Computation is a process of making explicit, information that was implicit. In computing 5 as the solution to ∛125, for example, we move from a description that is not explicitly about 5 to one that is. We are drawing out numerical consequences to the description ∛125. We are extracting information implicit in the problem statement. Can we precisely state the difference between information thati s implicit in a state, structure or process and information that is explicit?

Some regularities enjoy only an attenuated existence in a body of training data. These are regularities whose statistical visibility depends on some systematic recoding of the data. The space of possible recodings is, however, infinitely large – it is the space of applicable Turing machines. As a result, mappings that pivot on such attenuated regularities cannot, in general, be found by brute-force search. The class of problems that present such mappings we call the class of “type-2 problems.” Type-1 problems, by (...) contrast, present tractable problems of search insofar as the relevant regularities can be found by sampling the input data as originally coded. Type-2 problems, we suggest, present neither rare nor pathological cases. They are rife in biologically realistic settings and in domains ranging from simple animat behaviors to language acquisition. Not only are such problems rife – they are standardly solved! This presents a puzzle. How, given the statistical intractability of these type-2 cases, does nature turn the trick? One answer, which we do not pursue, is to suppose that evolution gifts us with exactly the right set of recoding biases so as to reduce specific type-2 problems to type-1 mappings. Such a heavy-duty nativism is no doubt sometimes plausible. But we believe there are other, more general mechanisms also at work. Such mechanisms provide general strategies for managing problems of type-2 complexity. Several such mechanisms are investigated. At the heart of each is a fundamental ploy – namely, the maximal exploitation of states of representation already achieved by prior, simpler learning so as to reduce the amount of subsequent computational search. Such exploitation both characterizes and helps make unitary sense of a diverse range of mechanisms. These include simple incremental learning, modular connectionism, and the developmental hypothesis of “representational redescription”. In addition, the most distinctive features of human cognition – language and culture – may themselves be viewed as adaptations enabling this representation/computation trade-off to be pursued on an even grander scale. (shrink)

Fodor and Pylyshyn (1988), Fodor and McLaughlin (1990) and McLaughlin (1993) challenge connectionists to explain systematicity without simply implementing a classical architecture. In this paper I argue that what makes the challenge difficult for connectionists to meet has less to do with what is to be explained than with what is to count as an explanation. Fodor et al. are prepared to admit as explanatory, accounts of a sort that only classical models can provide. If connectionists are to meet the (...) challenge, they are going to have to insist on the propriety of changing what counts as an explanation of systematicity. Once that is done, there would seem to be as yet no reason to suppose that connectionists are unable to explain systematicity. (shrink)

systematicity is. Until systematicity is adequately systematicity. Most contributors to these debates have clarified, we cannot know whether classical paid little or no attention to the alleged empirical.

Human cognition is said to be systematic: cognitive ability generalizes to structurally related behaviours. The connectionist approach to cognitive theorizing has been strongly criticized for its failure to explain systematicity. Demonstrations of generalization notwithstanding, I show that two widely used networks (feedforward and recurrent) do not support systematicity under the condition of local input/output representations. For a connectionist explanation of systematicity, these results leave two choices, either: (1) develop models capable of systematicity under local input/output representations; or (2) justify the (...) choice of similarity-based (nonlocal) component representations sufficient for systematicity. (shrink)

At root, the systematicity debate over classical versus connectionist explanations for cognitive architecture turns on quantifying the degree to which human cognition is systematic. We introduce into the debate recent psychological data that provides strong support for the purely structure-based generalizations claimed by Fodor and Pylyshyn (1988). We then show, via simulation, that two widely used connectionist models (feedforward and simple recurrent networks) do not capture the same degree of generalization as human subjects. However, we show that this limitation is (...) overcome by tensor networks that support relational processing. (shrink)