Part 16

c. The neuron is capable of temporal and spatial integration. Many subthreshold stimuli arriving at the neuron from different sources, or at slightly different times, can add up to a sufficient level to fire the neuron.

d. Some inputs are excitatory, some are inhibitory.

e. There is a refractory period. Once fired, there is a subsequent period during which the neuron cannot be fired again, no matter how large the stimulus. This places an upper limit on the pulse rate of any particular neuron.

f. The neuron can learn. This property is conjectural in living neurons, since it appears that at the present time learning has not been clearly demonstrated in isolated living neurons. However, the learning property is basic to all self-organizing models.

Neuron models with the above characteristics have been built, although none seem to have incorporated all of them in a single model. Harman (3) at Bell Labs has built neuron models which have the characteristics (a) through (e), with which he has built extremely interesting devices which simulate portions of the peripheral neuron system.

Various attempts at learning elements have been made, perhaps best exemplified by those of Widrow (4). These devices are capable of “learning,” but are static, and lack all the temporal characteristics listed in (a) through (e). Such devices can be used to deal with temporal patterns only by a mapping technique, in which a temporal pattern is converted to a spatial one.

Having listed which seem to be the important properties of a neuron, it is possible to synthesize a simple model which has all of them.

A number of input stimuli are fed to the neuron through a resistive summing network which establishes the threshold and accomplishes spatial integration. The voltage at the summing junction triggers a “one-shot” circuit, which, by its very nature, accomplishes pulse generation and exhibits temporal integration and a refractory period. The polarity of an individual input determines whether it shall be excitatory or inhibitory. This much of the circuitry is very similar to Harmon’s model.

Learning is postulated to take place in the following way: when the neuron fires, an outside influence (the environment, or a “trainer”) determines whether or not the result of firing was desirable or not. If it was desirable, the threshold of the neuron is lowered, making it easier to fire the next time. If the result was not desirable, the threshold is raised, making it more difficult for the neuron to fire the next time.

In a self-organizing system, many model neurons would be interconnected. A “punish-reward” (P-R) signal would be connected to all neurons in common. However, means would be provided for only those which have recently fired to be susceptible to the effects of the P-R signal. Therefore, only those which had taken part in a recent response are modified. This idea is due to Stewart (5), who applies it to his electrochemical devices instead of to an electronic device.

The mechanization of the circuitry is rather straight-forward. A portion of the output of the pulse generator is routed through a “pulse-stretcher” or short-term memory which temporarily records the fact that the neuron has recently fired. The pulse-stretcher output controls a gate, which either accepts or rejects the P-R signal. The P-R signal can take on only three values, a positive level, zero, or a negative level, depending on whether the signal is “punish,” “no action,” or “reward.” Finally, the gate output controls a variable resistor, which is part of the resistive summing network. Figure 1 is a block diagram of the complete model.

Note that this device differs from the usual “Perceptron” configuration in that the threshold resistor is the only variable element, instead of having each input resistor a variable weighting element. This simplification could lead to a situation where, to prepare a specified task, more single-variable neurons would be required than would multivariable ones. This possible disadvantage is partially, at least, offset by the very simple control algorithm which is contained in the design of the model, and is not the matter of great concern which it seems to be for most multivariable models.

Hand simulations of the action of this type of model suggest that a certain amount of randomness would be desirable. It appears that a self-organizing system built of these elements, and of sufficient complexity to be interesting, would have a fair number of recirculating loops, so that spontaneous activity would be maintained in the absence of input stimulus. If this is the case, then randomness could easily be introduced by adding a small amount of noise from a random noise generator to the signal on the P-R bus. Thus, any neurons which spontaneously fire would be continually having their thresholds modified.

The mechanization of the model is not particularly complex, and can be estimated as follows: The one-shot pulse generator would require two transistors, the pulse stretcher one more. The bi-directional gate would require a transistor and at least two diodes.

Several candidates for the electrically-controllable variable resistor are available (6). Particularly good candidates appear to be the “Memistor” or plating cell developed by Widrow (7), the solid state version of it by Vendelin (8), and the “solion” (9). All are electrochemical devices in which the resistance between two terminals is controlled by the net charge flow through a third terminal. All are adaptable to this particular circuit.

Of the three, however, the solion appears at first glance to have the most promise in that its resistance is of the order of a few thousand ohms (rather than the few ohms of the plating cells) which is more compatible with ordinary solid-state circuitry. Solions have the disadvantage that they can stand only very low voltages (less than 1 volt) and in their present form require extra bias potentials. If these difficulties can be overcome, they offer considerable promise.

In summary, it appears that a rather simple neuron model can be built which can mimic most of the important functions of real neurons. A system built of these could be punished or rewarded by an observer, so that it could be trained to give specified responses to specified stimuli. In some cases, the observer could be simply the environment, so that the system would learn directly from experience, and would be therefore a self-organizing system.

REFERENCES

1. Hodgkin, A. L., and Huxley, A. L., “A Quantitative Description of Membrane Current and its Application to Conduction and Excitation in Nerve,” J. Physiol. =117=:500-544 (August 1952)

2. Crane, H. D., “Neuristor—A Novel Device and System Concept,” Proc. IRE =50=:2048-2060 (Oct. 1962)

3. Harmon, L. D., Levinson, J., and Van Bergeijk, W. A., “Analog Models of Neural Mechanism,” IRE Trans. on Information Theory =IT-8=:107-112 (Feb. 1962)

4. Widrow, B., and Hoff, M. E., “Adaptive Switching Circuits,” Stanford Electronics Lab Tech Report 1553-1, June 1960

5. Stewart, R. M., “Electrochemical Wave Interactions and Extensive Field Effects in Excitable Cellular Structures,” First Pasadena Invitational Symposium on Self-Organizing Systems, Calif. Institute of Technology, Pasadena, Calif., 14 Nov. 1963

6. Nagy, G., “A Survey of Analog Memory Devices,” IEEE Trans. on Electronic Cmptrs. EC-12:388-393 (Aug. 1963)

7. Widrow, B., “An Adaptive Adaline Neuron Using Chemical Memistors,” Stanford Electronics Lab Tech Report 1553-2, Oct. 1960

8. Vendelin, G. D., “A Solid State Adaptive Component,” Stanford Electronics Lab Tech Report 1853-1, Jan. 1963

9. “Solion Principles of Electrochemistry and Low-Power Electrochemical Devices,” Dept. of Comm., Office of Tech. Serv. =PB= 131931 (U. S. Naval Ord. Lab., Silver Spring, Md., Aug. 1958)

Selection of Parameters for Neural Net Simulations