Threshold Properties of Memory

Nina Nikolaevna Korzh graduated from the Psychology Department of the Faculty of Philosophy at Moscow State University (MSU) in 1958. Her scientific supervisor was Professor E.N. Sokolov, a world-renowned psychophysiologist, Academician of the USSR Academy of Pedagogical Sciences of the USSR (Russian Academy of Education). She returned to him for postgraduate studies in 1961 after three years of work at the Institute of Pediatrics of the USSR Academy of Medical Sciences, where she studied the age-related characteristics of fatigue in schoolchildren during learning activities under the direction of the institute’s director, Academician G.N. Speransky. Co-authoring with him, Nina Nikolaevna published an article in the Proceedings of the USSR Academy of Medical Sciences while still a very young scientist. After defending her PhD (Psychology) dissertation in 1964, she worked for 10 years in the Department of Psychiatry at the Institute for Advanced Medical Training of the USSR Academy of Medical Sciences, investigating problems of schizophrenia using a battery of psychological, clinical, and electrophysiological methods (including EEG recording), which she mastered.

The greater part of Nina Nikolaevna’s scientific career, starting from 1974, took place in the laboratories of psychophysics and cognitive processes at the Institute of Psychology of the USSR Academy of Sciences (Russian Academy of Sciences, RAS). As a leading research scientist, she conducted experimental-theoretical research on sensory memory and color perception and led the work of a group studying these processes.

In foreign psychophysical models of sensory processes involving learning, the influence of memory on decision-making processes was analyzed, i.e., memory was understood as one of the non-sensory factors of performance. Nina Nikolaevna studied the impact of memory on the characteristics of the sensory image itself, i.e., she investigated the sensory-perceptual level of memory, in contrast to the traditional study of its verbal level. Indeed, in tasks of detection, discrimination of sequential signals, identification and scaling, the perceived stimulus is evaluated in comparison to a response criterion stored in memory — whether it is with a previous stimulus or a standard one. The work of N.N. Korzh and her students established that information is stored in long-term memory not only in a generalized form but also in the form of individually perceived sensory features of signals. The authors’ psychophysical experiments involving delayed (from 1 ms to 2 s, and later up to days, months, and even a year) recognition of memorized simple visual and auditory stimuli among test stimuli differing from the standard in one parameter (loudness, duration, brightness, line length) yielded unexpected results. While at short delays, abrupt shifts of the sensory standard occur, during long-term storage it stabilizes and recognition accuracy increases. This contradicts theories of both trace decay and memory trace interference and is interpreted as the action of a neurophysiological mechanism of trace consolidation and activation. The effectiveness of this mechanism depends on experimental conditions and individual human characteristics, the role of which was revealed by Nina Nikolaevna.

Under the direction of N. N. Korzh, a method was developed for measuring differential auditory thresholds for sound signals that are simultaneously changing in two parameters: frequency and intensity. The method involves matching a test sound with a standard sound presented in pairs with it, or remembering it. Based on the results obtained, N.N. Korzh and Yu.P. Leonov constructed two-dimensional sensory and sensory-mnemonic spaces of auditory perception in the form of ellipses of threshold differences. Their similarity to the ellipses of color threshold differences obtained by D. Mac Adam (see Korzh, Leonov, 1990) and E.N. Sokolov, Ch.A. Izmailov (Sokolov, Izmailov, 1984), when two parameters of visible color were changed, led her to suggest that ellipticity might be a universal property of two-dimensional sensory spaces. These investigations into the structure and organization of sensory spaces made an important contribution to the realization of the main task of psychophysics, which is to clarify the principles of formation of sensory impressions. In studies by Nina Nikolaevna and her co-authors, it was discovered that errors in recognizing the hue and saturation of blue and green colors differed from errors in recognizing these features in the case of red and yellow colors. Furthermore, the reproduction of the blue color was more accurate than that of red. Theoretically, this means that the structure of the process of operating with color representations in memory differs for different parts of the color spectrum. Experiments with color naming also revealed structural heterogeneity of memory: a change in the dominance of imagistic and verbal-discrete phenomena and their transition into one another. The naming of perceived sensory-perceptual objects promotes the structuring of their subjective images and reflects individual mentality and uniqueness, the conscious and unconscious retrieval of personal memories and associations.

N.N. Korzh organized a Soviet – Swedish seminar on cognitive psychology on color perception and prepared the proceedings volume of the seminar “The Problem of Color in Psychology” (1993). She also compiled the collective monograph “Research on Memory” (1990) and the collection of scientific works “Interdisciplinary Research on Memory” (2009). Under her supervision, three Candidate of Sciences dissertations were defended.

Nina Nikolaevna’s work was continued by her followers: V.A. Sadov, N.G. Shpagonova, O.V. Safuanova, T.A. Rebeiko, E.A. Lupenko, N.V. Zubov.

Yuri Petrovich Leonov

Yuri Petrovich Leonov graduated from the Moscow Aviation Institute (MAI) and its postgraduate program, while simultaneously studying for three years at the Faculty of Mechanics and Mathematics of Moscow State University. Working for over 60 years at the Institute of Automation and Remote Control of the USSR Academy of Sciences/RAS, he concurrently lectured on signal detection theory at the Faculty of Psychology of MSU and on probability theory at the Moscow Physical-Technological Institute (MIPT), from where a number of postgraduate students came to him. He also ran the Moscow Discussion Seminar on Problems of Applied Mathematics for a number of years, which enjoyed immense popularity among specialists. Yuri Petrovich’s first scientific works received serious recognition and were published in international scientific journals.

Like Nina Nikolaevna Korzh, Yuri Petrovich Leonov collaborated for many years with Academician E.N. Sokolov in the field of psychophysics of sound and color perception, where he was engaged in the mathematical modeling of these processes. Two of Yuri Petrovich’s monographs on this topic became well-known among researchers.

The basis of Leonov’s book “Theory of Statistical Decisions and Psychophysics” (1977) was his lectures on signal detection theory at the Faculty of Psychology of MSU, in which he considered the basic concepts of psychophysics: threshold, space of sensations, scaling, etc.; from the standpoint of statistical decision theory, he substantiated the classical laws of Weber, spatial and temporal summation, and also defined the limits of applicability of detection theory for the study of perception. An analysis of the internal noise of the sensory system was conducted, and tables for its estimation for processing experimental data were provided. For the first time, relationships were established between describing the observer’s performance using receiver operating characteristics, introduced in detection theory, and psychometric functions, adopted in classical psychophysics, by modifying the latter, which was of paramount importance for experimental research. A fundamental achievement was also the justification of the applicability of statistical decision theory to the problems of subjective scaling, whereas previously these paradigms had developed independently of each other. The book proposed a new method for estimating the latent period of motor reaction.

In the 1940s-1950s, a number of phenomenological models of three-dimensional subjective color spaces were developed abroad. The transition to the neurophysiological mechanisms of color perception was made at the end of the 20th century by E.N. Sokolov, Ch.A. Chernorizov, and their co-authors, including Yu.P. Leonov, who constructed a four-dimensional spherical model of color perception based on data from a large series of experiments on the subjective scaling of color differences. On this basis, Leonov subsequently made a new step in substantiating the metrics of color spaces. Traditionally, the Euclidean metric was assumed, but it was not confirmed when measuring subjective color differences, as they did not correspond to Euclidean distances between color points. H. von Helmholtz had already suggested to use Riemannian metric, to be more general than Euclidean one, but it proved inapplicable to the linear Young-Helmholtz color space. Yu.P. Leonov managed to introduce a Riemannian metric because, in their joint model developed within E.N. Sokolov’s school, visible colors were located on the surface of a four-dimensional sphere, and Yu.P. Leonov proposed switching to the angular coordinates of this hypersphere. The conducted experiments proved that color space has Riemannian geometry. This theory is reflected in Leonov’s book “Colors in Space” (2014), which also characterizes other color spaces and empirical color systems used for defining various colors represented in atlases, and considers the characteristics of color impressions and the poorly studied spaces of colored bodies.

The works of N.N. Korzh and Yu.P. Leonov on the experimental study and theoretical modeling of sensory and sensory-mnemonic spaces have entered the golden fund of world science.

Threshold Properties of Memory

 Korzh N.N.^a, Leonov Yu.P.^b

 ^aInstitute of Psyhology of the Russian Academy of Sciences, Moscow, Russia

^bInstitute of Automation and Telemechanics, Russian Academy of Sciences, Moscow, Russia,

Korzh, N.N. & Leonov Yu.P. (1976). Threshold Properties of Memory. Advances in Psychophysics / Ed. by H.-G. Geissler, Yu. M. Zabrodin. Berlin: VEB, 1976. Pp. 195–203.

The paper was prepared by I.G. Skotnikova (Institute of Psychology of the Russian Academy of Sciences, Moscow, Russia).

Abstract: The aim of the present work was to use the statistical decision theory for describing a model of memorization and recognition of the standard stimulus. It has been shown that application of the theory to this model requires a non-monotonic function of likelihood ratio.

Introduction

An experiment was previously suggested to investigate memory function and the mechanism of decision-making (Korzh, Leonov, & Sokolov, 1969). Subjects were instructed to memorize a sound stimulus with a fixed intensity and then to respond to it. The 50 Hz stimulus, which was 25 dB above the threshold value, was used as the standard. This stimulus was presented to the participants once before the experiment. During the experiment, the standard stimulus was randomly presented among 70-80 stimuli that differed in intensity by 5-15 dB in steps of 5 dB symmetrically around the standard. The results showed that the subjects were not always able to identify the standard stimulus correctly. There were two types of errors: 1) stimuli that were not equal to the standard were sometimes perceived as being the standard; and 2) stimuli that were equal to the standard were not always identified as such. The data obtained showed that the standard was recognized by the subjects with the highest frequency (Fig. 1). We found a certain area of misinterpretation of the test stimuli. As the experiment progressed, detection improved within two or three weeks of the start. This improvement manifested itself in a reduction of the area of misperception and an increase in the frequency of the standard recognition. The experimental data are presented in the Figure 1.

Figure 1. Distribution of recognition results of the standard stimulus

Abscissa — intensities in dB of stimuli compared to the standard. Ordinate — frequencies of comparable stimuli which were recognized as equal to the standard

The aim of this study was to use statistical decision theory to describe the model of memorization and recognition of the standard stimulus. To do this, we needed to use a non-monotonic likelihood ratio function that emphasizes the importance of moving away from the concept of sensory threshold, as described by Fechner, towards the concept of a threshold based on statistical decision theory (Leonov, 1972, 1975).

Incorrect perception depends on the mechanisms of information fixation, extraction, and reproduction related to decision-making. From the perspective of statistical decision theory, individuals solve a problem by testing a simple hypothesis with two alternatives. On each stimulus, they must make a decision about whether it is a standard or non-standard stimulus. In this study, we attempted to apply statistical decision theory to a more complex scenario compared to the signal detection task, as in the noise/signal paradigm, where subjects had to compare standard stimuli stored in memory with test stimuli of varying intensities.

It may be assumed that the decision about this “standard” is made from a stimulus:

x = ∆Si + n                                                (1)

∆Si = Si – S*, where:

Si — signal intensity,

S*— standard signal intensity (contained in memory),

n — internal noise of the neuronal system.

The internal noise “n” in this equation integrates the effects of various factors on decision-making, including the imperfections in memory function when recalling the standard, as well as the imperfect comparison mechanism between the standard and test signals, and etc.

The decision on whether the presented signal is equal to the standard signal or not, that is, ∆Si = 0 or ∆Si ≠ 0, is based on the results of previous experiments included the standard audio signal. In any case, we can assume that decisions about the standard for different test signals are made independently when they are receiving as standards. According to the decision theory, a decision on a fixed standard is made based on a specific rule, which is stored in memory:

λ(x) <,> λ0                                                                (2)

λ0 — threshold (criterion) of decision making,

λ(x) — likelihood ratio.

If we use the normal a posteriori density of the probability f(x/∆Si) and f(x/S00), then the next expression may be written as:

λ(x) = f(x/∆Si)/f(x/S0)                       (3)

λ(x) = σs/σn  x  exp (1/2[x2/σn2 – (x–∆S)2/σs2]), where:

S0 = signal intensity at the sensory threshold level,

n — the internal noise of the system,

σs — the signal standard deviation of the signal ∆Si presented,

σn — the noise standard deviation when the signal ∆Si is not presented.

The study of memorization of the sound standard signal under these assumptions implies the investigation of a curve that exhibits the type of the “psychometric function”. Let a sound of the intensity S* be presented, a subject having to remember and to recognize it among signals of the intensity Si. Data obtained are presented as the theoretical probability densities of correct responses P* depending upon ∆Si = Si – S*. We assume that a subject identifies Si and S* on the basis of the value of the difference ∆Si (see Equation 1). The curve P* (∆Si) is shown in the Figure 2.

This curve is similar to the psychometric function, but it differs from the psychometric function: subjects have to remember S*and compare it in memory with the input signal intensity Si.

It is possible to study different types of memory when the interval between presentation of a sound stimulus S* and its reproduction varies.

Figure 2. The theoretical psychometric function describing the standard signal S* recognition among comparable signals Si
Abscissa — differences ∆Si between the standard signal S* and comparable signals Si. Ordinate — probability densities P* of correct responses about identification of ∆Si as = 0 or ≠ 0 (or identification of signals Si as equal or not equal to the standard signal S*)
∆S* — ∆Si = 0, i.e. Si = S*

The psychometric curve is calculated based on short-term memory. If the sound stimulus is presented only once, as in our experiment, long-term memory can be activated, and forgetting can be studied using psychometric curves obtained at different times after the beginning of presentation of the standard stimulus.

The present model can explain forgetting phenomena of the standard in addition to the function of memorization and reproduction. The process of forgetting may manifest itself in incorrect recognition of the standard. It results in a decrease in probability P_max of correct responses and an increase in the intensity zone of misperception. The process of forgetting can be described by the change (increase) in the level σ_n of the “internal” noise n. This ability is disturbed when the level of the internal noise σ_n is high. We assume that subjects use the difference ∆S_i = S_i – S* to make a decision. A more complicated model can be considered. If the decision rule of likelihood ratio (see Equation 2) is true, then the function ∆(x), is:

λ(x) = σ_s/σ_n  x  exp ([(x – S*)²/2σ₂² – (x– S_i)²/2σ₁²])                                                  (4), where:

σ₂ — the noise n standard deviation when S* is in memory,

σ₁ — the noise n standard deviation when test signals of the intensity S_i are presented.

The normal a posteriori densities f(x/∆S_i) and f(x/S₀) are used above as Equation (3). The likelihood ratio λ(x) cannot be described by a simple equation in this case. The function λ(x) is a specific feature in this model. It can be assumed that subjects use two sensory thresholds x*₁ and x*₂ for making a decision whether a stimulus x is the standard. If x*₁ ≤ x ≤ x*₂, then the decision “it is the standard” is made. If no, then it is considered that x is not the standard. This experimental situation can be described by a non-monotonic function of likelihood λ(x), which is presented in Figure 3. The sensory thresholds x*₁ and x*₂ are represented by the abscissa as corresponded to the crossing points of λ₀ to the curve λ(x).

Abscissa — stimuli x
x_st — the standard stimulus
x*₁ and x*₂ — sensory thresholds with which subjects compare each stimulus x to make a decision whether it is the standard
Ordinate — likelihood ratio λ(x)
λ₀ — threshold (criterion) of decision making

The receiver operating characteristic (ROC) of decision making corresponds to the function presented in Figure 4.

Figure 4. The receiver operating characteristic.

H1 — hypothesis about the presence of the standard,

h1 — the presence of the standard,

h2 — the presence of a stimulus different from the standard.

Abscissa — the probability P(H1/h2)

Ordinate — the probability P(H1/h1)

It should be noted that different ROCs correspond to different signal intensities Si (i = 1, 2, …, n). That is why subjects’ actions are described by a family of ROCs in this situation. Accordingly, it can be assumed that there is a family of the function λ(x), which depends on Si (Figure 3). Since λ(x) is bell-like, the standard deviations σ2 and σ1 of the densities f(x/S*) and f(x/Si) have convenient σ2/σ1 >1.

All parameters of the curve λ(x) can be determined experimentally. Indeed, if we represent this curve in decadic logarithm co-ordinates, then we can write:

ln λ0/µ = (1/2 σ22) [(x – S*)2 – µ2(x – Si)2] (5)

The criterion λ0 is determined by ROC. The parameters σ2 and µ = σ2/σ1 are calculated if x1*, x2* are known. µ is determined by the expression on the basis of equation (5) if the upper x1* and the lower x2* sensory thresholds are known:

µ2 = (x1 – S*)2 – (x2*– S*)2 / (x1*– Si)2 – (x2 – Si)2                                                                            (6)

σ1 and σ2 can be obtained from λ0.

Conclusions

The presented model of memorization and recognition is based on the statistical theory of decision-making, specifically on the concept of posterior probability. We have not used the concept of optimality, as we consider it to be less relevant for psychophysics compared to other technical sciences.

A key feature of this model is its use of a non-monotonic λ(x) function. According to the model, the statistical decision threshold (λ₀) is not equivalent to the sensory threshold (x1*) in the Weber-Fechner law, as there may be upper and lower sensory thresholds (x₁* and x₂*) that influence the decision.

In general, multiple sensory thresholds can correspond with the decision threshold λ₀. This model demonstrates the importance of using λ₀ as a criterion and its general applicability. Preliminary experiments on sound memory have shown the model’s effectiveness, but further research is needed to refine it.

References

1. Korzh, N.N., Leonov, Yu.P., & Sokolov, E.N. (1969). On memorization and recognition of a given intensity standard. Journal of Higher Nervous Activity named after I.P. Pavlov, 19(6), 989–995. In Russian. [Korzh N.N., Leonov Yu.P., Sokolov Ye.N. O zapominanii i uznavanii zadannogo etalona intensivnosti // Zhurnal VND im. I.P. Pavlova, 1969. T. 19. Vyp. 6. Str. 989–995].
2. Korzh N.N., Leonov Yu.P. (1990). The influence of memory on the metric of sensory space // Memory research / Ed. N.N. Korzh. Moscow: Nauka. Pp. 80–89. In Russian. [Korzh N.N., Leonov Yu.P. Vliyaniye pamyati na metriku sensornogo prostranstva // Issledovaniye pamyati / Pod red. N.N. Korzh. M.: Nauka, 1990. S. 80–89].
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4. Yu.P. (1975). Theory of decision making and the concept of threshold in psychophysics. Soviet Psychology, 13(3), 78–90. In Russian. [Leonov Yu.P. Teoriya prinyatiya resheniy i ponyatiye poroga v psikhofizike // Sovetskaya psikhologiya, 1975. T. 13. Vyp. 3. S. 78–90].
5. Sokolov E.N., Izmailov Ch.A. (1984). Color vision. Moscow: Moscow State University Press, 1984. In Russian. [Sokolov Ye.N., Izmaylov CH.A. Tsvetovoye zreniye. M.: Izd-vo MGU].