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Graphs, geometry, and representations for language models and networks of entities. (Graphes, géométrie et représentations pour le langage et les réseaux d'entités)

The automated treatment of familiar objects, either natural or artifacts, always relies on a translation into entities manageable by computer programs. The choice of these abstract representations is always crucial for the efficiency of the treatments and receives the utmost attention from computer scientists and developers. However, another problem rises: the correspondence between the object to be treated and "its" representation is not necessarily one-to-one! Therefore, the ambiguous nature of certain discrete structures is problematic for their modeling as well as their processing and analysis with a program. Natural language, and in particular its textual representation, is an example. The subject of this thesis is to explore this question, which we approach using combinatorial and geometric methods. These methods allow us to address the problem of extracting information from large networks of entities and to construct representations useful for natural language processing.Firstly, we start by showing combinatorial properties of a family of graphs implicitly involved in sequential models. These properties essentially concern the inverse problem of finding a sequence representing a given graph. The resulting algorithms allow us to carry out an experimental comparison of different sequential models used in language modeling.Secondly, we consider an application for the problem of identifying named entities. Following a review of recent solutions, we propose a competitive method based on the comparison of knowledge graph structures which is less costly in annotating examples dedicated to the problem. We also establish an experimental analysis of the influence of entities from capital relations. This analysis suggests to broaden the framework for applying the identification of entities to knowledge bases of different natures. These solutions are used today in a software library in the banking sector.Then, we perform a geometric study of recently proposed representations of words, during which we discuss a geometric conjecture theoretically and experimentally. This study suggests that language analogies are difficult to transpose into geometric properties, and leads us to consider the paradigm of distance geometry in order to construct new representations.Finally, we propose a methodology based on the paradigm of distance geometry in order to build new representations of words or entities. We propose algorithms for solving this problem on some large scale instances, which allow us to build interpretable and competitive representations in performance for extrinsic tasks. More generally, we propose through this paradigm a new framework and research leadsfor the construction of representations in machine learning.