Transfer of learning: rule acquisition or statistical learning?

of statistical learning: no need for algebraic rules, in Proc. 21st Annu. Conf. Cognit. Sci. Soc. and connectionism: analysis of a parallel distributed processing model of language We completely agree with Seidenberg and Elman 1 that what is important is 'understanding the behaviour of the network and the principles that govern it', but are mystified by their discussion of rules. Seidenberg and Elman's claim that 'the concept of " rule " has been altered to conform to the behaviour of connectionist networks' is a clever, ironic twist, but it actually has no substance, and reflects only Seidenberg and Elman's misunderstanding of our earlier point. As I emphasized in a series of recent articles , only a subset of neural networks implement rules 2–4 ; not all of them do. As we stated before 2 , the ones that depend on 'open-ended abstract relationships for which we can substitute arbitrary items' are the ones that implement rules. As it turns out, the neural network part of Seidenberg and Elman's system does not implement a rule. But, crucially , another part of the system that Seidenberg and Elman propose does implement a rule: the external teacher (this is what we meant by a 'hidden rule'). In particular, the external teacher incorporates a universally open-ended rule of the sort, for all syllables x, y, if x ϭ y then output 1 else output 0. This corresponds exactly to our characterization of rules. Since part of the system contains a rule, it follows that the system as a whole contains a rule. Seidenberg and Elman also point to models of Altmann and Dienes 5 and Christiansen and Curtin 6. We have discussed the Altmann and Dienes model elsewhere 7. The pointer to the Christiansen and Curtin model is at best premature: the difference underlying their crucial result was small, it has not been shown to be statistically significant, and it has not yet been replicated (for a more detailed response see my reply to Christiansen and Curtin, in this issue 8). We do not expect this discussion to die down any time soon; clearly, advocates of certain types of connectionism believe that a lot is at stake. But the proliferation of alternative models should not distract us from noticing limits on particular classes of models where such limits do exist. For it is only by taking limits seriously that we can hope to build …