Semantic composition is the task of understanding the meaning of text by composing the meanings of the individual words in the text. Semantic decomposition is the task of understanding the meaning of an individual word by decomposing it into various aspects (factors, constituents, components) that are latent in the meaning of the word. We take a distributional approach to semantics, in which a word is represented by a context vector. Much recent work has considered the problem of recognizing compositions and decompositions, but we tackle the more dicult generation problem. For simplicity, we focus on noun-modier bigrams and noun unigrams. A test for semantic composition is, given context vectors for the noun and modier in a noun-modier bigram ( red salmon), generate a noun unigram that is synonymous with the given bigram (sockeye). A test for semantic decomposition is, given a context vector for a noun unigram (snifter), generate a noun-modier bigram that is synonymous with the given unigram ( brandy glass). With a vocabulary of about 73,000 unigrams from WordNet, there are 73,000 candidate unigram compositions for a bigram and 5,300,000,000 (73,000 squared) candidate bigram decompositions for a unigram. We generate ranked lists of potential solutions in two passes. A fast unsupervised learning algorithm generates an initial list of candidates and then a slower supervised learning algorithm renes the list. We evaluate the candidate solutions by comparing them to WordNet synonym sets. For decomposition (unigram to bigram), the top 100 most highly ranked bigrams include a WordNet synonym of the given unigram 50.7 of the time. For composition (bigram to unigram), the top 100 most highly ranked unigrams include a WordNet synonym of the given bigram 77.8 of the time.
mitchell08,mitchell10 suggest element-wise multiplication as a composition operation, @math , where @math . Since @math , element-wise multiplication is not sensitive to word order. However, in an experimental evaluation of seven compositional models and two noncompositional models, element-wise multiplication had the best performance @cite_5 .
@cite_5
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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. Additive composition ( in Discourse Process 15:285---307, 1998; Landauer and Dumais in Psychol Rev 104(2):211, 1997; Mitchell and Lapata in Cognit Sci 34(8):1388---1429, 2010) is a widely used method for computing meanings of phrases, which takes the average of vector representations of the constituent words. In this article, we prove an upper bound for the bias of additive composition, which is the first theoretical analysis on compositional frameworks from a machine learning point of view. The bound is written in terms of collocation strength; we prove that the more exclusively two successive words tend to occur together, the more accurate one can guarantee their additive composition as an approximation to the natural phrase vector. Our proof relies on properties of natural language data that are empirically verified, and can be theoretically derived from an assumption that the data is generated from a Hierarchical Pitman---Yor Process. The theory endorses additive composition as a reasonable operation for calculating meanings of phrases, and suggests ways to improve additive compositionality, including: transforming entries of distributional word vectors by a function that meets a specific condition, constructing a novel type of vector representations to make additive composition sensitive to word order, and utilizing singular value decomposition to train word vectors. We present a general learning-based approach for phrase-level sentiment analysis that adopts an ordinal sentiment scale and is explicitly compositional in nature. Thus, we can model the compositional effects required for accurate assignment of phrase-level sentiment. For example, combining an adverb (e.g., "very") with a positive polar adjective (e.g., "good") produces a phrase ("very good") with increased polarity over the adjective alone. Inspired by recent work on distributional approaches to compositionality, we model each word as a matrix and combine words using iterated matrix multiplication, which allows for the modeling of both additive and multiplicative semantic effects. Although the multiplication-based matrix-space framework has been shown to be a theoretically elegant way to model composition (Rudolph and Giesbrecht, 2010), training such models has to be done carefully: the optimization is non-convex and requires a good initial starting point. This paper presents the first such algorithm for learning a matrix-space model for semantic composition. In the context of the phrase-level sentiment analysis task, our experimental results show statistically significant improvements in performance over a bag-of-words model. 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.