The categorical compositional approach to meaning has been successfully applied in natural language processing, outperforming other models in mainstream empirical language processing tasks. We show how this approach can be generalized to conceptual space models of cognition. In order to do this, first we introduce the category of convex relations as a new setting for categorical compositional semantics, emphasizing the convex structure important to conceptual space applications. We then show how to construct conceptual spaces for various types such as nouns, adjectives and verbs. Finally we show by means of examples how concepts can be systematically combined to establish the meanings of composite phrases from the meanings of their constituent parts. This provides the mathematical underpinnings of a new compositional approach to cognition.
In the current work, we have restricted ourselves to grammatical composition, and in particular pregroup grammar. However, the categorical compositional scheme can be instantiated in a number of ways. The grammar can be changed from pregroup grammar to another categorial grammar, as in @cite_20 , or a compositional scheme that is not grammatically based may be used. Indeed, one of the challenges of this approach is to find a model of composition that accurately reflects human behaviour. One way of doing so would be to use an approach in which the syntactic scheme is generated by the semantics of the universe of discourse. Furthermore, since phrases and sentences are represented as sets equipped with a convex algebra, the model can in future work be extended to include logical composition.
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The Distributional Compositional Categorical (DisCoCat) model is a mathematical framework that provides compositional semantics for meanings of natural language sentences. It consists of a computational procedure for constructing meanings of sentences, given their grammatical structure in terms of compositional type-logic, and given the empirically derived meanings of their words. For the particular case that the meaning of words is modelled within a distributional vector space model, its experimental predictions, derived from real large scale data, have outperformed other empirically validated methods that could build vectors for a full sentence. This success can be attributed to a conceptually motivated mathematical underpinning, something which the other methods lack, by integrating qualitative compositional type-logic and quantitative modelling of meaning within a category-theoretic mathematical framework. The type-logic used in the DisCoCat model is Lambekʼs pregroup grammar. Pregroup types form a poset al compact closed category, which can be passed, in a functorial manner, on to the compact closed structure of vector spaces, linear maps and tensor product. The diagrammatic versions of the equational reasoning in compact closed categories can be interpreted as the flow of word meanings within sentences. Pregroups simplify Lambekʼs previous type-logic, the Lambek calculus. The latter and its extensions have been extensively used to formalise and reason about various linguistic phenomena. Hence, the apparent reliance of the DisCoCat on pregroups has been seen as a shortcoming. This paper addresses this concern, by pointing out that one may as well realise a functorial passage from the original type-logic of Lambek, a monoidal bi-closed category, to vector spaces, or to any other model of meaning organised within a monoidal bi-closed category. The corresponding string diagram calculus, due to Baez and Stay, now depicts the flow of word meanings, and also reflects the structure of the parse trees of the Lambek calculus. We present an approach to learning a model-theoretic semantics for natural language tied to Freebase. Crucially, our approach uses an open predicate vocabulary, enabling it to produce denotations for phrases such as "Republican front-runner from Texas" whose semantics cannot be represented using the Freebase schema. Our approach directly converts a sentence's syntactic CCG parse into a logical form containing predicates derived from the words in the sentence, assigning each word a consistent semantics across sentences. This logical form is evaluated against a learned probabilistic database that defines a distribution over denotations for each textual predicate. A training phase produces this probabilistic database using a corpus of entity-linked text and probabilistic matrix factorization with a novel ranking objective function. We evaluate our approach on a compositional question answering task where it outperforms several competitive baselines. We also compare our approach against manually annotated Freebase queries, finding that our open predicate vocabulary enables us to answer many questions that Freebase cannot. This paper illustrates a hierarchical generative model for representing and recognizing compositional object categories with large intra-category variance. In this model, objects are broken into their constituent parts and the variability of configurations and relationships between these parts are modeled by stochastic attribute graph grammars, which are embedded in an And-Or graph for each compositional object category. It combines the power of a stochastic context free grammar (SCFG) to express the variability of part configurations, and a Markov random field (MRF) to represent the pictorial spatial relationships between these parts. As a generative model, different object instances of a category can be realized as a traversal through the And-Or graph to arrive at a valid configuration (like a valid sentence in language, by analogy). The inference recognition procedure is intimately tied to the structure of the model and follows a probabilistic formulation consisting of bottom-up detection steps for the parts, which in turn recursively activate the grammar rules for top-down verification and searches for missing parts. We present experiments comparing our results to state of art methods and demonstrate the potential of our proposed framework on compositional objects with cluttered backgrounds using training and testing data from the public Lotus Hill and Caltech datasets. Modelling compositional meaning for sentences using empirical distributional methods has been a challenge for computational linguists. We implement the abstract categorical model of (arXiv:1003.4394v1 [cs.CL]) using data from the BNC and evaluate it. The implementation is based on unsupervised learning of matrices for relational words and applying them to the vectors of their arguments. The evaluation is based on the word disambiguation task developed by Mitchell and Lapata (2008) for intransitive sentences, and on a similar new experiment designed for transitive sentences. Our model matches the results of its competitors in the first experiment, and betters them in the second. The general improvement in results with increase in syntactic complexity showcases the compositional power of our model. Modelling the compositional process by which the meaning of an utterance arises from the meaning of its parts is a fundamental task of Natural Language Processing. In this paper we draw upon recent advances in the learning of vector space representations of sentential semantics and the transparent interface between syntax and semantics provided by Combinatory Categorial Grammar to introduce Combinatory Categorial Autoencoders. This model leverages the CCG combinatory operators to guide a non-linear transformation of meaning within a sentence. We use this model to learn high dimensional embeddings for sentences and evaluate them in a range of tasks, demonstrating that the incorporation of syntax allows a concise model to learn representations that are both effective and general. Combinatory Categorial Grammar (CCG) offers a new approach to the theory of natural language grammar. Coordination, relativization, and related prosodic phenomena have been analyzed in CCG in terms of a radically revised notion of surface structure. CCG surface structures do not exhibit traditional notions of syntactic dominance and command, and do not constitute an autonomous level of representation. Instead, they reflect the computations by which a sentence may be realized or analyzed, to synchronously define a predicate-argument structure, or logical form. Surface Structure and Interpretation shows that binding and control can be captured at this level, preserving the advantages of CCG as an account of coordination and unbounded dependency.The core of the book is a detailed treatment of extraction, a focus of syntactic research since the early work of Chomsky and Ross. The topics addressed include the sources of subject-object asymmetries and phenomena attributed to the Empty Category Principle (ECP), asymmetric islands, parasitic gaps, and the relation of coordination and extraction, including their interactions with binding theory. In his conclusion, the author relates CCG to other categorial and type-driven approaches and to proposals for minimalism in linguistic theory.Linguistic Inquiry Monograph No. 30 The compositionality of meaning extends beyond the single sentence. Just as words combine to form the meaning of sentences, so do sentences combine to form the meaning of paragraphs, dialogues and general discourse. We introduce both a sentence model and a discourse model corresponding to the two levels of compositionality. The sentence model adopts convolution as the central operation for composing semantic vectors and is based on a novel hierarchical convolutional neural network. The discourse model extends the sentence model and is based on a recurrent neural network that is conditioned in a novel way both on the current sentence and on the current speaker. The discourse model is able to capture both the sequentiality of sentences and the interaction between different speakers. Without feature engineering or pretraining and with simple greedy decoding, the discourse model coupled to the sentence model obtains state of the art performance on a dialogue act classification experiment. The compositionality of meaning extends beyond the single sentence. Just as words combine to form the meaning of sentences, so do sentences combine to form the meaning of paragraphs, dialogues and general discourse. We introduce both a sentence model and a discourse model corresponding to the two levels of compositionality. The sentence model adopts convolution as the central operation for composing semantic vectors and is based on a novel hierarchical convolutional neural network. The discourse model extends the sentence model and is based on a recurrent neural network that is conditioned in a novel way both on the current sentence and on the current speaker. The discourse model is able to capture both the sequentiality of sentences and the interaction between different speakers. Without feature engineering or pretraining and with simple greedy decoding, the discourse model coupled to the sentence model obtains state of the art performance on a dialogue act classification experiment. Formal and distributional semantic models offer complementary benefits in modeling meaning. The categorical compositional distributional model of meaning of (2010) (abbreviated to DisCoCat in the title) combines aspects of both to provide a general framework in which meanings of words, obtained distributionally, are composed using methods from the logical setting to form sentence meaning. Concrete consequences of this general abstract setting and applications to empirical data are under active study (, 2011; Grefenstette and Sadrzadeh, 2011). In this paper, we extend this study by examining transitive verbs, represented as matrices in a DisCoCat. We discuss three ways of constructing such matrices, and evaluate each method in a disambiguation task developed by Grefenstette and Sadrzadeh (2011). We introduce a novel compositional language model that works on PredicateArgument Structures (PASs). Our model jointly learns word representations and their composition functions using bagof-words and dependency-based contexts. Unlike previous word-sequencebased models, our PAS-based model composes arguments into predicates by using the category information from the PAS. This enables our model to capture longrange dependencies between words and to better handle constructs such as verbobject and subject-verb-object relations. We verify this experimentally using two phrase similarity datasets and achieve results comparable to or higher than the previous best results. Our system achieves these results without the need for pretrained word vectors and using a much smaller training corpus; despite this, for the subject-verb-object dataset our model improves upon the state of the art by as much as ∼10 in relative performance. Categorical compositional distributional models unify compositional formal semantic models and distributional models by composing phrases with tensor-based methods from vector representations. For the tensor-based compositions, (2014) showed that word vectors obtained from the continuous bag-of-words (CBOW) model are competitive with those from co-occurrence based models. However, because word vectors from the CBOW model are trained assuming additive interactions between context words, the word composition used for the training mismatches to the tensor-based methods used for evaluating the actual compositions including pointwise multiplication and tensor product of context vectors. In this work, we show whether the word embeddings from extended CBOW models using multiplication or tensor product between context words, reflecting the actual composition methods, can show better performance than those from the baseline CBOW model in actual tasks of compositions with multiplication or tensor-based methods. This paper presents the task on the evaluation of Compositional Distributional Semantics Models on full sentences organized for the first time within SemEval2014. Participation was open to systems based on any approach. Systems were presented with pairs of sentences and were evaluated on their ability to predict human judgments on (i) semantic relatedness and (ii) entailment. The task attracted 21 teams, most of which participated in both subtasks. We received 17 submissions in the relatedness subtask (for a total of 66 runs) and 18 in the entailment subtask (65 runs). The complex compositional structure of language makes problems at the intersection of vision and language challenging. But language also provides a strong prior that can result in good superficial performance, without the underlying models truly understanding the visual content. This can hinder progress in pushing state of art in the computer vision aspects of multi-modal AI. In this paper, we address binary Visual Question Answering (VQA) on abstract scenes. We formulate this problem as visual verification of concepts inquired in the questions. Specifically, we convert the question to a tuple that concisely summarizes the visual concept to be detected in the image. If the concept can be found in the image, the answer to the question is "yes", and otherwise "no". Abstract scenes play two roles (1) They allow us to focus on the highlevel semantics of the VQA task as opposed to the low-level recognition problems, and perhaps more importantly, (2) They provide us the modality to balance the dataset such that language priors are controlled, and the role of vision is essential. In particular, we collect fine-grained pairs of scenes for every question, such that the answer to the question is "yes" for one scene, and "no" for the other for the exact same question. Indeed, language priors alone do not perform better than chance on our balanced dataset. Moreover, our proposed approach matches the performance of a state-of-the-art VQA approach on the unbalanced dataset, and outperforms it on the balanced dataset. The development of compositional distributional models of semantics reconciling the empirical aspects of distributional semantics with the compositional aspects of formal semantics is a popular topic in the contemporary literature. This paper seeks to bring this reconciliation one step further by showing how the mathematical constructs commonly used in compositional distributional models, such as tensors and matrices, can be used to simulate different aspects of predicate logic. This paper discusses how the canonical isomorphism between tensors and multilinear maps can be exploited to simulate a full-blown quantifier-free predicate calculus using tensors. It provides tensor interpretations of the set of logical connectives required to model propositional calculi. It suggests a variant of these tensor calculi capable of modelling quantifiers, using few non-linear operations. It finally discusses the relation between these variants, and how this relation should constitute the subject of future work. The complex compositional structure of language makes problems at the intersection of vision and language challenging. But language also provides a strong prior that can result in good superficial performance, without the underlying models truly understanding the visual content. This can hinder progress in pushing state of art in the computer vision aspects of multi-modal AI. In this paper, we address binary Visual Question Answering (VQA) on abstract scenes. We formulate this problem as visual verification of concepts inquired in the questions. Specifically, we convert the question to a tuple that concisely summarizes the visual concept to be detected in the image. If the concept can be found in the image, the answer to the question is "yes", and otherwise "no". Abstract scenes play two roles (1) They allow us to focus on the high-level semantics of the VQA task as opposed to the low-level recognition problems, and perhaps more importantly, (2) They provide us the modality to balance the dataset such that language priors are controlled, and the role of vision is essential. In particular, we collect fine-grained pairs of scenes for every question, such that the answer to the question is "yes" for one scene, and "no" for the other for the exact same question. Indeed, language priors alone do not perform better than chance on our balanced dataset. Moreover, our proposed approach matches the performance of a state-of-the-art VQA approach on the unbalanced dataset, and outperforms it on the balanced dataset. We present an approach for learning context-dependent semantic parsers to identify and interpret time expressions. We use a Combinatory Categorial Grammar to construct compositional meaning representations, while considering contextual cues, such as the document creation time and the tense of the governing verb, to compute the final time values. Experiments on benchmark datasets show that our approach outperforms previous stateof-the-art systems, with error reductions of 13 to 21 in end-to-end performance. One of the main aims of this paper is to show that the nature of the communication mechanism of concurrent constraint languages is essentially different from the classical paradigms of CCS, CSP and ACP. We define indeed a compositional semantics based on linear sequences, while more complicated structures, like trees and failure sets, are needed to model composition ally CCS, CSP and ACP. From this model we are able to derive a fully abstract semantics by imposing some saturation conditions, that model the monotonic nature of communication in concurrent constraint languages. Finally, we show that if we eliminate the consistency check, and drop the distinction between success and deadlock, then our model is isomorphic to the semantics based on Scott’s closure operators proposed in [SRP91]. Combinatory Categorial Grammar is a generalization of classical Categorial Grammar that is at the least greater level of expressive power than context-free grammar that has yet been identified. The paper reviews its use for the explanatory analysis of natural language grammar, particularly with respect to bounded and unbounded constructions, multiple dependencies, relativization, and coordination. In this paper we present a compositional and-or graph grammar model for human pose estimation. Our model has three distinguishing features: (i) large appearance differences between people are handled compositionally by allowing parts or collections of parts to be substituted with alternative variants, (ii) each variant is a sub-model that can define its own articulated geometry and context-sensitive compatibility with neighboring part variants, and (iii) background region segmentation is incorporated into the part appearance models to better estimate the contrast of a part region from its surroundings, and improve resilience to background clutter. The resulting integrated framework is trained discriminatively in a max-margin framework using an efficient and exact inference algorithm. We present experimental evaluation of our model on two popular datasets, and show performance improvements over the state-of-art on both benchmarks. We present a novel and effective approach for generating new clothing on a wearer through generative adversarial learning. Given an input image of a person and a sentence describing a different outfit, our model “redresses” the person as desired, while at the same time keeping the wearer and her his pose unchanged. Generating new outfits with precise regions conforming to a language description while retaining wearer’s body structure is a new challenging task. Existing generative adversarial networks are not ideal in ensuring global coherence of structure given both the input photograph and language description as conditions. We address this challenge by decomposing the complex generative process into two conditional stages. In the first stage, we generate a plausible semantic segmentation map that obeys the wearer’s pose as a latent spatial arrangement. An effective spatial constraint is formulated to guide the generation of this semantic segmentation map. In the second stage, a generative model with a newly proposed compositional mapping layer is used to render the final image with precise regions and textures conditioned on this map. We extended the DeepFashion dataset [8] by collecting sentence descriptions for 79K images. We demonstrate the effectiveness of our approach through both quantitative and qualitative evaluations. A user study is also conducted.