Despite the remarkable success of large large-scale neural networks, we still lack unified notation for thinking about and describing their representational spaces. We lack methods to reliably describe how their representations are structured, how that structure emerges over training, and what kinds of structures are desirable. This thesis introduces quantitative methods for identifying systematic structure in a mapping between spaces, and leverages them to understand how deep-learning models learn to represent information, what representational structures drive generalisation, and how design decisions condition the structures that emerge. To do this I identify structural primitives present in a mapping, along with information theoretic quantifications of each. These allow us to analyse learning, structure, and generalisation across multi-agent reinforcement learning models, sequence-to-sequence models trained on a single task, and Large Language Models. I also introduce a novel, performant, approach to estimating the entropy of vector space, that allows this analysis to be applied to models ranging in size from 1 million to 12 billion parameters. The experiments here work to shed light on how large-scale distributed models of cognition learn, while allowing us to draw parallels between those systems and their human analogs. They show how the structures of language and the constraints that give rise to them in many ways parallel the kinds of structures that drive performance of contemporary neural networks.

The paper investigates a phenomenon of free word order through the analysis by reduction. It exploits its formal background and data types and studies the word order freedom by means of the minimal number of word order shifts (word order changes preserving syntactic correctness, individual word forms, their morphological characteristics and/or their surface dependency relations). The investigation focuses upon an interplay of two phenomena related to word order: (non-)projectivity of a sentence and number of word order shifts within the analysis by reduction. This interplay is exemplified on a sample of Czech sentences with clitics.