What Forms the Chunks in a Subject’s Performance? Lessons from the CHREST Computational Model of Learning

Computational models of learning provide an alternative technique for identifying the number and type of chunks used by a subject in a specific task. Results from applying CHREST to chess expertise support the theoretical framework of Cowan and a limit in visual short-term memory capacity of 3-4 items. An application to learning from diagrams illustrates different identifiable forms of chunk. Cowan’s theoretical framework (Section 2) assumes that the “focus of attention is capacitylimited”, and that “deliberately recalled [information] is restricted to this limit in the focus of attention.” This framework is compatible with the EPAM/CHREST family of computational models, and this commentary highlights the role that a model of learning can play in clarifying the nature of chunks. CHREST (Chunk Hierarchy and REtrieval STructure) is a computational model of expert memory in chess players (Gobet, 1998; Gobet & Simon, in press), and is based on the earlier EPAM model (Feigenbaum & Simon, 1984) of perceptual memory. CHREST possesses an input device (simulated eye), a visual short-term memory (STM) for storing intermediate results (equivalent to the focus of attention), and a long-term memory (LTM) based around a discrimination network for retrieving chunks of information. Each chunk is learnt from information in the visual field, using the STM to compose information across one or more eye fixations. The classic recall task (Chase & Simon, 1973; Cowan, Section 3.4.1; De Groot, 1946/1978) has been used to show that subjects recall information in chunks. The task requires the model/subject to observe a display for a set time period, and then reconstruct the stimulus from memory; in simulations, the chunks within the model’s STM are used as the reconstructed response. In a study of chess expertise, Gobet (1998) showed how the accuracy of the reconstructed position depends on the number and size of chunks which the model identifies; the size of chunk depends on the level of expertise, but the number can be systematically varied, and a value of 3 or 4 was found to best match the performance of different levels of player, providing further empirical support for the findings of Cowan. Also significant is that the better performance of experts is explained by their use of larger chunks (typically, master chess players recall chunks of twice the size of average club players), and the number and content of these chunks may be extracted from the model (see also Gobet & Simon, 1998, in press). Chase and Simon (1973) did, however, find that expert chess players appeared to recall more chunks than novices. As discussed in Gobet and Simon (1998), these findings do not contradict the existence of a fixed capacity limit, because additional factors affect the subject’s performance; in this case, the number of pieces which the player can pick up. So, are the chunks observed in the subject’s performance due to previously learnt information or to other factors relating to the task or cognitive performance? This question may be answered through a simulation of the learning process. The role of learnt knowledge in producing chunks in performance is currently being explored in a problem-solving version of CHREST (Lane, Gobet & Cheng, 2000a) which learns a diagrammatic representation for solving electric circuit problems. In Lane, Gobet and Cheng (2000b) different computational models were analysed based on their respective representational, learning and retrieval strategies for handling high-level information. From these two studies, it is clear that chunks observed in the model’s performance may arise from a number of causes. Three of the more apparent are as follows: • First, a chunk may be observed in the output because of an explicit representation in the system’s LTM, which is the underlying representation used in the EPAM/CHREST family of computational models. For example, Richman, Gobet, Staszewski and Simon (1996) describe a chunk as “any unit of information that has been familiarised and has become meaningful”. • Second, a chunk may be observed in the output because the input has matched a stored chunk based on some similarity-based criterion; this is familiar from neural network approaches. • Third, a single chunk may be observed although it is based on a functional composition/decomposition of the stimulus and its subcomponents. For example, subjects may retrieve and store multiple chunks within their STM, but the performance based on these multiple chunks may then give the appearance of a single chunk. The presence of three distinct processes yielding chunk-like behaviour in such models clarifies how the observational characteristics of chunks inter-relate with learnt knowledge, and hence clarifies the connection between observed and learnt chunks. This connection assists in developing a deeper understanding of the capacity limit, especially in areas where the subject is continuously learning new chunks for composite objects. Most importantly, only by modelling the entire learning history of each subject can we really attempt to probe the content and format of chunks manipulated in STM, and thereby estimate STM capacity.