Here's a source analogue for the model proposed in this target article: A politician wants to start a space program. Lacking typical prerequisites such as rockets, he gets his assistant to climb the highest lookout tower in the land. We have lift-off!

Analogical reasoning is a canonical case of role-based relational reasoning (RRR), a capability (perhaps uniquely human) that typically emerges around age 5 years (Doumas & Hummel Reference Doumas, Hummel, Holyoak and Morrison2005b; Halford Reference Halford1993; Penn et al. Reference Penn, Holyoak and Povinelli2008). Consider the example of 4-year-old Lori, a participant in one of the earliest experiments on analogy development (Holyoak et al. Reference Holyoak, Junn and Billman1984). Lori was read a fairy tale about a genie faced with the problem of transferring a number of jewels from his current bottle to a new home in a different bottle. The genie's solution was to command his magic carpet to roll itself into a tube, place it between the two bottles, and then roll his jewels through it. Without mentioning any connection with the fairy tale, the experimenter asked Lori to figure out how to transfer some small balls from one bowl to another at some distance (while remaining seated). A variety of objects were available, including a large rectangular sheet of paper. Lori referred to the balls as “pretend jewels.” Looking at the sheet of paper she said, “That will be a magic carpet.” She laughed as she picked it up and rolled it. “I did it just like the genie!”

Lori's reasoning exploited systematic correspondences between objects filling parallel roles. For example, the genie wants to move his jewels from one bottle to another just as Lori wants to move balls across bowls. More generally, RRR implies the ability to draw inferences about entities based on the roles they fill in relations, where the roles are not predictable by features of the entities and the relations cannot be coded as role-less chunks (Penn et al. Reference Penn, Holyoak and Povinelli2008).

The target article illustrates an all-too-common approach to connectionist modeling of those cognitive processes most central to human intelligence: suck the essence out, then force-fit what's left into an associationist straitjacket. The project begins by reducing analogical reasoning to a glorified paired associates task. Leech et al. focus on four-term analogies, which have the virtue (for associationist purposes) of providing a highly stereotyped format. Their three-layered network is trained with “facts” glossed along the lines “apple+knife→sliced apple” and “bread+knife→sliced bread.” After extensive training, the model is given the inputs “apple” and “sliced apple,” thereby activating “knife,” which is then clamped so that when “bread” is added as input it combines with “knife” to yield “sliced bread.” Analogy solved?

Leech et al. talk about such problems using concepts such as “causal transformations,” but the model itself simply learns bidirectional conditional paired associates. Let “object at time 1” be S _i, “causal relation” be C _i, and “object at time 2” be R _i. The model is trained with triples, including <S ₁, C ₁, R ₁> and <S ₂, C ₁, R ₂>. The key to the model's performance is that it initially learns all pairwise conditional associations, including <S _i, C _i>→R _i and <S _i, R _i>→C _i. At test, the input <S ₁, R ₁> outputs C ₁; then S ₂ is added, and <S ₂, C ₁> outputs R ₂.

The model operates without explicit representations of relational roles, such as “cause,” “effect,” or “instrument.” In order to fit the four-term analogy format, the modelers hand-code the assignments of roles to predetermined banks in the input and output layers. But although four-term analogies are indeed stereotyped, they are nonetheless richer than conditional paired associates. Consider a couple of small variations. People who understand what a knife does could also solve the analogy

where the role assignments are reversed. We suspect that the Leech et al. model will be unable to solve this simple variation without additional training, as it has never previously seen, for example, “sliced apple” assigned to its input layer. The only way the model could solve this rearranged analogy is if Leech et al. hand-code the familiar role assignments for it. But if such hand-holding is acceptable, it seems the model will be led into a different, equally embarrassing error. Given the problem

people will likely reject it or else complete it with “knife.” However, if Leech et al. help their model along by placing “knife” in its familiar bank and clamping the output as usual, it seems that the model will output “sliced bread” as a fine “analogical completion.” Perhaps Leech et al. can provide simulation results for these examples in their response.

The model's role-less, paired-associate-style representations, inadequate for even the simplest four-term analogies, render it incapable of solving any problem requiring integration of information across multiple roles. Such capabilities, illustrated by the protocol from Lori, are present in preschool children (Halford Reference Halford1993). In a gesture toward extending the model to adult performance, Leech et al. apply it to “a large, complex analogy” (sect. 4.2, para. 1): that between World War II and the first Gulf War (Spellman & Holyoak Reference Spellman and Holyoak1992). The most interesting data reported by Spellman and Holyoak, showing that people were systematic in mapping leaders and countries in pairs (either Churchill, Britain→Hussein, Iraq, or else FDR, US→Hussein, Iraq), can only be explained by a model capable of relational integration (Hummel & Holyoak Reference Hummel and Holyoak1997). But rather than modeling how a reasoner could sort out the interrelationships among two source countries (Britain and the United States) and their leaders with respect to Hitler's Germany, Leech et al. simply eliminate this difficulty – by adopting representations of World War II that leave the United States out of it.

Relational priming is an important phenomenon. But as Spellman et al. (Reference Spellman, Holyoak and Morrison2001) reported in demonstrating it, it requires attentional resources (contrary to Leech et al.'s claim that “relational priming is a robust psychological phenomenon that does not require explicit strategic control”; sect. 2.1, para. 4). Neuroimaging data indicate that evaluating causal (as opposed to merely associative) relations activates the prefrontal cortex (Satpute et al. Reference Satpute, Fenker, Waldmann, Tabibnia, Holyoak and Lieberman2005), a brain area that is slow to develop. In fact, we are unaware of any demonstration of relational priming in children (and Leech et al. do not mention any). In the absence of evidence that young children actually exhibit relational priming, it seems premature to assume that it precedes, rather than follows, development of relational roles. For a recent model of how relational roles could be acquired from experience, see Doumas et al. (Reference Doumas, Hummel and Sandhofer2008).

Returning to the “space program” analogy: Lacking any sense of relational roles, the target model won't get the point of the analogy. Do you?