Mathematical Psychology and Psychophysiology

By Stephen Grossberg | Go to book overview

Sperling [ 1970] is that a neuron at level z in one column facilitates neurons at and near to level z in adjacent columns, by inhibiting neurons elsewhere in the adjacent columns. In effect, the neuron attempts to influence adjacent columns to respond more-or-less in the same way as its own column. It makes inhibitory feedback connections to neurons at different levels in adjacent columns as in its own column. Lateral excitatory connections between same-level neighbors strengthen the cooperativity beyond that achieved by inhibiting-the-inhibition. But it is necessary that lateral interactions between neighbors be different from vertical interactions within a column. Otherwise, the whole NBF would function like a single column. The lateral connections to adjacent columns are not so strong that they override strong input signals. When inputs are weak or ambiguous, the effect of cooperation/ competition interaction is to build "planes of influence" at the z level of the model neurons that happen to have the strongest input signals. When there is a depth-ambiguous area between two unambiguous areas, the boundary between the two planes of influence can be quite unstable. [In stereograms constructed to satisfy these conditions, it is sometimes possible actually to see the rapid sweep of one depth plane over another ( Sperling [ 1970]).]

The interaction between adjacent model neurons that represent different depth planes can result in far-reaching effects that travel like a wave. In other words, local cooperation/competition can result in global interactions. This is one of the features that makes cooperation/competition models so interesting and attractive to theorists. While systems like the one proposed here have been simulated, I do not know of a comprehensive mathematical treatment; it seems to be a worthwhile area of investigation.

The cooperation/competition mechanism that serves binocular vision quite probably serves other perceptual functions that involve local/global interactions, such as figure/ground relations and depth perception. Interpreting a portion of a scene as figure causes the area interpreted as figure to spread and to extend its boundaries to the limits of the area interpreted as ground. Similarly, seeing an ambiguous motion stimulus (composed of many points) moving in one direction in one part of a stimulus causes the motion interpretation to be applied to all other parts.

Summary and conclusion. Simple demonstrations of path-dependent perceptual states led to simple, useful descriptive models (potential theory) and to formidable process models (cooperation/competition networks) that still present substantial mathematical challenges.


REFERENCES

Allen J. B., 1977a. "Two-dimensional cochlear fluid model: New results", J. Acoust. Soc. Amer. 61, 110-119.

_____, 1977b. "Cochlear micromechanics-a mechanism for transforming mechanical to neural tuning within the cochlea", J. Acoust. Soc. Amer. 62, 930 - 939.

Boring E. G., 1933. The physical dimensions of consciousness, Century Co., New York.

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