The provision of compositionality in distributional models of meaning, where a word is represented as a vector of co-occurrence counts with every other word in the vocabulary, offers a solution to the fact that no text corpus, regardless of its size, is capable of providing reliable co-occurrence statistics for anything but very short text constituents. The purpose of a compositional distributional model is to provide a function that composes the vectors for the words within a sentence, in order to create a vectorial representation that re ects its meaning. Using the abstract mathematical framework of category theory, Coecke, Sadrzadeh and Clark showed that this function can directly depend on the grammatical structure of the sentence, providing an elegant mathematical counterpart of the formal semantics view. The framework is general and compositional but stays abstract to a large extent. This thesis contributes to ongoing research related to the above categorical model in three ways: Firstly, I propose a concrete instantiation of the abstract framework based on Frobenius algebras (joint work with Sadrzadeh). The theory improves shortcomings of previous proposals, extends the coverage of the language, and is supported by experimental work that improves existing results. The proposed framework describes a new class of compositional models thatfind intuitive interpretations for a number of linguistic phenomena. Secondly, I propose and evaluate in practice a new compositional methodology which explicitly deals with the different levels of lexical ambiguity (joint work with Pulman). A concrete algorithm is presented, based on the separation of vector disambiguation from composition in an explicit prior step. Extensive experimental work shows that the proposed methodology indeed results in more accurate composite representations for the framework of Coecke et al. in particular and every other class of compositional models in general. As a last contribution, I formalize the explicit treatment of lexical ambiguity in the context of the categorical framework by resorting to categorical quantum mechanics (joint work with Coecke). In the proposed extension, the concept of a distributional vector is replaced with that of a density matrix, which compactly represents a probability distribution over the potential different meanings of the specific word. Composition takes the form of quantum measurements, leading to interesting analogies between quantum physics and linguistics.

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Contemporary transnational literature presents a unique interpretive problem, due to new methods of language and culture negotiation in the information age. The resulting condition, transnational compositionality, is evidenced by specific linguistic artifacts; to illustrate this I use three American novels as a case study: Nowhere Man by Aleksandar Hemon, Absurdistan by Gary Shteyngart, and The Brief Wondrous Life of Oscar Wao by Junot Díaz. By extension, many conventional literary elements are changed in the transnational since modernity: satire is no longer a lampooning of cultures but a questioning of the methods by which humans blend cultures together; similarly, complex symbolic constructions may no longer be taken at face value, for they now communicate more about cultural identity processes than static ideologies. If scholars are to achieve adequate interpretations of these elements, we must consider the global framework that has so intimately shaped them in the twenty-first century.

L'utilisation d'architectures neuronales profondes associée à des innovations spécifiques telles que les méthodes adversarielles, l’entraînement préalable sur de grands ensembles de données et l'estimation de l'information mutuelle a permis, ces dernières années, de progresser rapidement dans de nombreuses tâches de vision par ordinateur complexes telles que la classification d'images de catégories préalablement inconnues (apprentissage zéro-coups), la génération de scènes ou la classification multimodale. Malgré ces progrès, il n’est pas certain que les méthodes actuelles d’apprentissage de représentations suffiront à atteindre une performance équivalente au niveau humain sur des tâches visuelles arbitraires et, de fait, cela pose des questions quant à la direction de la recherche future. Dans cette thèse, nous nous concentrerons sur deux aspects des représentations qui semblent nécessaires pour atteindre de bonnes performances en aval pour l'apprentissage des représentations : la localité et la compositionalité. La localité peut être comprise comme la capacité d'une représentation à retenir des informations locales. Ceci sera pertinent dans de nombreux cas, et bénéficiera particulièrement à la vision informatique, domaine dans lequel les images naturelles comportent intrinsèquement des informations locales, par exemple des parties pertinentes d’une image, des objets multiples présents dans une scène... D'autre part, une représentation compositionnelle peut être comprise comme une représentation qui résulte d'une combinaison de parties plus simples. Les réseaux neuronaux convolutionnels sont intrinsèquement compositionnels, et de nombreuses images complexes peuvent être considérées comme la composition de sous-composantes pertinentes : les objets et attributs individuels dans une scène, les attributs sémantiques dans l'apprentissage zéro-coups en sont deux exemples. Nous pensons que ces deux propriétés détiennent la clé pour concevoir de meilleures méthodes d'apprentissage de représentations. Dans cette thèse, nous présentons trois articles traitant de la localité et/ou de la compositionnalité, et de leur application à l'apprentissage de représentations pour des tâches visuelles complexes. Dans le premier article, nous introduisons des méthodes de mesure de la localité et de la compositionnalité pour les représentations d'images, et nous démontrons que les représentations locales et compositionnelles sont plus performantes dans l'apprentissage zéro-coups. Nous utilisons également ces deux notions comme base pour concevoir un nouvel algorithme d'apprentissage des représentations qui atteint des performances de pointe dans notre cadre expérimental, une variante de l'apprentissage "zéro-coups" plus difficile où les informations externes, par exemple un pré-entraînement sur d'autres ensembles de données d'images, ne sont pas autorisées. Dans le deuxième article, nous montrons qu'en encourageant un générateur à conserver des informations locales au niveau de l'objet, à l'aide d'un module dit de similarité de graphes de scène, nous pouvons améliorer les performances de génération de scènes. Ce modèle met également en évidence l'importance de la composition, car de nombreux composants fonctionnent individuellement sur chaque objet présent. Pour démontrer pleinement la portée de notre approche, nous effectuons une analyse détaillée et proposons un nouveau cadre pour évaluer les modèles de génération de scènes. Enfin, dans le troisième article, nous montrons qu'en encourageant une forte information mutuelle entre les représentations multimodales locales et globales des images médicales en 2D et 3D, nous pouvons améliorer la classification et la segmentation des images. Ce cadre général peut être appliqué à une grande variété de contextes et démontre les avantages non seulement de la localité, mais aussi de la compositionnalité, car les représentations multimodales sont combinées pour obtenir une représentation plus générale. / The use of deep neural architectures coupled with specific innovations such as adversarial methods, pre-training on large datasets and mutual information estimation has in recent years allowed rapid progress in many complex vision tasks such as zero-shot learning, scene generation, or multi-modal classification. Despite such progress, it is still not clear if current representation learning methods will be enough to attain human-level performance on arbitrary visual tasks, and if not, what direction should future research take. In this thesis, we will focus on two aspects of representations that seem necessary to achieve good downstream performance for representation learning: locality and compositionality. Locality can be understood as a representation's ability to retain local information. This will be relevant in many cases, and will specifically benefit computer vision where natural images inherently feature local information, i.e. relevant patches of an image, multiple objects present in a scene... On the other hand, a compositional representation can be understood as one that arises from a combination of simpler parts. Convolutional neural networks are inherently compositional, and many complex images can be seen as composition of relevant sub-components: individual objects and attributes in a scene, semantic attributes in zero-shot learning are two examples. We believe both properties hold the key to designing better representation learning methods. In this thesis, we present 3 articles dealing with locality and/or compositionality, and their application to representation learning for complex visual tasks. In the first article, we introduce ways of measuring locality and compositionality for image representations, and demonstrate that local and compositional representations perform better at zero-shot learning. We also use these two notions as the basis for designing class-matching deep info-max, a novel representation learning algorithm that achieves state-of-the-art performance on our proposed "Zero-shot from scratch" setting, a harder zero-shot setting where external information, e.g. pre-training on other image datasets is not allowed. In the second article, we show that by encouraging a generator to retain local object-level information, using a scene-graph similarity module, we can improve scene generation performance. This model also showcases the importance of compositionality as many components operate individually on each object present. To fully demonstrate the reach of our approach, we perform detailed analysis, and propose a new framework to evaluate scene generation models. Finally, in the third article, we show that encouraging high mutual information between local and global multi-modal representations of 2D and 3D medical images can lead to improvements in image classification and segmentation. This general framework can be applied to a wide variety of settings, and demonstrates the benefits of not only locality, but also of compositionality as multi-modal representations are combined to obtain a more general one.

[pt] O meu objetivo é investigar o colapso e abandono do Tractatus tomado como um projeto para desenvolver a atraente imagem de uma lógica completamente combinatória, sintática e neutra. Há neste projeto uma tensão insolúvel entre a imagem de uma lógica neutra e a demanda que ela deveria ser usada para analisar completamente os fatos do mundo. Há mais articulações lógicas que a lógica tractariana com suas tautologias, contradições e verafuncionalidade pode expressar. Assim eu lido aqui com quatro colapsos inevitáveis do Tractatus, nomeadamente: I) a composicionalidade; II a tabela de verdade, III) a Bildkonzeption; e IV) a Neutralidade da Lógica. Há também quatro pontos centrais que eu cubro com esta investigação: 1) Problemas com a expressao vero-funcional de cores e números, e sua relação com intuições funcionais e espaciais; 2) o papel central e limites da tabela de verdade como um sistema notacional privilegiado para revelar a essência da linguagem e para evitar absurdos; 3) a crítica da interpretação recorrente de isomorfismo entre proposições elementares e fatos atômicos no Tractatus; 4) o papel central de um holismo tractariano que forma o pano de fundo para inevitável colisão entre lógica e sua aplicação. Eu então evidencio o tipo de invasão de organizações e elementos empíricos no (alegado) domínio neutro da lógica. Lógica não poderia então tomar conta de si mesma. / [en] My aim is to investigate the collapse and abandonment of the Tractatus held as a project to develop the attractive picture of a logic completely combinatorial, syntactical and neutral. There is in this project an unsolvable tension between this image of a neutral logic and the demand that it must be used to completely analyze the facts in the world. There are more logical connections than the tractarian logic, with its tautologies, contradictions and truth-functionality, can express. Thereby I deal here with four unavoidable collapses of Tractatus maininterdependent pillars, namely: I) the Compositionality; II) the truth tables; III) the Bildkonzeption; and IV) the Neutrality of Logic. There are four central points that I cover respectively in this investigation: 1) Problems with a truth-functional expression of colors and numbers, and its relation with functional and spatial intuitions; 2) the central role and limits of the truth tables as a special notation to reveal the essence of the language and to avoid absurdities; 3) a criticism of the recurrent interpretation of an isomorphism between elementary propositions and atomic facts in the Tractatus; and 4) the central role of a tractarian holism which forms the background to the unavoidable collision between logic and its application. I highlight then the kind of conceptual invasion of empirical arrangements and elements in the (allegedly) neutral domain of logic. Logic could not at last take care of itself.

Although there are units larger than the word in language, linguists have not been able to agree on a definition of these units. This study examines a variety of notions, relevant in the study of ”fixed” or ”frozen” expressions in contemporary French. Criteria such as memorization, unique context, non-compositionality, marked syntax, lexical blocking and grammatical blocking are analyzed in detail. A closer look at them reveals that in fact only one of them, lexical blocking, is both necessary and sufficient in the description of a fixed expression. The other criteria are, however, also important to the notion of ”fixedness”. It may well be that the criteria that have often been proposed in linguistic literature would benefit from being organized in a family resemblance rather than being used as necessary and sufficient conditions.