It is widely appreciated (e.g. Marr, 1982) that the difficulty of a particular computation varies according to how the input data are presented. What is less well understood is the effect of this computation/representation trade-off within familiar learning paradigms. We argue that existing learning algorithms are often poorly equipped to solve problems involving a certain type of important and widespread statistical regularity, which 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'. 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.

There is a form of representation that is naturally emergent in the organization of interactive systems. Interactive representation has claims to be the fundamental form of representation, from which all others are derivative. In particular, it naturally satisfies a meta-epistemological criterion that is not addressed by standard approaches in contemporary literature, and is arguably impossible to satisfy within any version those standard approaches. Furthermore, the interactive approach naturally avoids other multiple aporias that bedevil standard approaches. Much effort has been devoted in recent literature to attempts to satisfy a critical meta-epistemological criterion: representation must be capable of being in error. The criterion that I will apply is a strengthening of this one: representation must be capable of being in error in such a way that that condition of being in error is detectable by the agent or system that is doing the representing --- the meta-epistemological crite...

In 1988 Fodor and Pylyshyn issued a challenge to the newly-popular connectionism: explain the systematicity of cognition without merely implementing a so-called classical architecture. Since that time quite a number of connectionist models have been put forward, either by their designers or by others, as in some measure demonstrating that the challenge can be met (e.g., Pollack, 1988, 1990; Smolensky, 1990; Chalmers, 1990; Niklasson and Sharkey, 1992; Brousse, 1993). Unfortunately, it has generally been unclear whether these models actually do have this implication (see, for instance, the extensive philosophical debate in Smolensky, 1988; Fodor and McLaughlin, 1990; van Gelder, 1990, 1991; McLaughlin, 1993a, 1993b; Clark, 1993). Indeed, we know of no major supporter of classical orthodoxy who has felt compelled, by connectionist models and arguments, to concede in print that connectionists have in fact delivered a non-classical explanation of systematicity.

Several connectionist models have been supplying non-classical explanations to the challenge of explaining systematicity, i.e., structure sensitive processes, without merely being implementations of classical architectures. However, lately the challenge has been extended to include learning related issues. It has been claimed that when these issues are taken into account, only a restricted form of systematicity could be claimed by the connectionist models put forward so far. In this paper we investigate this issue further, and supply a model and results that satisfies even the revised challenge.

... values in life --- is a central theme of the discussion. Finally, 3) the dependence of the analysis on an underlying pragmatic or action framework is highlighted: contemporary alternative frameworks for modeling development cannot satisfactorily address these issues of the social constitution of persons.

Fodor and Pylyshyn argued that connectionist models could not be used to exhibit and explain a phenomenon that they termed systematicity, i.e., compositional syntax and semantics for mental representations and structure sensitivity of mental processes. This inability, they argued, was particularly serious since it meant that connectionist models could not be used as alternative models to classical symbolic models to explain cognition. In this paper, a connectionist model is used to identify some properties which show that connectionist networks supply means for accomplishing a stronger version of systematicity than Fodor and Pylyshyn opted for. Specifically, it is argued that context-dependent systematicity is achievable within a connectionist framework. The arguments put forward rest on a particular formulation of content and context of connectionist representation, firmly and technically based on connectionist primitives in a learning environment. The perspective is motivated by the fundamental differences between the connectionist and classical architectures, in terms of prerequisites, lower-level functionality and inherent constraints. 2 1

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ABSTRACT In biology experiments, oligonucleotide microarrays are contacted with a solution of long nucleic acid targets. The hybridized probes thus carry long tails. When the surface density of the oligonucleotide probes is high enough, the progress of hybridization gives rise to a polyelectrolyte brush due to mutual crowding of the nucleic acid tails. The free-energy penalty associated with the brush modifies both the hybridization isotherms and the rate equations: the attainable hybridization is lowered significantly as is the hybridization rate. When the equilibrium hybridization fraction, xeq, is low, the hybridization follows a Langmuir type isotherm, xeq/(1 ÿ xeq) ctK where ct is the target concentration and K is the equilibrium constant. K is smaller than its bulk value by a factor (n/N) 2/5 due to wall effects where n and N denote the number of bases in the probe and the target. At higher xeq, when the brush is formed, the leading correction is xeq/(1 ÿ xeq) ctK exp [ÿconst9(xeq 2/3 ÿ xB 2/3)] where xB corresponds to the onset of the brush regime. The denaturation rate constant in the two regimes is identical. However, the hybridization rate constant in the brush regime is lower, the leading correction being exp [ÿconst9(x 2/3 ÿ x B 2/3)].

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Several connectionist models have been supplying non-classical explanations to the challenge of explaining systematicity, i.e., structure sensitive processes, without merely being implementations of classical architectures. However, lately the challenge has been extended to include learning related issues. It has been claimed that when these issues are taken into account, only a restricted form of systematicity could be claimed by the connectionist models put forward so far. In this paper we investigate this issue further, and supply a model and results that satisfies even the revised challenge. Introduction As is well known, in 1988, Fodor & Pylyshyn, arch-defenders of mainstream orthodoxy, threw down the mantle to connectionists, challenging them to explain the (so-called) systematicity of cognitive capacities without merely implementing a (so-called) classical cognitive architecture. Since then a number of connectionist models have been put forward, either by their author...