Common-onset masking simulated with a distributed-code model

A distributed-coding model incorporating lateral inhibition in a simulated nerve network has been successful in accounting for many properties of backward masking (Bridgeman, 1971, 1978), linking modeling with neurophysiology and psychophysics. Metacontrast is a variety of backward masking that is of particular interest in uncovering properties of visual coding because target and mask do not overlap in time or space, and it is the first stimulus that is reduced in visibility, not the second. The lateral inhibitory model can also simulate common-onset masking, where a target and mask appear simultaneously but the mask disappears after a variable delay, and it can reproduce qualitatively the effects of attention on object substitution by varying the time interval over which sensory codes are analyzed.


INTRODUCTION
How is sensory information coded and processed in the brain? Our understanding of the answer to this question will be in terms of theories of brain function, theories that can be instantiated in mathematical models. Successful models will simulate real behavior and experience, and they will consist of parts that are identifiable with known brain structures. It is here that the development of useful models can begin.
Neuroanatomy can be described as a series of layers of neurons linked by parallel connections (Bridgeman, 1989, Ch. 2). Within these layers, neurons inhibit one another, a definition of lateral inhibition (Ratliff, 1965) that is known to take place at several levels in the afferent visual system. It is distinct from forward inhibition, where neurons inhibit neurons in a subsequent layer, and backward inhibition, where a more peripheral layer is inhibited.
The implications of lateral inhibition for sensory coding are not yet completely worked out, however.
The inhibition does more than just suppress activity -it also normalizes output, so that the output of a layer undergoing lateral inhibition is less affected by the gross level of afferent activity than the input to that layer (Bridgeman, 1971). This point was later elaborated by Grossberg (1973). Lateral inhibition also restructures the coding of afferent sensory information, as will be explored below.

Application to metacontrast
In metacontrast (Stigler, 1910), a target is adjacent to a non-overlapping mask that is often of equal energy.
If target and mask are presented briefly and simultaneously, both are seen. But if the mask's appearance is delayed by about 50-100 ms, the target is no longer visible. It is a form of backward masking, so named because the effect seems to operate backward in time.
Because the target and mask do not overlap either in time or in space at the peak of masking, the phenomenon promises to provide insight into both spatial and  A simple 'busy signal' model of the sort often invoked for forward masking can be eliminated immediately as an explanation for metacontrast, because it is the first stimulus that is masked, not the second. In these models, an incoming stimulus occupies processing resources so that a second stimulus that arrives before the processing of the first one is complete does not get processed (Arnell & Jolicoeur, 1999).
The first models of metacontrast invoked a few neurons; one slowly conducting neuron sensed the target, while a faster-conducting neuron sensed the mask (Weisstein, 1968). At a subsequent neural layer, the fast 'mask' signal caught up to the slow 'target' signal and inhibited it by forward inhibition. Simulations showed that a simple, mathematically analyzable nerve network could simulate backward masking (reviewed by Breitmeyer, 1984). Breitmeyer and Ganz (1976) later suggested a similar 2-stage architecture, again relying on differing conduction speeds in different channels and with a single cell as the hypothesized output, but without a mathematical model.
A model's linking hypothesis is the output of the model that eventually links to perception. For Weisstein, the output of a single 'detector' neuron or feature detector coded the presence of a perceived object. The idea seemed to fit well with the feature detectors described in the visual systems of the cat and monkey. Problems with coding by feature detectors soon appeared, however (Weisstein, 1972). How could the brain identify novel objects with existing detectors, and who looks at the activities of the detectors to decide what is present?

Distributed coding
An alternative to the feature detector scheme is distributed coding (Pribram, 1971), where it is not the gross level of activity of one or a group of neurons that codes a meaningful visual stimulus, but rather the combinations of activities of a large number of neurons. The combinatorics of this scheme are so much more efficient than the detector idea that its advantages become compelling even for relatively small neural nets. Consider the simplified case of binary, on-off detectors. Detecting 1024 distinct states with these detectors, for example, requires 1024 neurons, and a subsequent layer that must know the meaning of each of the 1024 messages. A distributed code, how-ever, can handle the same message with just 10 neurons assembled as a 10-bit binary number. Efficiency increases 100-fold. As the number of detectable objects increases, the economies of distributed coding become even more extreme.
Modeling of distributed codes followed quickly on the theory. A lateral inhibitory model of visual masking (Bridgeman, 1971) started with simulation of very general consequences of lateral inhibition for information coding in neural networks. Stimulating a neuron in a layer of simulated neurons linked by lateral inhibition causes a reduction in the activity of the neuron's neighbors. But the neighbors of those cells, experiencing less inhibition, will increase their activity. The next set of neighbors will be more inhibited and will decrease their activity, and so on. Because the inhibition requires a delay, the result is a series of damped oscillations that proceed from the original point of disturbance like ripples in a pond. Eventually the whole pond's activity is changed by the single disturbance.
One can no longer talk of feature detectors in this environment, because now stimulus-specific information is distributed across the relative activities of a large number of neurons. More complex stimuli will yield more complex patterns of excitation and inhibition, because each edge or contour in the image elicits an extensive series of waves. Each wave pattern is specific to the stimulus that elicited it; neuron-by-neuron illustrations of network states demonstrating this are given in Bridgeman (1971). In the resulting coding, any stimulus entering the network eventually becomes coded (with varying information density) over the entire network.
A new linking hypothesis accompanies the new coding. If a stimulus changes activity across an entire network, then the presence of the stimulus must be coded in the network-wide pattern rather than in a particular cell. The identity of an incoming stimulus can be found by comparing the new activity with the activity elicited by other known stimuli. In the model used here this is done with squared correlations, reflecting the proportion of variance in the nerve net's activity that is attributable to a particular stimulus. High correlations indicate the presence of the target stimulus, while low correlations signal masking.
This coding scheme is different from feature detectors because no particular neuron's activity is identified with a particular stimulus -it is the pattern that is important. Correlation is a way to measure the similarity of two patterns of stimulation, in the case of masking a target-alone pattern and a target-mask pattern, to identify whether and when activity attributable to a http://www.ac-psych.org target stimulus remains present in the modeled nerve net.
These ideas are incorporated in a computer simulation of a lateral inhibitory nerve net. The scheme has been successful in modeling a number of properties of metacontrast masking (Bridgeman 1971(Bridgeman , 1978(Bridgeman , 2001. It was also the most successful of a group of mathematical models in simulating a variation on backward masking, where target and mask were temporally contiguous and the mask was varied in duration (Di Lollo, von Mühlenen, Enns & Bridgeman, 2004).

simultaneous-onset and object substitution masking
In the 1960s and 1970s it was thought that stimulus onset asynchrony (SOA) was the critical timing variable in backward masking. Subsequent work, however, has identified interstimulus interval (ISI) and stimulus termination asynchrony (STA) as more important (Francis, Rothmayer & Hermens, 2004). A new masking paradigm, simultaneous-onset, brought a new challenge for mathematical modelers (Di Lollo, Bischof & Dixon, 1993). This paradigm presents a target and mask with geometries similar to metacontrast designs.
They appear simultaneously, and the mask disappears after the target with a varying delay. Bischof and Di Lollo (1995) showed that metacontrast masking could be obtained with a simultaneous-onset paradigm. These are the model parameters and stimulus sizes used to simulate metacontrast masking with the model (Bridgeman, 1978;2001). Durations of target and mask in the current simulations are 1 iteration of inhibition, representing 30msec of real time, except where noted below. The program is that of Francis (2003), with changes as noted below to simulate novel conditions.

Constant-intensity condition
Object-substitution masking was simulated with a constant mask intensity for each masking curve, so that increasing the duration of the mask also increases its total energy.

Design of the lateral inhibitory nerve net. Coefficients K1 to K3 define the fraction of a neuron's output that is relayed to inhibit neighboring neurons. Stimulus presence is modeled as the activity over the entire 30-neuron net, of which connections of 1 neuron and a sample of 7 neurons are shown here.
Output(x,t) = Input(x,t-1) -(Sum of Inhibitions) < Inputs >

Compensated-intensity condition
What happens when the modeled mask intensity is compensated, its intensity becoming lower as its du-

With identical stimulus parameters, simulations are run for 4, 8, or 12 iterations of lateral inhibition. In each case, mask intensity is adjusted as its duration is varied to match psychophysically derived equal-brightness stimulation. Total mask duration is 30msec longer than indicated on the horizontal axis, because target and mask appear simultaneously.
is lower than the corresponding psychophysical function, the results correspond to those of Di Lollo et al.

DIsCUssION
The prediction of Di Lollo et al. (2000) that an explanation of object substitution masking will require reentrant processes appears to have been contradicted, as the single-layer lateral inhibitory model can account  If the mask is introduced later, when the target's representation has spread to many neurons, interference with the small area of the mask has less effect. This is the standard metacontrast condition.
In object substitution (figure 3), with the briefest integration condition the interactions are similar to those in standard metacontrast; when target and mask offset are close together in time, the mask interferes with the target's spreading activity, but with larger mask delay the target is already firmly coded in redundant activity of many neurons when the mask appears.
Four iterations of activity are not enough to allow the mask to dominate. With longer integration intervals, however, damped oscillations emanating from target offset and mask offset mix together in the network, interfering with one another and preventing target-like activity from reasserting itself. Since the mask remains present, it continues to exert a strong effect on total network activity. These qualitative descriptions are no substitute for mathematical modeling, of course, but hopefully they give a flavor of the sorts of interactions that lateral inhibition creates.