Context-free and context-sensitive dynamics in recurrent neural networks

Continuous-valued recurrent neural networks can learn mechanisms for processing context-free languages. The dynamics of such networks is usually based on damped oscillation around fixed points in state space and requires that the dynamical components are arranged in certain ways. It is shown that qualitatively similar dynamics with similar constraints hold for a(n)b(n)c(n), a context-sensitive language. The additional difficulty with a(n)b(n)c(n), compared with the context-free language a(n)b(n), consists of 'counting up' and 'counting down' letters simultaneously. The network solution is to oscillate in two principal dimensions, one for counting up and one for counting down. This study focuses on the dynamics employed by the sequential cascaded network, in contrast to the simple recurrent network, and the use of backpropagation through time. Found solutions generalize well beyond training data, however, learning is not reliable. The contribution of this study lies in demonstrating how the dynamics in recurrent neural networks that process context-free languages can also be employed in processing some context-sensitive languages (traditionally thought of as requiring additional computation resources). This continuity of mechanism between language classes contributes to our understanding of neural networks in modelling language learning and processing.

Formal methods within a totally functional approach to programming

Taking functional programming to its extremities in search of simplicity still requires integration with other development (e.g. formal) methods. Induction is the key to deriving and verifying functional programs, but can be simplified through packaging proofs with functions, particularly folds, on data (structures). Totally Functional Programming avoids the complexities of interpretation by directly representing data (structures) as platonic combinators - the functions characteristic to the data. The link between the two simplifications is that platonic combinators are a kind of partially-applied fold, which means that platonic combinators inherit fold-theoretic properties, but with some apparent simplifications due to the platonic combinator representation. However, despite observable behaviour within functional programming that suggests that TFP is widely-applicable, significant work remains before TFP as such could be widely adopted.

Language, discourse and politics

After discussing the meaning of the word politics, this paper shows that there are four possible approaches to the issue of the relationships between language, discourse and politics: a) the intrinsic political nature of language; b) the relations of power between discourses and their political dimension; c) the relations of power between languages and the political dimension of their usage and; d) linguistic policies. This paper addresses only the first two of these items. Languages have an intrinsically political nature because they subject their speakers to their order. The acts of silencing operationalized in discourse manifest a relation of power. The spread of discourses in the social space is also subject to the order of power. The use of language may be the space of pertinence, but is also that of exclusion, separation and even the elimination of the other. Therefore, language is not a neutral communication tool, but it is permeated by politics, by power. Because of the dislocations that it produces, literature is a form of swindling language, unveiling the powers that are imprinted on it.