A Model of Brain Function

A metaphor for the patterns of neural interconnection in much of the neocortex is a geometric figure consisting of a large number of pins around the border and with string or thread stretched across the figure between the pins. Interesting patterns arise within the body of the figure due to the large number of threads crossing the area of the figure. In this brain model, the pattern of interconnecting threads changes rapidly and dynamically as computations are carried out.

This brain model was inspired primarily by two studies, Edelman's theories, including his Theory of Neuronal Group Selection and the exploratory work in modelling the basal ganglia as reported by Houk, Davis and Beiser.

The cortex appears to have something like a million, possibly up to ten million of such points available for interlinking. But not all point pairs are linkable. Only those pairs of points which are connected by neural axons are potentially interconnectable on a logical level. There are many bundles of interconnecting axons throughout the brain, the best known of which (the corpus callosum) has roughly 1/4 billion axonal fibers. Such point-to-point linking patterns are less common in the mid-brain and hind-brain areas, where the structures appear to have more complex, prewired interconnections

There are actually three discernable levels of interconnections, which I call local, regional and long-distance. Within small, local areas covering a few millimeters in diameter, there is almost 100% total interconnectivity. This is true for most of the cerebral cortex and the cerebellum, less so in brain stem areas. These interconnecting axons lie entirely within the thin cortical layer. Throughout the cortex, especially in the frontal lobes, there are numerous regional bundles which loop down into the white matter and generally cover distances on the order of a few centimeters. There are many thousands of such bundles, with a total interconnectivity on the order of perhaps millions to billions of point pairs, but still far short of "total interconnectivity", even of all points within a few centimeters. The third, or long-distance, level involves the major tracts, such as the CC. For example, running back-to-front along the sides of each hemisphere, in the white matter below the surface of the temporal and frontal lobes, are several major tracts which account for many millions of fibers. There are also major bundles of interconnection between various areas of the frontal lobes and corresponding areas in the thalamus. But again, the numbers are far, far short of total interconnectivity.

I have not said any more about just what these "points" are. The question is how many neurons are involved in a "point" (a terminal node). Some evidence suggests that a node may be on the order of a hundred neurons, perhaps corresponding roughly to "minicolumns" in the cortex. This seems to differ in other areas. Houk et al cite the discovery of interconnecting circuits between the thalamus and the cortex in which individual pairs of neurons are connected so as to behave something like an SR flip-flop. These links are "set" in response to a broad pattern detecting net, very much like a traditional artificial neural net. They are "reset" by specific motor-related activity in the basal ganglia. There are on the order of millions of such flip-flops in parallel arrays.

As for how this system operates, something like the following emerges. All short-term memory, thoughts, perceptions and consciousness, are implemented dynamically in the form of these interconnections. A particular, instantaneous "pattern" may consist of thousands of simultaneously active nodes, widely scattered throughout the brain. It is not clear how many independent patterns may be simultaneously active. Edelman suggests the number may be "a few". Some other work suggests that oscillation frequencies (at least in some areas) may serve to isolate larger numbers of interconnection patterns which would otherwise interfere. This might allow up to "dozens" of patterns, overlapping in their areas of interconnection.

Such oscillation-based patterns would be slower than direct "active-axon" feedback patterns. With oscillation frequencies in the alpha and beta bands (below 100 Hz), such patterns would have response times on the order of 1/10s of a second, compared to 1/100s of a second for feedback-based patterns.

Long term memory seems to be implemented by the growth of synaptic connections between the nodes. Once established, these synapses connect nodes without requiring an short-term pattern to be active. The growth of such synaptic connections is determined by both the short-term link activations and by the ever-present chemical soup environment. An even longer-term structure is related to the growth of patterns in synaptic connections specified (directly or indirectly) by the DNA. Many hundreds of such connections are innately specified for each one that survives through the first few years of life. In other words, the neonate brain is highly over-connected and most of these synapses are "decommissioned" if they are not exercised by the activities of the child during the first few years. Thereafter, synapses are continually being created and destroyed according to the short-term dynamic patterns and the current state of the chemical soup of "neuromodulator" molecules. This is a whole nuther topic.

Two major questions arise. First is my description of the point-to-point links as being binary in nature, that is, either on or off. Edelman has described mechanisms which could support multiple levels of activity, but (with some possible exceptions) these seem to be concerned more with the decision to activate a link (see below) than allowing multiple activation levels. For now, I take it as a simplifying assumption that all point-to-point link activations are binary in nature. Although the links are considered to be binary, there is still a wide variety of response times.

Second, what causes a particular link to turn on or off, whether to join up with an existing pattern or to start up a new pattern? I have ealier discussed the neural network-type of pattern recognizer which appears to be connected so as to activate the flip-flop-type thalamocortical circuits. To some extent, such a pattern detector may also be available for the multi-neuron type of nodes. Another mechanism is available in the multi-neuron nodes. Each of the neurons in such a node is connected to its own unique set of input conditions, including the selective activity of a limited number of the neurons at the opposite end of the link. Edelman describes such an architecture as having perhaps 1/10 as many axonal link connections as there are neurons in the node at each end. Thus, in addition to whatever local connections exist at each end of the link, the node is also sensitive to a "reduced" version of the activity at the opposing node. For a possible account of the effect of such reduced activity, I note a description by Dumais of a neural network model of the matrix reduction technique known as singular value decomposition. Dumais' neural net model bears a striking resemblance to Edelman's reentrant link model.

A significant statement this model makes is that memory contents do not "move around", that is, they do not get copied from one place to another as we typically think when regarding computer memory. The only mention I am aware of on this issue is a comment by Dennett in his review of a book by Allen Newell.

For some discussion on applying this brain model to various cognitive systems, see
Semantic Networks
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