Relational priming

The role of priming in analogical reasoning is well documented empirically (e.g., Kokinov Reference Kokinov1990; Schunn & Dunbar Reference Schunn and Dunbar1996). It also features prominently in several models, including Associative Memory-Based Reasoning (AMBR) (Kokinov 1994; Kokinov & Petrov Reference Kokinov, Petrov, Gentner, Holyoak and Kokinov2001) and Copycat (French Reference French1995; Hofstadter Reference Hofstadter1984; Mitchell Reference Mitchell1993). All of these models implement priming as residual activation. The present proposal thus adds to an emerging consensus of the importance of priming and of its underlying mechanism.

Not all relations can be cast as functions

Leech et al. claim that “for the purposes of analogy it may be sufficient to conceptualize relations as transformations between items” (sect. 2.2, para. 2). The main idea is to cast each binary relation R(a,b) as an equivalent univariate functionFootnote ¹b=F _R(a). The model uses hand-coded representations, rep, such that rep(F _R(a))=rep(a)+rep(R). The authors argue this is beneficial because “relations do not have to be represented explicitly, avoiding the difficulties of learning explicit structured representations” (sect. 5.1.1, para. 1). However, this benefit comes at the cost of rendering the model incapable of scaling up to adult-level performance.

The problem is that a relation can be cast as a function only if it is deterministic: that is, if for each a there is precisely one b that satisfies R(a,b) (Halford et al. Reference Halford, Wilson and Phillips1998). Many important relations violate this condition. Consider the transitive inference task: taller(Ann,Beth), taller(Beth,Chris)→taller(Ann,Chris). Now, if the relation taller(a,b) is cast as a function b=shrink(a), the query shrink(Ann) = ? becomes ambiguous. There are techniques for supporting nondeterministic functions in connectionist networks (e.g., Hinton & Sejnowski Reference Hinton, Sejnowski, Rumelhart and McClelland1986) that can be incorporated into the model. However, the priming account faces a deeper challenge: Why should Chris be produced as the answer to the above query after the system has been primed with Beth=shrink(Ann)?

Many relationships in the world are indeed near-deterministic transformations such as bread→cut bread. It is an important developmental constraint that young children find such regular, familiar relations easier to deal with (e.g., Goswami & Brown Reference Goswami and Brown1989). These strong environmental regularities shape coarse-coded distributed representations that can support generalization and inference (Cer & O'Reilly Reference Cer, O'Reilly, Zimmer, Mecklinger and Lindenberger2006; Hinton Reference Hinton1990; Rogers & McClelland Reference Rogers and McClelland2004; St. John & McClelland Reference St. John and McClelland1990). The target article demonstrates the utility of relational priming in these cases. However, there are also relationships such as left of that are quite accidental and changeable. To process them, the brain relies on sparse conjunctive representations (McClelland et al. Reference McClelland, McNaughton and O'Reilly1995) that do not support priming well. Finally, adult-level analogies involve higher-order relations and nested propositions (Gentner Reference Gentner1983). Their brain realization is an active research topic (e.g., Smolensky & Legendre Reference Smolensky and Legendre2006). One promising approach relies on dynamic gating in the basal ganglia and prefrontal cortex (O'Reilly Reference O'Reilly2006; Rougier et al. Reference Rougier, Noelle, Braver, Cohen and O'Reilly2005). Priming does play a role in these gated networks, but the critical functionality rests on other mechanisms.

The role of mapping

Proportional analogies are often presented in a multiple-choice format (e.g., Goswami & Brown Reference Goswami and Brown1989; Reference Goswami and Brown1990). An important limitation of the priming model is that its activation dynamics is not influenced by the available responses. The network simply produces an output pattern and stops. Then some unspecified control mechanism compares this pattern to the response representations. The limitations of this approach can be demonstrated by analogies with identical premises but different response sets, as illustrated in Figure 1. As Leech et al. argue in Figure 11 of the target article, the model should select response R2 when the choices are R1 and R2. Arguably, it should select response R3 when the choices are R1 and R3. To do this, the model must produce a pattern that is less similar to rep(R1) than it is to both rep(R2) and rep(R3). This seems to contradict the reasonable assumption that rep(R1) lies between rep(R2) and rep(R3) because of the intermediate size of R1.

Figure 1.

Demonstration of the importance of the available responses in a proportional analogy. Different response sets (R1–R2 vs. R1–R3) produce different analogies when paired with the same premises (A:B::C:?). Compare with Figure 11 in the target article.

Examples such as this highlight the role of mapping in analogy-making. The most important contribution of the target article, in our opinion, is to lay bare that a model (or a child or an ape) lacking any mapping capabilities can still perform proportional analogies quite well. The bold claim that “explicit mapping is no longer necessary for analogy to occur, but instead describes a subset of analogies” (sect. 5.4, para. 6) is a terminological matter. The take-home lesson for us is that proportional analogies can be solved by nonstructural means and thus cannot represent the class of analogies for which mapping is necessary.

The “psychologist's fallacy.”

This alerts us to a variant of the psychologist's fallacy wherein experimenters confuse their own understanding of a phenomenon with that of the subject (Oden et al. Reference Oden, Thompson, Premack, Gentner, Holyoak and Kokinov2001). Proportional analogies can be solved by structure mapping; they are also solved at above-chance levels by many 4-year-olds. Still, it does not follow that “the ability to reason by analogy is present by at least age four” (Goswami Reference Goswami, Holyoak, Gentner and Kokinov2001, p. 443), not if this ability is understood to imply structure mapping.

The transitive inference task is another case in point. It has been argued that this task is more complex than proportional analogies (Halford et al. Reference Halford, Wilson and Phillips1998; Maybery et al. Reference Maybery, Bain and Halford1986). And yet even pigeons and rats can make transitive inferences (Davis Reference Davis1992; Van Elzakker et al. Reference Van Elzakker, O'Reilly and Rudy2003; von Fersen et al. Reference von Fersen, Wynne, Delius and Staddon1991). Does that mean that the ability to reason by analogy is present in pigeons and rats? No, it means that transitive inferences can be made by nonstructural mechanisms (Frank et al. Reference Frank, Rudy and O'Reilly2003). Human adults can make such inferences by verbal and nonverbal strategies that can be dissociated (Frank et al. Reference Frank, Rudy, Levy and O'Reilly2005; Reference Frank, O'Reilly and Curran2006).