We argue that existing learning algorithms are often poorly equipped to solve problems involving a certain type of important and widespread regularity that we call “type-2 regularity.” The solution in these cases is to trade achieved representation against computational search. We investigate several ways in which such a trade-off may be pursued including simple incremental learning, modular connectionism, and the developmental hypothesis of “representational redescription.”.

Explicitness has usually been approached from two points of view, labelled by Kirsh the structural and the process view, that hold opposite assumptions to determine when information is explicit. In this paper, we offer an intermediate view that retains intuitions from both of them. We establish three conditions for explicit information that preserve a structural requirement, and a notion of explicitness as a continuous dimension. A problem with the former accounts was their disconnection with psychological work on the issue. We (...) review studies by Karmiloff-Smith, and Shanks and St. John to show that the proposed conditions have psychological grounds. Finally, we examine the problem of explicit rules in connectionist systems in the light of our framework. (shrink)

Explicitness has usually been approached from two points of view, labelled by Kirsh the structural and the process view, that hold opposite assumptions to determine when information is explicit. In this paper, we offer an intermediate view that retains intuitions from both of them. We establish three conditions for explicit information that preserve a structural requirement, and a notion of explicitness as a continuous dimension. A problem with the former accounts was their disconnection with psychological work on the issue. We (...) review studies by Karmiloff-Smith, and Shanks and St. John to show that the proposed conditions have psychological grounds. Finally, we examine the problem of explicit rules in connectionist systems in the light of our framework. (shrink)

Beyond modularityattempts a synthesis of Fodor's anticonstructivist nativism and Piaget's antinativist constructivism. Contra Fodor, I argue that: (1) the study of cognitive development is essential to cognitive science, (2) the module/central processing dichotomy is too rigid, and (3) the mind does not begin with prespecified modules; rather, development involves a gradual process of “modularization.” Contra Piaget, I argue that: (1) development rarely involves stagelike domain-general change and (2) domainspecific predispositions give development a small but significant kickstart by focusing the infant's (...) attention on proprietary inputs. Development does not stop at efficient learning. A fundamental aspect of human development (“representational redescription”) is the hypothesized process by which information that isina cognitive system becomes progressively explicit knowledgetothat system. Development thus involves two complementary processes of progressive modularization and progressive “explicitation.” Empirical findings on the child as linguist, physicist, mathematician, psychologist, and notator are discussed in support of the theoretical framework. Each chapter concentrates first on the initial state of the infant mind/brain and on subsequent domain-specific learning in infancy and early childhood. It then goes on to explore data on older children's problem solving and theory building, with particular focus on evolving cognitive flexibility. Emphasis is placed throughout on the status of representations underlying different capacities and on the multiple levels at which knowledge is stored and accessible. Finally, consideration is given to the need for more formal developmental models, and a comparison is made between representational redescription and connectionist simulations of development. In conclusion, I consider what is special about human cognition by speculating on the status of representations underlying the structure of behavior in other species. (shrink)

This piece is a commentary on a precis of Maggie Boden's book "The creative mind" published in Behavioral and Brain Sciences.

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)

We focus on Karmiloff-Smith's Representational redescription model, arguing that it poses some problems concerning the architecture of a redescribing system. To discuss the topic, we consider the implicit/explicit dichotomy and the relations between natur al language and the language of thought. We argue that the model regards how knowledge is employed rather than how it is represented in the system.

What is creativity? One new idea may be creative, whereas another is merely new: What's the difference? And how is creativity possible? These questions about human creativity can be answered, at least in outline, using computational concepts. There are two broad types of creativity, improbabilist and impossibilist. Improbabilist creativity involves novel combinations of familiar ideas. A deeper type involves METCS: the mapping, exploration, and transformation of conceptual spaces. It is impossibilist, in that ideas may be generated which – with respect (...) to the particular conceptual space concerned – could not have been generated before. The more clearly conceptual spaces can be defined, the better we can identify creative ideas. Defining conceptual spaces is done by musicologists, literary critics, and historians of art and science. Humanist studies, rich in intuitive subtleties, can be complemented by the comparative rigour of a computational approach. Computational modelling can help to define a space, and to show how it may be mapped, explored, and transformed. Impossibilist creativity can be thought of in “classical” Al terms, whereas connectionism illuminates improbabilist creativity. Most Al models of creativity can only explore spaces, not transform them, because they have no self-reflexive maps enabling them to change their own rules. A few, however, can do so. A scientific understanding of creativity does not destroy our wonder at it, nor does it make creative ideas predictable. Demystification does not imply dehumanization. (shrink)