al. actually operates in a parameter regime in which the inhibition is not strong enough to fully cancel the non-linear component of the LGN input, so that many cells respond to stimuli of all orientations. In this model, cells are assumed to receive input from all other cells within a given distance, and as a result a cells orientation tuning depends on its location in the orientation map. Cells located in linear regions of the map, where nearby cells all have similar preferred orientations, receive inhibition only from cells of similar preferred orientation, and these cells respond to all orientations although showing a tuning peak at the preferred. Cells located near orientation pinwheels, points where cells of all preferred orientations converge, receive inhibition from cells of all preferred orientations and hence show sharp orientation tuning. The prediction that cells in linear regions show broader orientation tuning than cells in pinwheels seems not to be correct in cats (Ruthazer et al., 1996
; Maldonado et al., 1997
), but the case in monkeys is not known.
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A Developmental Model of Cortical Layer 4 and Columnar Invariance |
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This suggests the more general hypothesis that layer 4 of any piece of cortex may develop through simple Hebb-like rules, guided simply by the statistical structure of its inputs activities. This and the dominance of inhibition leads naturally to opponent inhibition, in the generalized sense in which we defined it above: a cell becomes selective for a preferred pattern of inputs, and also becomes strongly inhibited by the input pattern that is most anticorrelated with the preferred pattern, which we can call the opposite pattern. As we argued above, this solves the problem posed by the rectification of the thalamic input and endows layer 4 with magnitude-invariant form recognition: it enables a cell to respond to its preferred stimulus even at low magnitude, and not to respond to a non-preferred stimulus even at high magnitude, even though the latter stimulus may provide a cell with as much thalamic input as the former stimulus. To this basic idea must be added a role for non-specific, broadly tuned inhibitory cells, such as the complex cells reported by Hirsch et al. (2000). Whether opponent inhibition is indeed an idea that generalizes across cortical areas, and how the opponent inhibition and the non-specific inhibition relate to one another, remain to be worked out.
The hypothesis that layer 4 develops through Hebb-like rules and develops opponent inhibition leads to a more general hypothesis about cortical columnar organization (Kayser and Miller, 2002). Which cortical properties should show columnar invariance, i.e. an invariance across the cortical layers at a given tangential position? Such properties should in particular be locally invariant in layer 4. Given Hebbian development resulting in opponent inhibition, it turns out that if a given stimulus pattern is represented in a local region of layer 4, the opposite pattern will also be represented in the same local region. That is, a local region will include cells that represent stimulus pairs that are as dissimilar as possible, where dissimilarity is measured by anticorrelation of the input patterns evoked by the stimuli. This contrasts with the more common idea that cells in a column all represent a similar set of response properties. As a result, the only properties that can be locally invariant in layer 4, and hence that are candidates for being invariant across a column, are properties that are shared by a stimulus and its opposite. Properties that differ between a stimulus and its opposite cannot show columnar invariance by this reasoning.
For simple cells in cat V1 layer 4, a preferred stimulus is a pattern of light and dark bars matching the cells subregions, while its opposite is a pattern of the same orientation but with opposite phase light in place of dark and vice versa. Thus, for V1, the prediction is that orientation, which is shared by an input pattern and its opposite, should show local invariance in layer 4, while phase, which differs between an input pattern and its opposite, should not. It is well known that preferred orientation shows columnar invariance in cat V1, and it appears that preferred phase does not (DeAngelis et al., 1999). It remains to be seen whether this hypothesis can account for the properties that show columnar invariance in other cortical areas.
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Conclusion: Understanding Layer 4 |
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Footnotes |
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