Coherent Hexagonal Copying from Fuzzy Neuroanatomy
WILLIAM H. CALVIN
Department of Psychiatry and Behavioral Sciences,
University of Washington
Seattle, Washington 98195-1800 USA
WCalvin@U.Washington.edu
Calvin, William H. (1993). Error-correcting codes: Coherent hexagonal copying from fuzzy neuroanatomy. World Congress on Neural Networks 1:101-104 (1993).
Copyright 1993 by W. H. Calvin.
Since Hebb's 1949 cell-assembly proposal1, we have realized that evoking a memory could involve an ensemble of cortical neurons, each of which helps to implement other memories as well. Different schemas might be characterized by different firing patterns in time and space. The analogous problem in genetic memory, that of the genetic code, was solved by first identifying which physical patterns could be reliably copied. But copying has not been on the neurophysiological agenda; we usually assume transformations rather than cloning when information is moved.
Many movement command clones were, however, inferred2,3 from the need to reduce timing jitter during precision throwing. And the notion of convergence zones for associative memories4 raises the issue of maintaining the identity of a cerebral code during long-distance corticocortical transmission, such as through the corpus callosum. Because of the reciprocal connections between distant cortical regions, any distortions of the original spatiotemporal firing pattern during forwards transmission would need to be compensated during reverse transmission in order to maintain the pattern as the local code for a sensory or motor schema. Here I suggest an error-correction mechanism in both directions that avoids the need for an inverse transform.
Even if the synaptic strengths were high, much longer axons are required for a reverberating loop. But even weak coupling between relaxation oscillators is known to produce entrainment10,11, and that is the feature utilized here. Were the cells otherwise active, they would soon tend to produce some spikes at about the same time (Fig. 1A). This intermittent synchrony12 suggests the entrainment of other superficial pyramidal neurons located at the two points which are equidistant from the first pair (Fig. 1B).
If sufficient axons traveled in approximately the right directions (up to six, at 60deg angles from a point), this recruitment could continue to eventually form a mosaic of synchronous activity at 0.5 mm spacings (Fig. 2A). While the most efficient anatomy would be six equally-spaced axon branches from the same cell (Fig. 1B, Fig. 3AB), a more general wiring principle would be enough neighboring work-alike neurons to collectively send axons in all directions and thereby create an annulus of excitation. Cells in cortical minicolumns are often interested in the same kinds of stimuli (orientation columns) and fire in synchrony (at least in development); since there are about 100 neurons in such a column, coverage may well be sufficient without individual axons being able to branch at 60deg angles. Because simultaneous arrivals at the outlying neuron are the actual criterion rather than equal length, the standard axon can vary so long as conduction velocity or synaptic delay is tuneable. Thus fuzzy anatomy, so long as the 60deg directions are not avoided, can yield a self-organizing triangular mosaic. The largest copyable pattern is a 0.5 mm hexagon (Fig. 2B). Concurrent nonhexagonal activities may well be compatible, especially in other cortical layers. Indeed, something needs to get the cells firing so that weak coupling can entrain them (this also suggests that mosaics can be erased with diffuse waves of inhibition). Note that hexagons are not an assumption: they are an emergent property of standard axon lengths and weak excitatory coupling that entrains.
Two hexagonal patterns could be superimposed, via either local or long-distance copying, and so form a new category, an episodic memory, or an association between a sensory schema and a response schema. If the dot matrix is sparsely populated (and estimates suggest that a dozen minicolumns might be active, out of 300 in the hexagon), the composite could serve as a form of associative memory in the manner of a double exposure. I discuss elsewhere13 the implications of hexagonal copying competitions for implementing a msec-to-minute version of the same darwinian process familiar from the immune response and species evolution. Neurallike networks could also 1) use hexagonal dot-matrix patterns as item representations, could 2) form associations, and 3) so implement a novel computing architecture with wiring that is diffuse enough to perform multiple tasks.
2. Calvin, W. H., J. Theor Biol. 104, 121-135 (1983).
3. Calvin, W. H., The Cerebral Symphony(Bantam, New York, 1989).
4. Damasio, A.R., Cognition 33, 25-62 (1989).
5. Stevens, C. F., Neural Computation 1, 473-479 (1989).
6. Katz, L.C., Callaway, E.M., Ann. Rev. Neurosci. 15, 31-56(1992).
7. Rockland, K.S., Lund, J.S., Science 215, 1532-1534 (1982).
8. Gilbert, C.D., Hubel, D.H., J. Neurosci. 3, 1116-1133 (1983).
9. White, E.L., Cortical Circuits: Synaptic Organization of the Cerebral Cortex Structure, Function, and Theory (Birkhauser, Boston, 1989).
10. Winfree, A. T., The Geometry of Biological Time (Springer Verlag, Berlin, 1980).
11. Somers, D., Kopell, N., Biol. Cybernetics (in press, 1992).
12. Engel, A.K., Koenig, P., Kreiter, A.K., Schillen, T.B., Singer, W., Trends Neurosci. 15, 218-226 (1992).
13. Calvin, W. H., Soc. Neurosci. Abstr. 18, 214.18 (1992)
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Revised 23 September 1995 WHC