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Mathematical Modeling of Language Learning


When modeling language mathematically, we can look both at how an individual learns language, and at how language develops throughout a population. When considering individual learning, the fascinating ability of humans to modify the linguistic input and "create" a language has been widely discussed. In this thesis, we first look at two studies that have investigated language learning phenomena. We create two variants of a novel learning algorithm of the reinforcement-learning type which exhibits the patterns in Hudson Kam and Newport (2009) and Fedzechkina et al. (2012), and suggests ways to explain them. Hudson Kam and Newport (2009) explores the differences between adults and children when it comes to processing inconsistent linguistic input and making it more consistent. We introduce an asymmetry to our algorithm that sheds light on the differences between how children and adults regularize language. Fedzechkina et al. (2012) looks at how adults are able to restructure their linguistic input in order to improve communication. Finally, we look at mathematical modeling of language at the level of a population. We consider a scenario where language is a genetic mutation that has appeared in a population without language, and we study how language will develop in the population. We see that the language individuals have an advantage when they are able to communicate with each other and we find conditions that enable them to "invade" the population more quickly.

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