What’s magic about magic numbers? Chunking and data compression in short-term memory

Mathy, Fabien; Feldman, Jacob

doi:10.1016/j.cognition.2011.11.003

Cited by 224 publications

(192 citation statements)

References 97 publications

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“…We defer the task of comparing variants of the TBRS2 to future research, as it is not the main goal of the current study. Using Theorem 4, we derived participantwise estimates of the simple span and found that, although we imposed only loose constraints on this simple span, the resulting estimates are in line with previous research, suggesting a simple span of 5-9 (Mathy & Feldman, 2012;Miller, 1956). In fact, only two participants did not fall within this range.…”

Section: Discussionsupporting

confidence: 68%

Mathematical transcription of the ‘time‐based resource sharing’ theory of working memory

Gauvrit

Mathy

2017

Brit J Math & Statis

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The time-based resource sharing (TBRS) model is a prominent model of working memory that is both predictive and simple. TBRS is a mainstream decay-based model and the most susceptible to competition with interference-based models. A connectionist implementation of TBRS, TBRS*, has recently been developed. However, TBRS* is an enriched version of TBRS, making it difficult to test general characteristics resulting from TBRS assumptions. Here, we describe a novel model, TBRS2, built to be more transparent and simple than TBRS*. TBRS2 is minimalist and allows only a few parameters. It is a straightforward mathematical transcription of TBRS that focuses exclusively on the activation level of memory items as a function of time. Its simplicity makes it possible to derive several theorems from the original TBRS and allows several variants of the refresh process to be tested without relying on particular architectures.

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Section: Discussionsupporting

confidence: 68%

Mathematical transcription of the ‘time‐based resource sharing’ theory of working memory

Gauvrit

Mathy

2017

Brit J Math & Statis

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“…Hence, classically, items that constitute a chunk are either simultaneously presented or in immediate succession (e.g., Bor & Owen, 2007;Cowan et al, 2004;Chen & Cowan, 2005;Gobet & Clarkson, 2004;Mathy & Feldman, 2012). However, as we have seen earlier, a well-established WM paradigm that has shown its ability to predict high-level cognition is precisely one in which processing phases are interleaved between successive memoranda.…”

Section: Wm Maintenance Mechanisms Contributing To Recall Performancementioning

confidence: 99%

“…For Miller, this recoding mechanism is Ban extremely powerful weapon for increasing the amount of information that we can deal with^ (Miller, 1956, p. 95). Even if the WM storage limitation and its value were discussed in recent decades, a WM capacity of about three or four chunks seems now to be widely accepted (Chen & Cowan, 2005;Cowan, 2001;Cowan, Chen, & Rouder, 2004;Gobet & Clarkson, 2004;Mathy & Feldman, 2012).…”

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confidence: 99%

“…When studying the effects of chunks in immediate memory, 1 paradigms with sequential or simultaneous presentation of memoranda are preferred (e.g., Bor & Owen, 2007;Chen & Cowan, 2005;Cowan et al, 2004;Gobet & Clarkson, 2004;Mathy & Feldman, 2012;but, see Naveh-Benjamin, Cowan, Kilb, & Chen, 2007). The consequence is that WM and chunking have been living parallel experimental lives.…”

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confidence: 99%

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Promoting the experimental dialogue between working memory and chunking: Behavioral data and simulation

et al. 2015

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Working memory (WM) is a cognitive system allowing short-term maintenance and processing of information. Maintaining information in WM consists, classically, in rehearsing or refreshing it. Chunking could also be considered as a maintenance mechanism. However, in the literature, it is more often used to explain performance than explicitly investigated within WM paradigms. Hence, the aim of the present paper was (1) to strengthen the experimental dialogue between WM and chunking, by studying the effect of acronyms in a computer-paced complex span task paradigm and (2) to formalize explicitly this dialogue within a computational model. Young adults performed a WM complex span task in which they had to maintain series of 7 letters for further recall while performing a concurrent location judgment task. The series to be remembered were either random strings of letters or strings containing a 3-letter acronym that appeared in position 1, 3, or 5 in the series. Together, the data and simulations provide a better understanding of the maintenance mechanisms taking place in WM and its interplay with long-term memory. Indeed, the behavioral WM performance lends evidence to the functional characteristics of chunking that seems to be, especially in a WM complex span task, an attentional time-based mechanism that certainly enhances WM performance but also competes with other processes at hand in WM. Computational simulations support and delineate such a conception by showing that searching for a chunk in long-term memory involves attentionally demanding subprocesses that essentially take place during the encoding phases of the task.

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“…For instance, one could split the sequence "AAABABABA" into the two substrings "AAA" and "BABABA". Very much in line with this idea, Mathy and Feldman (2012) provided evidence for the hypothesis that chunks are units of "maximally compressed code". In the above situation, both "AAA" and "BABABA" are supposedly of low complexity, and the chunks tailored to minimize the length of the resulting compressed information.…”

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confidence: 48%

Algorithmic complexity for psychology: a user-friendly implementation of the coding theorem method

et al. 2015

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Kolmogorov-Chaitin complexity has long been believed to be impossible to approximate when it comes to short sequences (e.g. of length 5-50). However, with the newly developed coding theorem method the complexity of strings of length 2-11 can now be numerically estimated. We present the theoretical basis of algorithmic complexity for short strings (ACSS) and describe an R-package providing functions based on ACSS that will cover psychologists' needs and improve upon previous methods in three ways: (1) ACSS is now available not only for binary strings, but for strings based on up to 9 different symbols, (2) ACSS no longer requires time-consuming computing, and (3) a new approach based on ACSS gives access to an estimation of the complexity of strings of any length. Finally, three illustrative examples show how these tools can be applied to psychology. Keywords Algorithmic complexity · Randomness · Subjective probability · Coding theorem method Randomness and complexity are two concepts which are intimately related and are both central to numerous recent developments in various fields, including finance (Taufemback et al., 2011, Brandouy et al., 2012, linguistics (Gruber, 2010;Naranan, 2011), neuropsychology (Machado et al., 2010;Fernández et al., 2011Fernández et al., , 2012, psychiatry (Yang and Tsai, 2012;Takahashi 2013), genetics (Yagil, 2009;Ryabko et al. 2013), sociology (Elzinga, 2010 and the behavioral sciences (Watanabe et al., 2003;Scafetta et al., 2009). In psychology, randomness and complexity have recently attracted interest, following the realization that they could shed light on a diversity of previously undeciphered behaviors and mental processes. It has been found, for instance, that the subjective difficulty of a concept is directly related to its "boolean complexity", defined as the shortest logical description of a concept (Feldman, 2000(Feldman, , 2003(Feldman, , 2006. In the same vein, visual detection of shapes has been shown to be related to contour complexity (Wilder et al., 2011).More generally, perceptual organization itself has been described as based on simplicity or, equivalently, likelihood (Chater, 1996;Chater and Vitányi, 2003), in a model reconciling the complexity approach (perception is organized to minimize complexity) and a probability approach (perception is organized to maximize likelihood), very much in line with our view in this paper. Even the perception of similarity may be viewed through the lens of (conditional) complexity (Hahn et al., 2003).Randomness and complexity also play an important role in modern approaches to selecting the "best" among a set of candidate models (i.e., model selection; e.g., Myung et Behav Res (2016) 48:314-329 315 al., 2006Kellen et al., 2013), as discussed in more detail below in the section called "Relationship to complexity based model selection".Complexity can also shed light on short term memory storage and recall, more specifically, on the process underlying chunking. It is well known that the short term memory span lies b...

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What’s magic about magic numbers? Chunking and data compression in short-term memory

Cited by 224 publications

References 97 publications

Mathematical transcription of the ‘time‐based resource sharing’ theory of working memory

Mathematical transcription of the ‘time‐based resource sharing’ theory of working memory

Promoting the experimental dialogue between working memory and chunking: Behavioral data and simulation

Algorithmic complexity for psychology: a user-friendly implementation of the coding theorem method

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