Feedforward networks are a class of regression techniques that can be used to learn to perform some task from a set of examples. The question of generalization of network performance from a finite training set to unseen data is clearly of crucial importance. In this article we first show that the generalization error can be decomposed in two terms: the approximation error, due to the insufficient representational capacity of a finite sized network, and the estimation error, due to insufficient information about the target function because of the finite number of samples. We then consider the problem of approximating functions belonging to certain Sobolev spaces with Gaussian Radial Basis Functions. Using the above mentioned decomposition we bound the generalization error in terms of the number of basis functions and number of examples. While the bound that we derive is specific for Radial Basis Functions, a number of observations deriving from it apply to any approximation t...

This paper considers the problem of language change. Linguists must explain not only how languages are learned but also how and why they have evolved along certain trajectories and not others. While the language learning problem has focused on the behavior of individuals and how they acquire a particular grammar from a class of grammars G, here we consider a population of such learners and investigate the emergent, global population characteristics of linguistic communities over several generations. We argue that language change follows logically from specific assumptions about grammatical theories and learning paradigms. In particular, we are able to transform parameterized theories and memoryless acquisition algorithms into grammatical dynamical systems, whose evolution depicts a population's evolving linguistic composition. We investigate the linguistic and computational consequences of this model, showing that the formalization allows one to ask questions about diachronic that one ...

In this paper, I review arguments for and against the emergence and maintenance of an innate language acquisition device (LAD) via genetic assimilation. By a LAD, I mean nothing more or less than a learning mechanism which incorporates

Niyogi and Berwick have developed a deterministic dynamical model of language change from which they analytically derive logistic, Sshaped spread of a linguistic variant through a speech community given certain assumptions about the language learning procedure, the linguistic environment, and so forth. I will demonstrate that the same assumptions embedded in a stochastic model of language change lead to dierent and sometimes counterintuitive predictions. I will go on to argue that stochastic models are more appropriate and can support greater demographic and (psycho)linguistic realism, leading to more insightful accounts of the (putative) growth rates of attested changes. 1 Introduction It has been observed that language changes (often?) spread through a speech community following an S-shaped pattern, beginning slowly, spreading faster, then slowing o before nally extinguishing a competing variant (e.g. Weinreich et al. , 1968; Chen, 1972; Bailey, 1973:77; Lass, 1997; She...

Abstract Children will develop their parental languages correctly, since language learners come to obtain the one which they contact most in the community. At the same time, children would be affected by other languages, the influence of which is proportional to the population of those languages. In this paper, we revise the foregoing evolutionary theory of language, that is differential equations of the population dynamics. We propose that the transition rate in languages is sensitive to the distribution of population of each generation. In addition, we introduce the exposure probability that is the measure of influence from other languages. We show experimental results, in which we could observe the emergence of creole. Furthermore, we analysed which language would be dominant, dependent on the initial distribution of population, together with the exposure probability.

To be presented at:

Abstract. Selecting suitable topics in order to assess system effectiveness is a crucial part of any benchmark, particularly those for retrieval systems. This includes establishing a range of example search requests (or topics) in order to test various aspects of the retrieval systems under evaluation. In order to assist with selecting topics, we present a measure of topic complexity for crosslanguage image retrieval. This measure has enabled us to ground the topic generation process within a methodical and reliable framework for ImageCLEF 2005. This document describes such a measure for topic complexity, providing concrete examples for every aspect of topic complexity and an analysis of topics used in the ImageCLEF 2003, 2004 and 2005 ad-hoc task. 1

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