ON THE PROBLEM OF PATTERN RECOGNITION

Yu. K. Petrov

(Presented by the scientific seminar of the Faculty of Automation and Computer Engineering)

Statement of the Problem

In the second signal system a correspondence is established between the word \(\alpha\) and a set of material objects—\(A\)

\[ A=\{A_1;\ A_2;\ A_3;\ A_4\ldots\}, \]

where \(A_i\) are individual representatives of an infinite set of material objects. For example, if the symbol \(\alpha\) denotes the word apple, then \(A\) consists of individual apples. Each object is the bearer of a set of properties \(a, b,\) (Fig. 1), which are expressed in signal form and can be perceived by the first signal system. One can learn to recognize any representative of the set \(A\) only by isolating the subset of common properties

\[ \mathfrak{A}\subset A_i,\quad \mathfrak{U}=A_i \]

and by somehow attaching this subset to the word.
With reference to Fig. 1,

\[ \mathfrak{U}=\{r,\ e,\ z,\ u\}. \]

Strictly mathematically, the subset \(\mathfrak{U}\) should not contain the element \(z\); however, abstraction in biological systems is performed under conditions of the accidental absence of certain common features. The problem of abstraction is not essentially a human problem: every animal, in order to find food, must abstract the common properties of food objects. Thus the mechanism of abstraction must be very simple and must exclude intelligence.

Description of the model. According to I. M. Sechenov’s theory, the behavior of humans and animals is reflexive, i.e., it arises in response to irritation from the external environment, perceived immediately before the behavioral act or in the past. In Fig. 2 the Roman numeral “one” denotes the first signal system, which perceives signals of the material environment. The first signal system is a set of analyzers \(a'\), \(b'\), \(v'\), ... Each analyzer consists of a receptor that directly perceives an external signal and excites one nerve cell—

Fig. 1.

in the higher divisions of the brain. In the figure these cells are denoted by small circles. Receptors are specialized for the perception of signals of a definite kind of energy and spectrum and cannot perceive signals of another kind of energy and spectrum. For example, certain cones in the retina of the eye perceive only red rays of the light spectrum. They cannot perceive blue rays, still less sound vibrations. Only thanks to the specialization of receptors does the analyzer system form a logical field in which the primary and, in our opinion, final analysis of external signals takes place. For example, a total signal, complex in spectrum, ordinarily acts on the eardrum.

In the organ of Corti, each component frequency of the total signal excites its adequate resonator and, in this way, the signal is decomposed into components and the signal is analyzed. Since, upon repeated perceptions, identical signals are directed in sensations along the same channels, in the first signaling system a certain analogue of the table in Fig. 1 is constructed, so that signals $a$ are always recorded in column $a'$, signals $b$ in $b'$, and so on.

Fig. 2. Diagram of a biological model that automatically performs the operation of abstraction

As a result of the adaptation of organisms to the conditions of existence, a system of behavioral acts is developed in them. In Fig. 2 the system of behavioral acts is denoted by the Roman numeral two, and the behavioral acts themselves by the letters $a$–$\omega$. These are complex behavioral acts associated with finding and taking food, with exploring the surrounding environment, and with the functions of defense and reproduction. The second signaling system forms such behavioral acts, the result of which is worked out in signal form and can be perceived by the first signaling system. Feedback of this kind is shown in the figure by a dotted line. Already in higher animals the rudiments of a second signaling system appear, but only in man does the second signaling system attain extraordinary development.

The reflex connection between the first signaling system and the system of behavioral acts is established in the higher divisions of the brain; moreover, each behavioral act is included by its own pyramidal cell (shown in the diagram as a triangle). The pyramidal cells are collectively excited by the cells of the first signaling system (shown in the diagram as small circles). Neurons possess a system of dendritic processes that end in plaques on other neurons or on the dendritic processes of neurons. In Fig. 2 the neuron with a receptor is connected by plaques with all the other neurons. All the other neurons of the first signaling system possess the same connections. These connections are not shown in the figure. The abundance of connections corresponds to reality: some neurons have tens of thousands of dendritic processes.

A neuron is a threshold element and is excited as a result of the total action of all plaques through synapses. A neuron may also be excited through a single synapse if the resist—

there is little synapse resistance. It is precisely in this way that receptors are connected with their neurons, and this connection exists from birth.

Intercellular synaptic connection in the higher parts of the brain is not given from birth; it is formed through learning as a result of the organism’s adaptation to the surrounding environment. The laws governing the formation of such connections were studied in I. P. Pavlov’s experiments on conditioned reflexes (associations by simultaneity). In his experiments on dogs, for example, simultaneously with the presentation of food, or somewhat earlier, a signal was given by a bell. After repeated repetitions of the experiment, salivation in the dog began at the signal of the bell and was no less active than at the sight of the food itself.

Thus, the alimentary reflex is evoked by an indifferent stimulus that objectively had no relation whatever to food. If the conditioned stimulus is not experimentally reinforced, then its effect disappears with time. In I. P. Pavlov’s experiments the fundamental properties of memory are revealed. Any sensations at all are connected by memory if they appear jointly many times.

There is a theory according to which memory is associated with a plastic change in the resistance of synapses. Let us suppose that in the higher parts of the brain the initial resistance of synapses is so great that plaques, even collectively, cannot excite neurons. The cells indicated in the diagram by small circles can be excited only by external signals. It is natural to suppose that when a neuron is excited, the soma of the cell and its peripheral parts are charged with charges of different signs. Let us assume, without impairing the generality of the reasoning, that the soma acquires a negative charge, and the plaques a positive one. Then, under the action of signals, situations may arise that are indicated in Fig. 3 by the numbers 1, 2, and 3. Let us suppose that in the first and second cases (Fig. 3) the synapse is practically not deformed, and only in the situation marked by the number 3 in Fig. 3, when both cells separated by the synapse are excited simultaneously, does the synapse begin to conduct current and plastic deformation is formed in it. Plastic changes are eliminated as a result of metabolism; however, if situation 3 in Fig. 3 is repeated often, the plastic effect will accumulate, and as a result of repeated actions the neuron will begin to be excited by a single synapse in situation 2 of Fig. 3. Through adaptation, the rate of restoration of synapse resistances is established such that only the signals most frequently coinciding in time form connections in the synapses.

Fig. 3.

The model constructed in this way automatically performs the operation of abstraction.

Mechanism of abstraction. Let us suppose that certain sets of signals act successively in time on the first signal system (Fig. 1). Let each set be determined by the fact that it acts on the first signal system simultaneously. Let us suppose that the set of signals in each set is random both with respect to type of energy and spectrum; however, there exists some subset of adequate signals that is present in each set: a common subset of adequate signals. In this case inadequate signals will not be perceived at all. For example, the first signal system of a human being does not perceive infrared rays and ultrasound. Random adequate signals will evoke ephemeral connections of neurons, which co

will disintegrate over time. And only the common subset of adequate signals г, е, з, и in Fig. 1 will produce a lasting connection of elementary sensations in the representation. Thus the extraction of common properties, generalization, and abstraction take place.

Such abstraction is performed without any additional psychic or mental activity if the image perceived in sensations does not depend on the mutual position of subject and object in space. Let us call this condition the condition of invariance of the image. Obviously, the organs of hearing, the organs of taste, the organs of vision as regards color perception, and the organs of smell possess invariance of the image. The organs of vision, as regards perception of form, do not possess invariance of the image. The formation of representations of the form of objects is apparently accompanied by complex psychic activity.

The process described takes place in the sphere of the first signal system, without affecting behavioral acts. This does not contradict the teaching of I. P. Pavlov. I. P. Pavlov notes that the capacity of memory to bind together two sensations independently of behavioral acts has been established experimentally.

Formation of the rudiments of the second signal system. Such rudiments appear in higher animals and in man when he learns to speak. We shall show that generalized representations, formed in the sphere of the first signal system, also serve as those signals of the material environment that include any behavioral acts, including acts connected with the utterance of a word. In this case such connections are formed that the generalized image $\mathcal U$ evokes the behavioral act $\alpha$, while the generalized image $\mathfrak S$ evokes the behavioral act $\beta$. For example, the generalized image of an apple evokes the word apple, and the generalized image of a human being evokes the word human being. Such connections can be established by means of association by simultaneity; it is only necessary that the pyramidal cell that evokes the behavioral act $\alpha$ and the generalized image $\mathcal U$ be excited simultaneously. Simultaneity is ensured by feedback through the material environment.

In the first months of life the child does not distinguish words from the general background of other sounds that come from animate and inanimate objects. Words are devoid for him of any semantic content. The mother teaches the child to speak. She pronounces a word often so that the child will remember it. She pronounces the word in a meaningful situation; for example, the word “apple” is pronounced when the child is eating or holding an apple. The word “apple” is pronounced many times and each time simultaneously with the perception of an apple, and in this process memory binds into a single neurophysiological complex the sensations connected with the perception of the word “apple,” and the taste of the apple, and its smell, and its color, and its form. At a certain period of development the neurophysiological complex begins to be excited as a whole when some part of it is excited. It is especially easily excited upon perception of the word. The mother pronounces the words “do you want an apple,” and the child recalls the taste, color, and smell of the apple and expresses his desires in emotions.

When the child learns to speak, he himself pronounces the word and himself perceives it with his first signal system. In this case the entire generalized image is excited, and an association is established between the generalized image and the behavioral act. The association by simultaneity is established in the feedback connections of the corresponding pyramidal cells (Fig. 1). As a result of internal feedback connections, when the word is mentally pronounced, the entire generalized image is excited and the connections in the synapses are consolidated. Owing to the fact that pyramidal cells are threshold devices, and the connections in the synapses are estab-

are fused in such a way that a neuron is excited only under collective action; the same cells of the first signal system, in different combinations, include different behavioral acts.

We propose that the behavioral act associated with the utterance of a word and the generalized representations associated with it, which reflexively evoke this behavioral act, be called a realia. And the generalized representations that constitute the semantic content of a realia should be called the real content of the word. As many realia are formed as there are words denoting perceived objects. The formation of realia begins in childhood and continues in every act of perception throughout a person’s conscious life.

The common properties of objects are condensed by memory into realia, and the objective world is reflected in the ideal verbal form of thinking through realia, as through lenses, in whose focus the common properties of objects are gathered.

The possibility of technical implementation of the model. The specialization of human receptors is so diverse and complex that to manufacture such a system in its entirety at the present level of technology is apparently impossible. However, a system of analyzers of sound vibrations can already be built now, and machines that recognize sound patterns are especially necessary for organizing communication between humans and high-speed digital computers.

The model contains a multitude of elements of the same type for modeling neurons and synapses. Majority elements—analogues of neurons—have been developed and are used in perceptrons. The plastic properties of synapses are modeled, for example, by means of memistors [2, 3]. The resistance of a memistor is varied between a carbon electrode and a wire. Each time current passes, copper is deposited on the graphite electrode, thereby reducing the resistance between the wire and the electrode. If such an element is supplemented by some chemical process that will slowly destroy the copper coating, then the analogue of a synapse needed for our model will be obtained. The adaptation of organisms to the environment can be replaced by adaptation of the environment to the model. For this it is necessary to supply sound patterns to the receptors of the model at such time intervals that the action of common signals accumulates, while the action of random signals dissipates.

Neurons possess the property of refractoriness: after a period of neuronal activity there follows a period of complete inertia, when the neuron is not excited at all. Refractoriness can be modeled, for example, by a capacitor that is charged from a source of constant voltage through a very large resistance and discharged through a valve with a firing threshold. The refractory period will be determined by the charging time of the capacitor up to the firing-threshold voltage of the valve. If the model is provided with neurons with refractoriness, and the pyramidal cells are connected by links in such a way that excitation of one cell forbids excitation of all the other cells, then as a result of the action of external signals some analogue of behavior will be developed in the model: $\beta \to \gamma \to \omega \to \ldots$ With the actuating organs disconnected, such behavior will be ensured by internal feedbacks.

In addition to key generalized signals, the first signal system of animals is acted upon by a mass of other signals that lower the firing thresholds of neurons, and thus an orienting efferentation is created. Orienting efferentation can be studied-

modeled. Innate efferentation is connected with the biological needs of organisms and is not modeled by means of the device we have proposed.

REFERENCES

1. V. P. Sochivko. Electrical Models of Neurons. Library on Automation. Energiya Publishing House, 1965.

2. V. P. Sochivko, V. S. Otrishko. An electrochemical memistor as a synapse of a plastic neuron. Abstracts of papers of the 18th Scientific and Technical Conference devoted to Radio Day. LPI Publishing House, Leningrad, 1963.

3. B. U. Droу, U. Kh. Piro, I. B. Anjel. Birth, life, and death of microelectronic systems. Foreign Radio Electronics, No. 6, 1962.