Response probability and latency: a straight line, an operational definition of meaning and the structure of short term memory

The functional relationship between response probability and time is investigated in data from Rubin, Hinton and Wenzel (1999) and Anderson (1981). Recall/recognition probabilities and search times are linearly related through stimulus presentation lags from 6 seconds to 600 seconds in the former experiment and for repeated learning of words in the latter. The slope of the response time vs. probability function is related to the meaningfulness of the items used. The Rubin et al data suggest that only one memory structure is present or that all memory structures probed show the same linear relation of response probability and time. Both sets of data also suggest that the memory items, presumably in the neocortex, have a finite effective size that shrinks in a logarithmic fashion as the time since stimulus presentation increases or the overlearning decreases, away from the start of the search. According to the logarithmic decay, the size of the memory items decreases to a couple of neurons at about 1500 seconds for recall and 1100 seconds for recognition – this could be the time scale for a short term memory being converted to a long term memory. The incorrect recall time saturates in the Rubin et al data (it is not linear throughout the experiments), suggesting a limited size of the short term memory structure: the time to search through the structure for recall is 1.7 seconds. For recognition the corresponding time is about 0.4 seconds, to compare with the 0.243 seconds given by the data analysis of Cavanagh of Sternberg-like experiments (1972)

The Atkinson-Shiffrin model is ill-defined and does not correctly describe the Murdock free recall data

The Atkinson-Shiffrin (1968) model, the de facto standard model of short term memory cited thousands of times, fits the characteristically bowed free recall curves from Murdock (1962) well. However, it is long overdue to note that it is not a theoretically convincing explanation and that it does not fit all of the experimental relationships in the Murdock data.\ud To obtain a qualitatively correct fit of the bowing I show that four model concepts have to work together. “Long term memory” is needed in the short term memory experiment, conscious or subconscious rehearsal of four items has to take place, this “rehearsal buffer” has to drop items randomly rather than according to a first-in firstout model, and the rehearsal buffer has to be empty before the experiment starts.\ud Beyond the qualitative fit to the bowed recall curves, other relationships in the data are not borne out by the model. First, the “primacy strength”, the ratio of the probability of recall of the first item to the smallest probability of recall of an intermediate item, shows a significant experimental variation with presentation rate but no such variation is predicted by theory. Second, randomly emptying the rehearsal buffer predicts incorrectly that the number of recalled items should be the highest when the first recalled item is the last list item. Third, a simplified Atkinson-Shiffrin model is found to predict exact relationships between the recall probabilities of the initial items which do not seem to be borne out by the Murdock data. Fourth, the theory predicts a discontinuity in the differences between free recall graphs with different presentation rates for early list items which is probably not found in the Murdock data

Word Free Recall Search Scales Linearly With Number of Items Recalled

I find that the total search time in word free recall, averaged over item position, increases linearly with the number of items recalled. Thus the word free recall search algorithm scales the same as the low-error recognition of integers (Sternberg, 1966). The result suggests that both simple integer recognition and the more complex word free recall use the same search algorithm. The proportionality constant of 2-4 seconds per item (a hundred times larger than for integer recognition) is a power function of the proportion not remembered and seems to be the same function for word free recall in young and old subjects, high and low presentation rates and delayed and immediate free recall. The linear scaling of the search algorithm is different from what is commonly assumed to be the word free recall search algorithm, search by random sampling. The linearity of the word free recall extends down to 3 items which presents a challenge to the prevalent working memory theory in which 3-5 items are proposed to be stored in a separate high-availability store

Initial Free Recall Data Characterized and Explained By Activation Theory of Short Term Memory

The initial recall distribution in a free recall experiment is shown to be predictably different from the overall free recall distribution including an offset which can cause the least remembered items to be almost completely absent from the first recall. Using the overall free recall distribution as input and a single parameter describing the probability of simultaneous reactivated items per number of items in the presented list, activation theory not only qualitatively but quantitatively describes the initial recall distributions of data by Murdock (1962) and Kahana et al (2002). That the initial free recall can be simply explained in terms of the overall recall suggests that theories of memory based on interference or other context sensitive information are false since knowledge of the future would have to be incorporated to predict the initial recall

The Short Term Memory Structure In State-Of-The Art Recall/Recognition Experiments of Rubin, Hinton and Wentzel

Properties of a short term memory structure are discovered in the data of Rubin, Hinton and Wenzel (1999): Recall (recognition) probabilities and search times are linearly related through stimulus presentation lags from 6 seconds to 600 (350) seconds. This data suggest that only one memory structure is present in the Rubin, Hinton and Wenzel data. The data also suggest that the memory items have a finite effective size that shrinks to zero in a logarithmic fashion as the time since stimulus presentation increases, away from the start of the search. According to the logarithmic decay, the size of the memory items decreases to a couple of neurons at about 1200 seconds for recall and 350 seconds for recognition – this should be the time scale for a short term memory being converted to a long term memory. The incorrect recall time saturates, suggesting a limited size of the short term memory structure: the time to search through the structure for recall is 1.7 seconds. For recognition the corresponding time is about 0.4 seconds, a non-Sternberg experimental result to compare with the 0.243 seconds given by Cavanagh (1972))

Short Term Memory May Be the Depletion of the Readily Releasable Pool of Presynaptic Neurotransmitter Vesicles

The Tagging/Retagging model of short term memory was introduced earlier (1) to explain the linear relationship that exists between response time and correct response probability for word recall and recognition: At the initial stimulus presentation words tag the corresponding long term memory locations. The tagging process is linear in time and takes about one second to reach a tagging level of 100%. After stimulus presentation the tagging level decays logarithmically with time to 50% after 14 seconds and to 20% after 220 seconds. If a probe word is reintroduced the tagging level has to go back to 100% for the word to be properly identified, which leads to a delay in response time. This delay is proportional to the tagging loss which is in turn directly related to the decrease in probability of correct word recall and recognition.\ud Evidence suggests that the tagging level is the level of depletion of the Readily Releasable Pool (RRP) of neurotransmitter vesicles at presynaptic terminals. The evidence includes the initial linear relationship between tagging level and time as well as the subsequent logarithmic decay of the tagging level. The activation of a short term memory may thus be the depletion of RRP (exocytosis) and short term memory decay may be the ensuing recycling of the neurotransmitter vesicles (endocytosis).\u

Murdock free recall data: The initial recall search identifies the context by the location of the least remembered item and produces only better remembered items in proportion to the total recall difference.

The curious free recall data of Murdock (1962) shows an additional surprise that seems to have gone undetected until now: the probability of guessing an item in the initial recall is not identical to the overall free recall curve. Initial recall of an item is well correlated with the total recall of that item using a straight line but with an unexpected offset. The offset varies with the presentation rate and the total number of list items but in each case it is the same as the total recall probability of the least recalled item. Thus for the initial “freest” of recalls the location of the least remembered item is identified, in effect identifying the context, and from there the items recalled are those better remembered items, in proportion to the probability of total recall. Within the tagging/retagging model (Tarnow, 2008, 2009) the free recall starts by an identification of a discontinuity in the activity level and produces an item with a probability according to the relative activity level. \ud I speculate that the activation level and its discontinuity is detected by glial cells assisting in rebuilding post-activation empty presynaptic neurotransmitter vesicles