MAC/FAC: A model of similarity-based retrieval
Similarity-based remindings range from the sublime to the stupid. At one extreme, seeing the periodic table of elements reminds one of octaves in music. At the other, a bicycle reminds one of a pair of eyeglasses. Often, remindings are neither brilliant nor superficial but simply mundane, as when a bicycle reminds one of another bicycle. Theoretical attention is inevitably drawn to spontaneous analogy: i.e., to structural similarity unsupported by surface similarity, as in the octave/periodic table comparison. Such remindings seem clearly insightful and seem linked to the creative process, and should be included in any model of retrieval. But research on the psychology of memory retrieval points to a preponderance of the latter two types of similarity--(mundane) literal similarity, based on both structural and superficial commonalities, and (dumb) superficial similarity, based on surface commonalities. This is something of a paradox, since psychological evidence also indicates that the mapping process in transfer (see SME) is actually very sensitive to structural soundness, so that knowledge can be exported from one description into another. Hence the paradox: our memories often give us information we don't want. Any model of retrieval should explain this paradox.
Our MAC/FAC model (for "many are called but few are chosen") explains this phenomena in terms of the conflicting computational constraints on retrieval. The large number of cases in memory and the speed of human access suggests a computationally cheap process that can operate in parallel. But the requirement of judging soundness, essential to establishing whether a match can yield useful results, suggests a match process that creates correspondences between structured representations (i.e., SME). MAC/FAC satisfies these constraints by using a two-stage process:
- The MAC stage is a "wide-net" stage in which a computationally cheap, structurally stupid match processes are carried out between the probe case in working memory and each of a large corpus of cases stored in long-term memory. A small number of remindings, both sound and unsound, is typically obtained.
- The FAC stage uses SME in parallel on each of the results of the MAC stage, selecting the best structural match (or several, if they are sufficiently close to the best).
The psychological plausiblility of MAC/FAC requires that the MAC stage provide a reasonable estimate of the structural soundness of a match, while being tractable enough to scale to human-size memories. Our solution is to develop a secondary representation for memory items, called content vectors, which are derived algorithmically from the structural representation. The dot product of two content vectors provides a good estimate of the number of match hypotheses that SME would compute for the corresponding structural descriptions. The MAC stage computes a content vector for the probe, and performs a dot product of this vector with every item in memory to perform the initial filtering. This scheme is cheap, even on serial machines, and is very plausible for both massively parallel symbolic machines and connectionist implementations.
MAC/FAC has been successfully used to model the results of psychological experiments on similarity-based retrieval.
Selected Relevant Papers
Gentner, D. and Forbus, K. (1991). MAC/FAC: A model of similarity-based retrieval. Proceedings of the Cognitive Science Society.
Law, K. Forbus, K. and Gentner, D. (August, 1994). Simulating similarity-based retrieval: A comparison of ARCS and MAC/FAC. Proceedings of the Cognitive Science Society.
Forbus, K., Gentner, D. and Law, K. (April-June, 1995). MAC/FAC: A model of Similarity-based Retrieval. Cognitive Science, 19(2), 141-205. [NB: the paper incorrectly identifes the year of publication as 1994]