Chunks in expert memory: evidence for the magical number four ... or is it two?

This study aims to test the divergent predictions of the chunking theory (Chase & Simon, 1973) and template theory (Gobet & Simon, 1996a, 2000) with respect to the number of chunks held in visual short-term memory and the size of chunks used by experts. We presented game and random chessboards in both a copy and a recall task. In a within-subject design, the stimuli were displayed using two presentation media: (a) physical board and pieces, as in Chase and Simon's (1973) study; and (b) a computer display, as in Gobet and Simon's (1998) study. Results show that, in most cases, no more than three chunks were replaced in the recall task, as predicted by template theory. In addition, with game positions in the computer condition, chess Masters replaced very large chunks (up to 15 pieces), again in line with template theory. Overall, the results suggest that the original chunking theory overestimated short-term memory capacity and underestimated the size of chunks used, in particular with Masters. They also suggest that Cowan's (2001) proposal that STM holds four chunks may be an overestimate.     

Recall memory for visually presented chess positions

A series of three experiments replicated and extended earlier research reported by Chase and Simon (1973), de Groot (1965), and Charness (Note 1). The first experiment demonstrated that the relationship between memory for chess positions and chess skill varies directly with the amount of chess-specific information in the stimulus display. The second experiment employed tachistoscopic displays to incrementally "build" tournament chess positions by meaningful or nonmeaningful chunks and demonstrated that meaningful piece groupings during presentation markedly enhance subsequent recall performance. The third experiment tested memory for one of two positions presented in immediate sequence and demonstrated that explanations based on a limited-capacity short-term memory (Chase & Simon, 1973) are not adequate for explaining performance on this memory task.     

Five Seconds or Sixty? Presentation Time in Expert Memory

For many years, the game of chess has provided an invaluable task environment for research on cognition, in particular on the differences between novices and experts and the learning that removes these differences, and upon the structure of human memory and its paramaters. The template theory presented by Gobet and Simon based on the EPAM theory offers precise predictions on cognitive processes during the presentation and recall of chess positions. This article describes the behavior of CHREST, a computer implementation of the template theory, in a memory task when the presentation time is varied from one second to sixty, on the recall of game and random positions, and compares the model to human data. Strong players are better than weak players in both types of positions, especially with long presentation times, but even after brief presentations. CHREST predicts the data, both qualitatively and quantitatively. Strong players' superiority with random positions is explained by the large number of chunks they hold in LTM. Their excellent recall with short presentation times is explained by templates, a special class of chunks. CHREST is compared to other theories of chess skill, which either cannot account for the superiority of Masters in random positions or predict too strong a performance of Masters in such positions.     

Chess players' recall of auditorily presented chess positions

Abstract

Chess players' recall of auditorily presented chess positions were studied in three experiments. The results of the first two experiments showed that the skilled chess players are better at recalling game and random positions. This contradicts the standard finding that they perform better only in game positions. In the third experiment, the memory load was increased by increasing the number of positions to be recalled simultaneously from one to four positions. Skilled subjects are still far better at recalling game positions, but they score no more than moderately skilled subjects in recalling four random positions.

The results are in contradiction with the direct chunking hypothesis. Skilled chess players do not fail to recall random positions because there are no chunks in them, but because they are not, under some special conditions, able to encode them properly. It is necessary to postulate more complicated encoding mechanisms than a simple recognition-based activation of a chunk in long-term memory.     

Chunking in recall of symbolic drawings

Three experiments explored memory for symbolic circuit drawings using skilled electronics technicians and novice subjects. In the first experiment a skilled technician reconstructed circuit diagrams from memory. Recall showed marked “chunking”, or grouping, by functional units similar to Chess Masters’ recall of chess positions. In the second experiment skilled technicians were able to recall more than were novice subjects following a brief exposure of the drawings. This advantage did not hold for randomly arranged symbols. In the third experiment the size of chunks retrieved systematically increased with additional study time. Supplementary analyses suggested that the chunking by skilled subjects was not an artifact of spatial proximity and chunk statistics, and that severe constraints are placed on any explanation of the data based on guessing. It is proposed that skilled subjects identify the conceptual category for an entire drawing, and retrieve elements using a generate-and-test process.     

The role of constraints in expert memory

A great deal of research has been devoted to developing process models of expert memory. However, K. J. Vicente and J. H. Wang (1998) proposed (a) that process theories do not provide an adequate account of expert recall in domains in which memory recall is a contrived task and (b) that a product theory, the constraint attunement hypothesis (CAH), has received a significant amount of empirical support. We compared 1 process theory (the template theory; TT; F. Gobet & H. A. Simon, 1996c) with the CAH in chess. Chess players (N=36) differing widely in skill levels were required to recall briefly presented chess positions that were randomized in various ways. Consistent with TT, but inconsistent with the CAH, there was a significant skill effect in a condition in which both the location and distribution of the pieces were randomized. These and other results suggest that process models such as TT can provide a viable account of expert memory in chess.     

Recall or evaluation of chess positions revisited: the relationship between memory and evaluation in chess skill

We extend work by Holding and Reynolds (1982) on recall and problem solving with quasirandom chess positions. We tested 17 chess players on both quasirandom and structured chess positions. Consistent with the earlier study, initial recall of quasirandom chess positions is unrelated to chess skill level, and quality of the move selected in subsequent problem solving is related to skill level. However, recall following problem solving is related to chess skill level. These results support the view that pattern recognition processes underlie superior performance by skilled chess players, contrary to the conclusions of Holding and Reynolds (1982). Mechanisms such as long-term working memory retrieval structures (Ericsson & Kintsch, 1995) or templates (Gobet & Simon, 1996a) could explain the effective encoding of quasirandom positions during problem solving.     

Skilled perception in Go: Deducing memory structures from inter-response times

Experts appear able to handle much larger amounts of specialized information than nonexperts, and handle it without an apparent superior memory capacity. This finding, based on research on chess players with chess information, was replicated on Go players with Go information. Assuming this superiority occurs because the experts process chunks of information through their limited capacities rather than individual elements, the question then becomes one of defining what the chunks are and how they are related. To this end, the technique of partitioning recall and reproduction data into chunks on the basis of inter-response times (IRTs) (introduced in their work on chess by Chase and Simon, 1973) was applied to the reproduction and recall of Go patterns by a Go Master and a Go beginner. Unlike its application in chess, no single IRT was able to produce consistent, veridical chunks for either Go player. Subsequent analysis of the underlying assumptions of the technique showed it to be limited to only those patterns that can be partitioned into a linear set of chunks, not nested chunks, and to situations in which retrieval and overt recall of each chunk is completed before retrieval of the next chunk. In a supplementary task, the Master Go player indicated that the Go patterns were not seen as linear chunks nor as strictly nested hierarchies, but rather as overlapping clusters. IRTs were found to be correlated with this structure, but were not reliable enough to reflect its details.     

Experts’ memory superiority for domain-specific random material generalizes across fields of expertise: A meta-analysis

Experts’ remarkable ability to recall meaningful domain-specific material is a classic result in cognitive psychology. Influential explanations for this ability have focused on the acquisition of high-level structures (e.g., schemata) or experts’ capability to process information holistically. However, research on chess players suggests that experts maintain some reliable memory advantage over novices when random stimuli (e.g., shuffled chess positions) are presented. This skill effect cannot be explained by theories emphasizing high-level memory structures or holistic processing of stimuli, because random material does not contain large structures nor wholes. By contrast, theories hypothesizing the presence of small memory structures—such as chunks—predict this outcome, because some chunks still occur by chance in the stimuli, even after randomization. The current meta-analysis assessed the correlation between level of expertise and recall of random material in diverse domains. The overall correlation was moderate but statistically significant (\( \overline{r} = .41,p < .001 \)), and the effect was observed in nearly every study. This outcome suggests that experts partly base their superiority on a vaster amount of small memory structures, in addition to high-level structures or holistic processing.     

Mental imagery and chunks: Empirical and computational findings

To investigate experts' imagery in chess, players were required to recall briefly presented positions in which pieces were placed on the intersections between squares (intersection positions). Position types ranged from game positions to positions in which both the piece distribution and the location were randomized. Simulations were run with the CHREST model (Gobet & Simon, 2000). The simulations assumed that pieces had to be centered back, one by one, to the middle of the squares in the mind's eye before chunks could be recognized. Consistent with CHREST's predictions, chess players (N = 36), ranging from weak amateurs to grandmasters, exhibited much poorer recall for intersection positions than for standard positions (pieces placed on the centers of the squares). For the intersection positions, the skill difference in recall was larger for game positions than for the randomized positions. The participants recalled bishops better than they recalled knights, suggesting that Stroop-like interference impairs recall of the latter. The data supported both the time parameter in CHREST for shifting pieces in the mind's eye (125 msec per piece) and the seriality assumption. In general, the study reinforces the plausibility of CHREST as a model of cognition.     

In search of templates

This study reflects a recent shift towards the study of early stages of expert memory acquisition for chess positions. Over the course of 15 sessions, two subjects who knew virtually nothing about the game of chess were trained to memorise positions. Increase in recall performance and chunk size was captured by power functions, confirming predictions made by the template theory [Cogn. Psychol. 31 (1996) 1; Memory 6 (1998) 225; Cogn. Sci. 24 (2000) 651]. The human data were compared to that of a computer simulation run on CHREST (Chunk Hierarchy and REtrieval STructures), an implementation of the template theory. The model accounts for the pattern of results in the human data, although it underestimates the size of the largest chunks and the rate of learning. Evidence for the presence of templates in human subjects was found.     

工作记忆中“组块”概念的演化及理论模型

在Miller提出“神奇的数字7±2”之后, “块”被很多理论作为个体工作记忆加工过程中具有稳定结构并可用于衡量记忆容量的单位。但随着研究者对“组块”研究的深入, 他们对组块的定义也在发生着改变。与此同时, 不少研究发现个体的年龄阶段与其主要采用的组块层级相对应, 但尚不清楚组块层级的转换是否存在固定的年龄区间, 且对组块机制的解释仍存在分歧。因此本文针对组块定义的发展与演变、年龄阶段特征及其机制三方面展开综合讨论。未来的研究可以更多探讨长时记忆在工作记忆组块运行机制中的作用, 完善不同年龄阶段个体的组块特征, 以及怎样发挥复述策略和“少即是多”原则在组块过程中的优势等问题。     

STM capacity for Chinese and English language materials

This paper delineates the theoretical implications of a program of research on short-term memory using Chinese characters as stimuli, and compares the findings with studies of short-term memory that use English language materials. The 14 experiments on which it is principally based, carried out in the People’s Republic of China and in the U.S.A., are reported in detail in Yu et al. (1984), W. Zhanget al. (1984), and G. Zhang and Simon (this issue). One major theoretical product of this research is an experimentally tested model that reconciles the chunking theory of STM capacity with the articulatory loop theory of Baddeley, making good quantitative predictions of capacity compatible with both. Another result, obtained by using homophones as stimuli, is a demonstration that STM is mainly acoustically encoded, but that there are an additional two or three chunks of visually or semantically encoded short-term memory available. Chunks are shown to play the same role in immediate recall and rote learning in both the Chinese language and English language stimuli; and STM capacity, measured in chunks, is essentially the same for materials in both languages.     

A Pattern-recognition Theory of Search in Expert Problem Solving

Understanding how look-ahead search and pattern recognition interact is one of the important research questions in the study of expert problem solving. This paper examines the implications of the template theory (Gobet & Simon, 1996a), a recent theory of expert memory, on the theory of problem solving in chess. Templates are “chunks” (Chase & Simon, 1973) that have evolved into more complex data structures and that possess slots allowing values to be encoded rapidly. Templates may facilitate search in three ways: (a) by allowing information to be stored into LTM rapidly; (b) by allowing a search in the template space in addition to a search in the move space; and (c) by compensating loss in the “mind's eye” due to interference and decay. A computer model implementing the main ideas of the theory is presented, and simulations of its search behaviour are discussed. The template theory accounts for the slight skill difference in average depth of search found in chess players, as well as for other empirical data.     

Developing TODAM: Three models for serial-order information

TODAM2, a theory of distributed associative memory, shows how item and associative information can be considered special cases of serial-order information. Consequently, it is important to get the right model for serial-order information. Here, we analyze and compare three distributed-memory models for serial-order information that use TODAM’s convolution-correlation formalism. These models are the chaining model, the chunking model, and a new model, the power-set model. The chaining model associates each item with its predecessor; the chunking model uses multiple convolutions andn-grams to form chunks; and the power-set model interassociates all items in a set in a particular way to form a chunk. The models are compared in terms of their performance on seven basic tests of serial-order information—namely, serial recall, backward recall, recall of missing items, sequential probe tests, positional probe tests, serial-to-paired-associate transfer, and item recognition. The strengths and weaknesses of each model are discussed.     

Perception in chess and beyond: Commentary on Linhares and Freitas (2010)

Linhares and Freitas (2010; LF) argue that experts use analogical or semantic similarity, similarities that are not available from direct surface representations. LF make their case using a critique of Chase and Simon (1973b) and the presentation of a few chess positions and examples from other domains. Their conclusion is that models such as CHREST (Gobet et al., 2001) and theories such as the chunking theory (Chase & Simon, 1973b) and the template theory ( [Gobet and Simon, 1996a] and [Gobet and Simon, 1996b]) are inadequate for dealing with these issues. They propose an alternative paradigm, which they call “experience recognition.” Although we find this issue an interesting one, the separation between pattern recognition and problem solving is a lot more complex than LF portray. We instead suggest that a “revolution” in our to date successful modelling is not necessary. Especially in the chess domain, LF’s examples do not make the point they claim. Furthermore, their criticisms of CS are incorrect, and they have failed to mention a large number of experimental results that have supported the hypothesis of location-specific encodings. Although we agree that experts use semantic information and similarities, these ideas already possess analogues in CHREST, which can form the basis of further evolution of the theory.     

The mind's eye in blindfold chess

Visual imagery plays an important role in problem solving, and research into blindfold chess has provided a wealth of empirical data on this question. We show how a recent theory of expert memory (the template theory; Gobet & Simon, 1996b, 2000) accounts for most of these data. However, how the mind's eye filters out relevant from irrelevant information is still underspecified in the theory. We describe two experiments addressing this question, in which chess games are presented visually, move by move, on a board that contains irrelevant information (static positions, semistatic positions, and positions changing every move). The results show that irrelevant information affects chess masters only when it changes during the presentation of the target game. This suggests that novelty information is used by the mind's eye to select incoming visual information and separate “figure” and “ground”. Mechanisms already present in the template theory can be used to account for this novelty effect.     

Chess knowledge predicts chess memory even after controlling for chess experience: Evidence for the role of high-level processes

The expertise effect in memory for chess positions is one of the most robust effects in cognitive psychology. One explanation of this effect is that chess recall is based on the recognition of familiar patterns and that experts have learned more and larger patterns. Template theory and its instantiation as a computational model are based on this explanation. An alternative explanation is that the expertise effect is due, in part, to stronger players having better and more conceptual knowledge, with this knowledge facilitating memory performance. Our literature review supports the latter view. In our experiment, a sample of 79 chess players were given a test of memory for chess positions, a test of declarative chess knowledge, a test of fluid intelligence, and a questionnaire concerning the amount of time they had played nontournament chess and the amount of time they had studied chess. We determined the numbers of tournament games the players had played from chess databases. Chess knowledge correlated .67 with chess memory and accounted for 16% of the variance after controlling for chess experience. Fluid intelligence accounted for an additional 13% of the variance. These results support the conclusion that both high-level conceptual processing and low-level recognition of familiar patterns play important roles in memory for chess positions.     

Statistically Induced Chunking Recall: A Memory-Based Approach to Statistical Learning

The computations involved in statistical learning have long been debated. Here, we build on work suggesting that a basic memory process, chunking, may account for the processing of statistical regularities into larger units. Drawing on methods from the memory literature, we developed a novel paradigm to test statistical learning by leveraging a robust phenomenon observed in serial recall tasks: that short-term memory is fundamentally shaped by long-term distributional learning. In the statistically induced chunking recall (SICR) task, participants are exposed to an artificial language, using a standard statistical learning exposure phase. Afterward, they recall strings of syllables that either follow the statistics of the artificial language or comprise the same syllables presented in a random order. We hypothesized that if individuals had chunked the artificial language into word-like units, then the statistically structured items would be more accurately recalled relative to the random controls. Our results demonstrate that SICR effectively captures learning in both the auditory and visual modalities, with participants displaying significantly improved recall of the statistically structured items, and even recall specific trigram chunks from the input. SICR also exhibits greater test–retest reliability in the auditory modality and sensitivity to individual differences in both modalities than the standard two-alternative forced-choice task. These results thereby provide key empirical support to the chunking account of statistical learning and contribute a valuable new tool to the literature.     

Cognitive advantage in sport: the nature of perceptual structures

To extend and clarify the nature of the perceptual processes used by sport experts to perceive schematic sport information, two experiments used schematic football diagrams that varied in structure (structured vs. unstructured) and complexity (complex vs. easy). The primary objective was to examine and characterize the nature of the perceptual structures (chunks) that are initially encoded, stored, and subsequently retrieved. In Experiment 1, compared with nonexperts, experts recalled larger perceptual structures following the initial stimulus presentation of structured stimuli only, replicating the recall findings of previous research in other skill domains. Experiment 2 used a long-term memory recognition task and a sorting task. Experts had superior recall and recognition of structured stimuli only, along with more discriminating sorting criteria of perceptual structures within long-term memory. This suggests that experts possess a highly refined semantic network or organized, structured schematic information. This research extends and clarifies the similarities between the perceptual processes of experts in sport (i.e., football) and experts in skill domains that require obvious cognitive involvement (i.e., chess). The results are discussed with reference to the perceptual and conceptual chunking hypotheses. It is proposed that sport experts' knowledge of a conceptual category enables them to retrieve elements using a "generate-and-test process."