| The thesis investigates language learning. The questions that motivate this analysis include: What is language learning as a computational procedure? How can a language be learned in principle? How can a language be learned given the physical constraints of a neural system? It is believed that insight into each of these questions may be provided by an better appreciation of the capacities of nonlinear dynamical systems to learn, represent and generate complex sequential patterns and formal languages. The analysis in this thesis begins with a characterization of the problem of language learning. The concept of language learning as learning a finitely specifiable system that generates the language is described and explained. We propose and advocate the notion that nonlinear dynamical systems are legitimate examples of generative systems of language. Dynamical systems are shown to share the generative capacities of both phrase-structure grammars and discrete automata. The original research presented in this thesis begins with the investigation of the learning capacities of dynamical systems. The mathematical foundations for language learning in dynamical systems are described. It is shown how a language, in virtue of its sequential nature, can be usefully described as a type of dynamical system known as a symbolic dynamical system. It is shown that symbolic dynamical systems can be mapped directly to any member of a large class of low-dimensional chaotic dynamical systems. The importance of this is that for a given chaotic dynamical system to be a model of a given language, we may set up a target probability distribution over its state-space, such that if it visits its state-space according to this distribution it will generate the language that is desired. A specific dynamical system is chosen as a model for learning. This is known as the 2-d tent-map. We derive a learning algorithm for this particular dynamical system. This algorithm is based on a matrix approximation of the Frobenius-Perron operator. Examples of learning regular, context-free and context-sensitive languages are provided. |
