Read Ebook: Self-Organizing Systems 1963 by Garvey James Emmett Editor

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Since we are attempting to duplicate processes other than chemical, per se, we will forego any reference to the extensive literature of neurochemistry. It should not be surprising though if, at the neglect of the fundamental biological processes of growth, reproduction and metabolism, it proves possible to imitate some learning mechanisms with grossly less complex molecular structures. There is also much talk of chemical versus electrical theories and mechanisms in neurophysiology. The distinction, when it can be made, seems to hinge on the question of the scale of size of significant interactions. Thus, "chemical" interactions presumably take place at molecular distances, possibly as a result of or subsequent to a certain amount of thermal diffusion. "Electrical" interactions, on the other hand, are generally understood to imply longer range or larger scale macroscopic fields.

The human brain contains approximately 10?? neurons to which the neuron theory assigns the primary role in central nervous activity. These cells occupy, however, a relatively small fraction of the total volume. There are, for example, approximately 10 times that number of neuroglia, cells of relatively indeterminate function. Each neuron comes into close contact with the dendrites of other neurones at some thousands of places, these synapses and "ephapses" being spaced approximately 5? apart . The total number of such apparent junctions is therefore of the order of 10??. In spite of infinite fine-structure variations when viewed with slightly blurred vision, the cellular structure of the brain is remarkably homogeneous. In the cortex, at least, the extensions of most cells are relatively short, and when the cortex is at rest, it appears from the large EEG alpha-rhythms that large numbers of cells beat together in unison. Quoting again from Sperry, "In short, current brain theory encourages us to try to correlate our subjective psychic experience with the activity of relatively homogeneous nerve cell units conducting essentially homogeneous impulses, through roughly homogeneous cerebral tissue."

A train of impulses simply travelling on a long fiber may, for example, be regarded as a short-term memory much in the same way as a delay line acts as a transient memory in a computer. A similar but slightly longer term memory may also be thought of to exist in the form of waves circulating in closed loops . In fact, it is almost universally held today that most significant memory occurs in two basic interrelated ways. First of all, such a short-term circulating, reverberatory or regenerative memory which, however, could not conceivably persist through such things as coma, anesthesia, concussion, extreme cold, deep sleep and convulsive seizures and thus, secondly, a long-term memory trace which must somehow reside in a semipermanent fine-structural change. As Hebb stated, "A reverbratory trace might cooperate with a structural change and carry the memory until the growth change is made."

The current most highly regarded specific conception of the synapse is largely due to and has been best described by Eccles : " ... the synaptic connections between nerve cells are the only functional connections of any significance. These synapses are of two types, excitatory and inhibitory, the former type tending to make nerve cells discharge impulses, the other to suppress the discharge. There is now convincing evidence that in vertebrate synapses each type operates through specific chemical transmitter substances ...". In response to a presentation by Hebb , Eccles was quoted as saying, "One final point, and that is if there is electrical interaction, and we have seen from Dr. Estable's work the complexity of connections, and we now know from the electronmicroscopists that there is no free space, only 200 ? clefts, everywhere in the central nervous system, then everything should be electrically interacted with everything else. I think this is only electrical background noise and, that when we lift with specific chemical connections above that noise we get a significant operational system. I would say that there is electrical interaction but it is just a noise, a nuisance." Eccles' conclusions are primarily based on data obtained in the peripheral nervous system and the spinal cord. But there is overwhelming reason to expect that cellular interactions in the brain are an entirely different affair. For example, "The highest centres in the octopus, as in vertebrates and arthropods, contain many small neurons. This finding is such a commonplace, that we have perhaps failed in the past to make the fullest inquiry into its implications. Many of these small cells possess numerous processes, but no axon. It is difficult to see, therefore, that their function can be conductive in the ordinary sense. Most of our ideas about nervous functioning are based on the assumption that each neuron acts essentially as a link in some chain of conduction, but there is really no warrant for this in the case of cells with many short branches. Until we know more of the relations of these processes to each other in the neuropile it would be unwise to say more. It is possible that the effective part of the discharge of such cells is not as it is in conduction in long pathways, the internal circuit that returns through the same fiber, but the external circuit that enters other processes, ..." .

The inhibitory chemical transmitter substance postulated by Eccles has never been detected in spite of numerous efforts to do so. The mechanism of inhibition is perhaps the key to the question of cellular interaction and, in one form or another, must be accounted for in any adequate theory.

Other rather specific forms of excitation and inhibition interaction have been proposed at one time or another. Perhaps the best example is the polar neuron of Gesell and, more recently, Retzlaff . In such a concept, excitatory and inhibitory couplings differ basically because of a macroscopic structural difference at the cellular level; that is, various arrangements or orientation of intimate cellular structures give rise to either excitation or inhibition.

Most modern theories of semipermanent structural change look either to the molecular level or to the cellular level. Various specific locales for the engram have been suggested, including modifications of RNA molecular structure, changes of cell size, synapse area or dendrite extensions, neuropile modification, and local changes in the cell membrane. There is, in fact, rather direct evidence of the growth of neurons or their dendrites with use and the diminution or atrophy of dendrites with disuse. The apical dendrite of pyramidal neurones becomes thicker and more twisted with continuing activity, nerve fibers swell when active, sprout additional branches and presumably increase the size and number of their terminal knobs. As pointed out by Konorski , the morphological conception of plasticity according to which plastic changes would be related to the formation and multiplication of new synaptic junctions goes back at least as far as Ramon y Cajal in 1904. Whatever the substrate of the memory trace, it is, at least in adults, remarkably immune to extensive brain damage and as Young has said: " ... this question of the nature of the memory trace is one of the most obscure and disputed in the whole of biology."

First, from Boycott and Young , "The current conception, on which most discussions of learning still concentrate, is that the nervous system consists essentially of an aggregate of chains of conductors, linked at key points by synapses. This reflex conception, springing probably from Cartesian theory and method, has no doubt proved of outstanding value in helping us to analyse the actions of the spinal cord, but it can be argued that it has actually obstructed the development of understanding of cerebral function."

Most observable evidence of learning and memory is extremely complex and its interpretation full of traps. Learning in its broadest sense might be detected as a semipermanent change of behavior pattern brought about as a result of experience. Within that kind of definition, we can surely identify several distinctly different types of learning, presumably with distinctly different kinds of mechanisms associated with each one. But, if we are to stick by our definition of a condition of semipermanent change of behavior as a criterion for learning, then we may also be misled into considering the development of a neurosis, for example, as learning, or even a deep coma as learning.

When we come to consider field effects, current theories tend to get fairly obscure, but there seems to be an almost universal recognition of the fact that such fields are significant. For example, Morrell says in his review of electrophysiological contributions to the neural basis of learning, "A growing body of knowledge suggests that the most significant integrative work of the central nervous system is carried on in graded response elements--elements in which the degree of reaction depends upon stimulus intensity and is not all-or-none, which have no refractory period and in which continuously varying potential changes of either sign occur and mix and algebraically sum." Gerard also makes a number of general comments along these lines. "These attributes of a given cell are, in turn, normally controlled by impulses arising from other regions, by fields surrounding them--both electric and chemical--electric and chemical fields can strongly influence the interaction of neurones. This has been amply expounded in the case of the electric fields."

EXPERIMENTAL TECHNIQUE

Experiments involving the growth by electrodeposition and study of metallic dendrites are done with an eye toward electrical, physical and chemical compatibility with the energy-producing system outlined above. Best results to date have been obtained by dissolving various amounts of gold chloride salt in 53-55% HNO?.

An apparatus has been devised and assembled for the purpose of containing and controlling our primary experiments. . Its two major components are a test chamber and a fluid exchanger . In normal operation the test chamber, which is very rigid and well sealed after placing the experimental assembly inside, is completely filled with electrolyte to the exclusion of all air pockets and bubbles. Thus encapsulated, it is possible to perform experiments which would otherwise be impossible due to instability. The instability which plagues such experiments is manifested in copious generation of bubbles on and subsequent rapid disintegration of all "excitable" material . Preliminary experiments indicated that such "bubble instability" could be suppressed by constraining the volume available to expansion. In particular, response and recovery times can now be decreased substantially and work can proceed with complex systems of interest such as aggregates containing many small iron pellets.

The test chamber is provided with a heater which makes possible electrochemical impulse response and recovery times comparable to those of the nervous system . The fluid-exchanger is so arranged that fluid in the test chamber can be arbitrarily changed or renewed by exchange within a rigid, sealed, completely liquid-filled loop. Thus, stability can be maintained for long periods of time and over a wide variety of investigative or operating conditions.

Most of the parts of this apparatus are made of stainless steel and are sealed with polyethylene and teflon. There is a small quartz observation window on the test chamber, two small lighting ports, a pressure transducer, thermocouple, screw-and-piston pressure actuator and umbilical connector for experimental electrical inputs and outputs.

BASIC EXPERIMENTS

The basic types of experiments described in the following sections are numbered for comparison to correspond roughly to related neurophysiological concepts summarized in the previous section.

The primary object of our research is the control and determination of dynamic behavior in response to electrical stimulation in close-packed aggregates of small pellets submerged in electrolyte. Typically, the aggregate contains iron and the electrolyte contains nitric acid, this combination making possible the propagation of electrochemical surface waves of excitation through the body of the aggregate similar to those of the Lillie iron-wire nerve model. The iron pellets are imbedded in and supported by a matrix of small dielectric pellets. Furthermore, with the addition of soluble salts of various noble metals to the electrolyte, long interstitial dendritic or fibrous structures of the second metal can be formed whose length and distribution change by electrodeposition in response to either internal or externally generated fields.

Figure 3 shows an iron loop wrapped with a silver wire helix which is quite stable in 53-55% acid and which will easily support a circulating pattern of three impulses. For demonstration, unilateral waves can be generated by first touching the iron with a piece of zinc and then blocking one of them with a piece of platinum or a small platinum screen attached to the end of a stick or wand. Carbon blocks may also be used for this purpose.

The smallest regenerative or reverberatory loop which we are at present able to devise is about 1 mm in diameter. Multiple waves, as expected, produce stable patterns in which all impulses are equally spaced. This phenomenon can be related to the slightly slower speed characteristic of the relative refractory period as compared with a more fully recovered zone.

If two touching pieces of iron are placed in a bath of nitric acid, a wave generated on one will ordinarily spread to the other. As is to be expected, a similar result is obtained if the two pieces are connected through an external conducting wire. However, if they are isolated, strong coupling does not ordinarily occur, especially if the elements are small in comparison with a "critical size," ?/? where ? is the surface resistivity of passive iron surface and ? is the volume resistivity of the acid . A simple and informative structure which demonstrates the essential conditions for strong electrical coupling between isolated elements of very small size may be constructed as shown in Figure 4. The dielectric barrier insures that charge transfer through one dipole must be accompanied by an equal and opposite transfer through the surfaces of the other dipole. If the "inexcitable" silver tails have sufficiently high conductance , strong coupling will occur, just as though the cores of the two pieces of iron were connected with a solid conducting wire.

If a third "dipole" is inserted through the dielectric membrane in the opposite direction, then excitation of this isolated element tends to inhibit the response which would otherwise be elicited by excitation of one of the parallel dipoles. Figure 5 shows the first such "logically-complete" interaction cell successfully constructed and demonstrated. It may be said to behave as an elementary McCulloch-Pitts neuron . Further analysis shows that similar structures incorporating many dipoles can be made to behave as general "linear decision functions" in which all input weights are approximately proportional to the total size or length of their corresponding attached dendritic structures.

Figure 6 shows a sample gold dendrite grown by electrodeposition from a 54% nitric acid solution to which gold chloride was added. When such a dendrite is attached to a piece of iron , activation of the excitable element produces a field in such a direction as to promote further growth of the dendritic structure. Thus, if gold chloride is added to the solution used in the elementary interaction cells described above, all input influence "weights" tend to increase with use and, hence, produce a plasticity of function.

Our measurements indicate that, during the refractory period following excitation, the surface resistance of iron in nitric acid drops to substantially less than 1% of its resting value in a manner reminiscent of nerve membranes . Thus, if a distributed or gross field exists at any time throughout a complex cellular aggregate, concomitant current densities in locally-refractive regions will be substantially higher than elsewhere and, if conditions appropriate to dendrite growth exist growth rates in such regions will also be substantially higher than elsewhere. It would appear that, as a result, recently active functional couplings should be significantly altered by widely distributed fields or massive peripheral shocks. This mechanism might thus explain the apparent ability of the brain to form specific temporal associations in response to spatially-diffuse effects such as are generated, for example, by the pain receptors.

SUMMARY

An attempt is being made to develop meaningful electrochemical model techniques which may contribute toward a clearer understanding of cortical function. Two basic phenomena are simultaneously employed which are variants of the Lillie iron-wire nerve model, and growth of metallic dendrites by electrodeposition. These phenomena are being induced particularly within dense cellular aggregates of various materials whose interstitial spaces are flooded with liquid electrolyte.

REFERENCES

Multi-Layer Learning Networks

R. A. STAFFORD

INTRODUCTION

In putting forth a model for such an adapting or "learning" network, a requirement is laid down that the complexity of the adaption process in terms of interconnections among elements needed for producing appropriate weight changes, should not greatly exceed that already required to produce outputs from inputs with a static set of weights. In fact, it has been found possible to use the output-from-input computing capacity of the network to help choose proper weight changes by observing the effect on the output of a variety of possible weight changes.

No attempt is made here to defend the proposed network model on theoretical grounds since no effective theory is known at present. Instead, the plausibility of the various aspects of the network model, combined with empirical results must suffice.

SINGLE ELEMENTS

To simplify the problem it is assumed that the network receives a set of two-valued inputs, x?, x?, ..., x?, and is required to produce only a single two-valued output, y. It is convenient to assign the numerical quantities +1 and -1 to the two values of each variable.

The simplest network would consist of a single linear threshold element with a set of weights, c?, c?, c?, ..., c?. These determine the output-input relation or function so that y is +1 or -1 according as the quantity, c? + c?x? + c?x? + ... + c?x?, is positive or not, respectively. It is possible for such a single element to exhibit an adaptive behavior as follows. If, for a given set, x?, x?, ..., x?, the output, y, is correct, then make no changes to the weights. Otherwise change the weights according to the equations

It has been shown by a number of people that the weights of such an element are assured of arriving at a set of values which produce the correct output-input relation after a sufficient number of errors, provided that such a set exists. An upper bound on the number of possible errors can be given which depends only on the initial weight values and the logical function to be learned. This does not, however, solve our network problem for two reasons.

NETWORKS OF ELEMENTS

It can be demonstrated that if a sufficiently large number of linear threshold elements is used, with the outputs of some being the inputs of others, then a final output can be produced which is any desired logical function of the inputs. The difficulty in such a network lies in the fact that we are no longer provided with a knowledge of the correct output for each element, but only for the final output. If the final output is incorrect there is no obvious way to determine which sets of weights should be altered.

As a result of considerable study and experimentation at Aeronutronic, a network model has been evolved which, it is felt, will get around these difficulties. It consists of four basic features which will now be described.

Positive Interconnecting Weights

The above restriction removes this difficulty. If the output of any element in the network is changed, say, from -1 to +1, the effect on the final element, if it is affected at all, is in the same direction.

It should be noted that this restriction does not seriously affect the logical capabilities of a network. In fact, if a certain logical function can be achieved in a network with the use of weights of unrestricted sign, then the same function can be generated in another network with only positive interconnecting weights and, at worst, twice the number of elements. In the worst case this is done by generating in the restricted network both the output and its complement for each element of the unrestricted network.

A Variable Bias

The central problem in network learning is that of determining, for a given input, the set of elements whose outputs can be altered so as to correct the final element, and which will do the least amount of damage to previous adaptations to other inputs. Once this set has been determined, the incrementing rule given for a single element will apply in this case as well , since the desired final output coincides with that desired for each of the elements to be changed .

In the process of arriving at such a decision three factors need to be considered. Elements selected for change should tend to be those whose output would thereby be affected for a minimum number of other possible inputs. At the same time it should be ascertained that a change in each of the elements in question does indeed contribute significantly towards correcting the final output. Finally, a minimum number of such elements should be used.

It would appear at first that this kind of decision is impossible to achieve if the complexity of the decision apparatus is kept comparable to that of the basic input-output network as mentioned earlier. However, in the method to be described it is felt that a reasonable approximation to these requirements will be achieved without an undue increase in complexity.

Now suppose that for a given input the final output ought to be +1 but actually is -1. Assume that b is then raised so high that this final output is corrected. Then commence a gradual decline in b. Various elements may revert to -1, but until the final output does, no weights are changed. When the final output does revert to -1, it is due to an element's having a sum which just passed down through zero. This then caused a chain effect of changing elements up to the final element, but presumably this element is the only one possessing a zero sum. This can then be the signal for the weights on an element to change--a change of final output from right to wrong accompanied simultaneously by a zero sum in the element itself.

After such a weight change, the final output will be correct once more and the bias can again proceed to fall. Before it reaches zero, this process may occur a number of times throughout the network. When the bias finally stands at zero with the final output correct, the network is ready for the next input. Of course if -1 is desired, the bias will change in the opposite direction.

It is possible that extending the weight change process a little past the zero bias level may have beneficial results. This might increase the life expectancy of each learned input-output combination and thereby reduce the total number of errors. This is because the method used above can stop the weight correction process so that even though the final output is correct, some elements whose output are essential to the final output have sums close to zero, which are easily changed by subsequent weight changes.

On the other hand this method requires little more added complexity to the network than it already has. Each element requires a bias, an error signal, and the desired final output, these things being uniform for all elements in a network. Some external device must manipulate the bias properly, but this is a simple behavior depending only on an error signal and the desired final output--not on the state of individual elements in the network. What one has, then, is a network consisting of elements which are nearly autonomous as regards their decisions to change weights. Such a scheme appears to be the only way to avoid constructing a central weight-change decision apparatus of great complexity. This rather sophisticated decision is made possible by utilizing the computational capabilities the network already possesses in producing outputs from inputs.

It should be noted here that this varying bias method requires that the variable bias be furnished to just those elements which have variable weights and to no others. Any fixed portion of the network, such as preliminary layers or final majority function for example, must operate independently of the variable bias. Otherwise, the final output may go from right to wrong as the bias moves towards zero and no variable-weight element be to blame. In such a case the network would be hung up.

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