| { |
| "paper_id": "D13-1014", |
| "header": { |
| "generated_with": "S2ORC 1.0.0", |
| "date_generated": "2023-01-19T16:43:05.539179Z" |
| }, |
| "title": "Modeling and Learning Semantic Co-Compositionality through Prototype Projections and Neural Networks", |
| "authors": [ |
| { |
| "first": "Masashi", |
| "middle": [], |
| "last": "Tsubaki", |
| "suffix": "", |
| "affiliation": { |
| "laboratory": "", |
| "institution": "Nara Institute of Science and Technology", |
| "location": { |
| "postCode": "8916-5, 630-0192", |
| "settlement": "Takayama, Ikoma", |
| "region": "Nara", |
| "country": "Japan" |
| } |
| }, |
| "email": "masashi-t@is.naist.jp" |
| }, |
| { |
| "first": "Kevin", |
| "middle": [], |
| "last": "Duh", |
| "suffix": "", |
| "affiliation": { |
| "laboratory": "", |
| "institution": "Nara Institute of Science and Technology", |
| "location": { |
| "postCode": "8916-5, 630-0192", |
| "settlement": "Takayama, Ikoma", |
| "region": "Nara", |
| "country": "Japan" |
| } |
| }, |
| "email": "kevinduh@is.naist.jp" |
| }, |
| { |
| "first": "Masashi", |
| "middle": [], |
| "last": "Shimbo", |
| "suffix": "", |
| "affiliation": { |
| "laboratory": "", |
| "institution": "Nara Institute of Science and Technology", |
| "location": { |
| "postCode": "8916-5, 630-0192", |
| "settlement": "Takayama, Ikoma", |
| "region": "Nara", |
| "country": "Japan" |
| } |
| }, |
| "email": "shimbo@is.naist.jp" |
| }, |
| { |
| "first": "Yuji", |
| "middle": [], |
| "last": "Matsumoto", |
| "suffix": "", |
| "affiliation": { |
| "laboratory": "", |
| "institution": "Nara Institute of Science and Technology", |
| "location": { |
| "postCode": "8916-5, 630-0192", |
| "settlement": "Takayama, Ikoma", |
| "region": "Nara", |
| "country": "Japan" |
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| "email": "" |
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| "abstract": "We present a novel vector space model for semantic co-compositionality. Inspired by Generative Lexicon Theory (Pustejovsky, 1995), our goal is a compositional model where both predicate and argument are allowed to modify each others' meaning representations while generating the overall semantics. This readily addresses some major challenges with current vector space models, notably the polysemy issue and the use of one representation per word type. We implement cocompositionality using prototype projections on predicates/arguments and show that this is effective in adapting their word representations. We further cast the model as a neural network and propose an unsupervised algorithm to jointly train word representations with co-compositionality. The model achieves the best result to date (\u03c1 = 0.47) on the semantic similarity task of transitive verbs (Grefenstette and Sadrzadeh, 2011).", |
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| "abstract": [ |
| { |
| "text": "We present a novel vector space model for semantic co-compositionality. Inspired by Generative Lexicon Theory (Pustejovsky, 1995), our goal is a compositional model where both predicate and argument are allowed to modify each others' meaning representations while generating the overall semantics. This readily addresses some major challenges with current vector space models, notably the polysemy issue and the use of one representation per word type. We implement cocompositionality using prototype projections on predicates/arguments and show that this is effective in adapting their word representations. We further cast the model as a neural network and propose an unsupervised algorithm to jointly train word representations with co-compositionality. The model achieves the best result to date (\u03c1 = 0.47) on the semantic similarity task of transitive verbs (Grefenstette and Sadrzadeh, 2011).", |
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| "text": "Vector space models of words have been very successful in capturing the semantic and syntactic characteristics of individual lexical items (Turney and Pantel, 2010) . Much research has addressed the question of how to construct individual word representations, for example distributional models (Mitchell and Lapata, 2010) and neural models (Collobert and Weston, 2008) . These word representations are used in various natural language processing (NLP) tasks such as part-of-speech tagging, chunking, named entity recognition, and semantic Figure 1 : Here, we capture the semantics of run in run company by projecting the original word representation of run to the prototype space of company (and vice versa).", |
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| "text": "(Turney and Pantel, 2010)", |
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| "text": "(Mitchell and Lapata, 2010)", |
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| "text": "(Collobert and Weston, 2008)", |
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| "section": "Introduction", |
| "sec_num": "1" |
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| "text": "role labeling (Turian et al., 2010; Collobert et al., 2011) . Recently, modeling of semantic compositionality (Frege, 1892) in vector space has emerged as another important line of research (Mitchell and Lapata, 2008; Mitchell and Lapata, 2010 ; Baroni and Zamparelli, 2010; Socher et al., 2012; Grefenstette and Sadrzadeh, 2011; Van de Cruys et al., 2013) . The goal is to formulate how individual word representations ought to be combined to achieve phrasal or sentential semantics.", |
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| "section": "Introduction", |
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| "text": "The main questions for semantic compositionality that we are concerned with are: (1) how can polysemy be handled by a single vector representation per word type, learned by either a distributional or neural model, and (2) how does composition resolve these ambiguities. To this end, we are inspired by the idea of type coercion and co-compositionality in Generative Lexicon Theory (Pustejovsky, 1995) . Co-compositionality advocates that instead of a predicate-argument view of composition, both predicate and argument influence/coerce each other to generate the overall meaning. For example, consider a polysemous word like run:", |
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| { |
| "text": "\u2022 (a) He runs the company.", |
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| "text": "\u2022 (b) He runs the marathon.", |
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| "text": "Run may have several senses, but the prototypical verbs that select for company differ from those that select for marathon, and thus the ambiguity at the word level is resolved at the sentence level. The same is true for the other direction, where the predicate also coerces meaning to the argument to fit expectation.", |
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| "text": "We believe that models for semantic composition ought to incorporate elements of cocompositionality. We propose such a model here, using what we call prototype projections. For each predicate, we transform its vector representation by projecting it into a latent space that is prototypical of its argument. This projection is performed analogously for each argument as well, and the final meaning is computed by composition of these transformed vectors (Figure 1 ). In addition, the model is cast as a neural network where word representations could be re-trained or fine-tuned. 1 Our contributions are two-fold:", |
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| "text": "1. We propose a novel model for semantic cocompositionality. This model, based on prototype projections, is easy to implement and achieves state-of-the-art performance in the sentence similarity dataset developed by Grefenstette and Sadrzadeh (2011).", |
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| "text": "word representations (eg., SDS and NLM in Section 2) are sufficiently effective at capturing 1 While we are inspired by co-compositionality, it is important to note that our model does not implement qualia structure and other important components of Generative Lexicon Theory. We operate within the vector space model of distributional semantics, so these ideas are implemented with matrix algebra, which is a natural fit with neural networks. polysemy, as long as we have the proper mechanism to tease out the proper sense during composition. We further propose an unsupervised neural network training algorithm that jointly fine-tunes the word representations within the co-composition model, resulting in even better performance on the sentence similarity task.", |
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| "section": "Our results empirically confirm that existing", |
| "sec_num": "2." |
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| "text": "We would like to emphasize the second contribution especially. Semantics research is divided in two strands, one focusing on learning word representations without consideration for compositionality, and the other focusing on compositional semantics using the representations only as an input. But issues are actually related from the linguistics perspective, and even more so if we adopt a Generative Lexicon perspective. Our neural network model bridges these two strands of research by modeling cocompositionality and learning word representations simultaneously. We note that methods using context effects have been explored by Erk and Pad\u00f3 (2008; 2009) and Thater et al. (2010; , but to the best of our knowledge, ours is the first model to perform co-compositionality and learning of word representations jointly.", |
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| "section": "Our results empirically confirm that existing", |
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| "text": "In the following, we first provide background to the word representations employed here (Section 2). We describe the model for co-compositionality in Section 3 and the corresponding neural network in Section 4. Evaluation and experiments are presented in Sections 5 and 6. Finally, we end with related work (Section 7) and conclusions (Section 8).", |
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| "section": "Our results empirically confirm that existing", |
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| "text": "Word meaning is often represented in a high dimensional space, where each element corresponds to some contextual element in which the word is found. Mitchell and Lapata (2010) present a co-occurrencebased semantic space called Simple Distributional Semantic space (SDS). Their SDS model uses a context window of five words on either side of the target word and 2,000 vector components, representing the most frequent context words (excluding a list of stop words). These components v i (t) were set to the ratio of the probability of the context word given the target word to the probability of the context word overall:", |
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| "section": "Simple Distributional Semantic space (SDS) word vectors", |
| "sec_num": "2.1" |
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| { |
| "text": "v i (t) = p(c i |t) p(c i ) = f req c i ,t \u00d7 f req total f req t \u00d7 f req c i (1)", |
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| "section": "Simple Distributional Semantic space (SDS) word vectors", |
| "sec_num": "2.1" |
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| "text": "where f req c i ,t , f req total , f req t and f req c i are the frequencies of the context word c i with the target word t, the total count of all word tokens, the frequency of the target word t, and the frequency of the context word c i , respectively.", |
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| "text": "Another popular way to learn word representations is based on the Neural Language Model (NLM) (Bengio et al., 2003) . In comparison with SDS, NLM tend to be low-dimensional (e.g. 50 dimensions) but employ dense features. These dense feature vectors are usually called word embeddings, and it has been shown that such vectors can capture interesting linear relationships, such as king \u2212 man + woman \u2248 queen (Mikolov et al., 2013) . In this work, we adopt the model by Collobert and Weston (2008) . The idea is to construct a neural network based on word sequences, where one outputs high scores for n-grams that occur in a large unlabeled corpus and low scores for nonsense n-grams where one word is replaced by a random word. This word representation with NLM has been used to good effect, for example in (Turian et al., 2010; Collobert et al., 2011; Huang et al., 2012) where induced word representations are used with sophisticated features to improve performance in various NLP tasks. Specifically, we first represent the word sequence as a vector", |
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| "section": "Neural Language Model (NLM) word embeddings", |
| "sec_num": "2.2" |
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| { |
| "text": "x = [d(w 1 ); d(w 2 ); . . . ; d(w m )],", |
| "cite_spans": [], |
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| "eq_spans": [], |
| "section": "Neural Language Model (NLM) word embeddings", |
| "sec_num": "2.2" |
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| "text": "where w i is i th word in the sequence, m is the window size, d(w) is the vector representation of word w (an n-dimensional column vector) and", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Neural Language Model (NLM) word embeddings", |
| "sec_num": "2.2" |
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| { |
| "text": "[d(w 1 ); d(w 2 ); . . . ; d(w m )]", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Neural Language Model (NLM) word embeddings", |
| "sec_num": "2.2" |
| }, |
| { |
| "text": "is the concatenation of word vectors as an input of neural network. Second, we compute the score of the sequence,", |
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| "section": "Neural Language Model (NLM) word embeddings", |
| "sec_num": "2.2" |
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| { |
| "text": "EQUATION", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [ |
| { |
| "start": 0, |
| "end": 8, |
| "text": "EQUATION", |
| "ref_id": "EQREF", |
| "raw_str": "score(x) = s T (tanh(Wx + b))", |
| "eq_num": "(2)" |
| } |
| ], |
| "section": "Neural Language Model (NLM) word embeddings", |
| "sec_num": "2.2" |
| }, |
| { |
| "text": "where W \u2208 R h\u00d7 (mn) and s \u2208 R h are the first and second layer weights of the neural network, and b \u2208 R h is the bias unit of hidden layer. The superscript T represents transposition, and tanh is applied element-wise. We also create a corrupted sequence", |
| "cite_spans": [ |
| { |
| "start": 15, |
| "end": 19, |
| "text": "(mn)", |
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| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Neural Language Model (NLM) word embeddings", |
| "sec_num": "2.2" |
| }, |
| { |
| "text": "x c = [d(w 1 ); d(w 2 ); . . . ; d(w m \u2032 )]", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Neural Language Model (NLM) word embeddings", |
| "sec_num": "2.2" |
| }, |
| { |
| "text": "where w m \u2032 is chosen randomly from the vocabulary. We compute the score of this implicit negative sequence x c with the same neural network, score(x c ) = s T (tanh(Wx c + b)). Finally, we get the cost function of this training algorithm as follow.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Neural Language Model (NLM) word embeddings", |
| "sec_num": "2.2" |
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| { |
| "text": "EQUATION", |
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| "raw_str": "J = max(0, 1 \u2212 score(x) + score(x c ))", |
| "eq_num": "(3)" |
| } |
| ], |
| "section": "Neural Language Model (NLM) word embeddings", |
| "sec_num": "2.2" |
| }, |
| { |
| "text": "In order to minimize this cost function, we optimize the parameters \u03b8 = (s, W, b, x) via backpropagation with stochastic gradient descent (SGD).", |
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| "section": "Neural Language Model (NLM) word embeddings", |
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| { |
| "text": "3 The Model", |
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| "section": "Neural Language Model (NLM) word embeddings", |
| "sec_num": "2.2" |
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| "text": "Generative Lexicon Theory (Pustejovsky, 1995) makes a distinction between accidental polysemy (homonyms, e.g. bank as financial institution vs. as river side) and logical polysemy (e.g. figure and ground meanings of door). Our model handles both cases using the concept of projection to latent prototype space. The fundamental idea is that for each word w and a syntactic/semantic (binary) relation R (such as verb-object relation), w has a set of prototype words with which it frequently occurs in relation R. For example, if w is a word company, and R is the object-verb relation, prototype words should include start, build, and buy ( Figure 1 ). For each word-relation pair, we pre-compute the latent semantic subspace spanned by these prototype words. Later, when we encounter a phrase expressing a relation R between two words w 1 and w 2 , each word is first projected onto a latent subspace determined by the other word and relation R. The projection operation shifts the meaning of individual words in accordance with context, and through this operation we realize coercion/co-composition. And finally, the meaning of the phrase is computed from the two projected points in the semantic space.", |
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| "text": "(Pustejovsky, 1995)", |
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| "text": "Figure 1", |
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| "section": "Prototype Projection", |
| "sec_num": "3.1" |
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| "text": "Let us describe how to compute the latent subspace associated with a word w 0 and a relation R. First, we collect from a corpus a set of prototype words that occur frequently in relation R with target word w 0 . So for example in Figure 1, company, and R = VerbOf is the object-verb relation,", |
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| "text": "Figure 1,", |
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| "text": "W (VerbOf, company) = {start, build, . . . , buy}. Now let W (R, w 0 ) = {w 1 , w 2 , \u2022 \u2022 \u2022 , w m }", |
| "cite_spans": [], |
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| "section": "Prototype Projection", |
| "sec_num": "3.1" |
| }, |
| { |
| "text": "be the m prototype words we collected, and let d(w) denote the n-dimensional (column) vector representation of word w (either by SDS or NLM representation). We make an m\u00d7n matrix C (R,w 0 ) by stacking the prototype word vectors, i.e.,", |
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| "raw_str": "C (R,w 0 ) = [d(w 1 ), d(w 2 ), \u2022 \u2022 \u2022 , d(w m )] T", |
| "eq_num": "(4)" |
| } |
| ], |
| "section": "Prototype Projection", |
| "sec_num": "3.1" |
| }, |
| { |
| "text": "and then apply Singular Value Decomposition (SVD) to extract the latent space from this matrix: Figure 2 shows the graphical representation of this matrix factorization. In NLP tasks, SVD is often applied to a term-document matrix, but in our model, we apply SVD to the matrix consisting of word vectors.", |
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| "start": 96, |
| "end": 104, |
| "text": "Figure 2", |
| "ref_id": "FIGREF0" |
| } |
| ], |
| "eq_spans": [], |
| "section": "Prototype Projection", |
| "sec_num": "3.1" |
| }, |
| { |
| "text": "C (R,w 0 ) \u2248 U k \u03a3 k V T k . (5) word 1 word vector dimension n word 2 word m m \u30fb \u30fb \u30fb \u30fb \u30fb \u30fb k k n \u30fb \u30fb \u30fb \u30fb \u30fb \u30fb \u30fb \u30fb \u30fb \u30fb \u30fb \u30fb \u30fb \u30fb \u30fb k k \u03a3 k V k T U k C \u2248", |
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| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Prototype Projection", |
| "sec_num": "3.1" |
| }, |
| { |
| "text": "Intuitively, \u03a3 k V T k represents the latent subspace formed by prototypical words", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Prototype Projection", |
| "sec_num": "3.1" |
| }, |
| { |
| "text": "W (R, w 0 ) = {w 1 , w 2 , \u2022 \u2022 \u2022 , w m }.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Prototype Projection", |
| "sec_num": "3.1" |
| }, |
| { |
| "text": "We call this matrix the prototype space of word w 0 with respect to relation R.", |
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| "eq_spans": [], |
| "section": "Prototype Projection", |
| "sec_num": "3.1" |
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| { |
| "text": "Note that the matrix of orthogonal projection onto this prototype space is given by", |
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| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Prototype Projection", |
| "sec_num": "3.1" |
| }, |
| { |
| "text": "P (R,w 0 ) = (\u03a3 k V T k ) T (\u03a3 k V T k )", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Prototype Projection", |
| "sec_num": "3.1" |
| }, |
| { |
| "text": ". Hence, when we observe a relation R(w 0 , w), the projected representation of word w in this context is computed by prpj (R,w 0 ) (w) defined as follows: ", |
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| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Prototype Projection", |
| "sec_num": "3.1" |
| }, |
| { |
| "text": "EQUATION", |
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| "eq_spans": [ |
| { |
| "start": 0, |
| "end": 8, |
| "text": "EQUATION", |
| "ref_id": "EQREF", |
| "raw_str": "prpj (R,w 0 ) (w) = P (R,w 0 ) d(w).", |
| "eq_num": "(6)" |
| } |
| ], |
| "section": "Prototype Projection", |
| "sec_num": "3.1" |
| }, |
| { |
| "text": "In order to model co-compositionality, we apply prototype projection to both the verb and the object. In particular, suppose verb is w v and object is w o , C (VerbOf,wo) is used to project w v and C (ObjOf,wv) is used to project w o . The vector that represents the overall meaning of verb-object with prototype projection is computed by:", |
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| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Co-Compositionality", |
| "sec_num": "3.2" |
| }, |
| { |
| "text": "cocomp(w v , w o ) = f (prpj (VerbOf,wo) (w v ), prpj (ObjOf,wv) (w o )) (7)", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Co-Compositionality", |
| "sec_num": "3.2" |
| }, |
| { |
| "text": "Function f can be a compositional computation like simple addition or element-wise multiplication of two vectors. This is graphically shown in Figure 1 .", |
| "cite_spans": [], |
| "ref_spans": [ |
| { |
| "start": 143, |
| "end": 151, |
| "text": "Figure 1", |
| "ref_id": null |
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| "section": "Co-Compositionality", |
| "sec_num": "3.2" |
| }, |
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| "text": "In this section, we propose a new neural language model that learns word representations while jointly accounting for compositional semantics. One central assumption of our work (and many other works in compositional semantics) is that a single vector per word type sufficiently represents the multiple meanings and usage patterns of a word. 3 That means that for a polysemous word, its word vector actually represents an aggregation of the distinctly different contexts it occurs in. We will show that such an assumption is quite reasonable under our model, since the prototype projections successfully tease out the proper semantics from these aggregate representations. However, it is natural to wonder whether one can do better if one incorporates the compositional model into the training of the word representations in the first place. To do so, we formulate a novel model called Compositional Neural Language Model (Section 4.1). This model is a combination of an unsupervised training algorithm with basic compositionality (addition/multiplications). Then, we extend this model with the projection idea in section 3.2 to formulate a Co-Compositional Neural Language Model (Section 4.2).", |
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| "start": 342, |
| "end": 343, |
| "text": "3", |
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| } |
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| "section": "Unsupervised Learning of Co-Compositionality", |
| "sec_num": "4" |
| }, |
| { |
| "text": "(C-NLM) Compositional Neural Language Model (C-NLM)", |
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| "eq_spans": [], |
| "section": "Compositional Neural Language Model", |
| "sec_num": "4.1" |
| }, |
| { |
| "text": "is a combination of a word representation learning method and compositional rule. In contrast to other compositional models based on machine learning, our model has no complex parameters for modeling composition. Composition is modeled using straightforward vector addition/multiplications; instead, what is learned is the word representation. Figure 3 shows the C-NLM. The learning algorithm is unsupervised, and works by artificially 3 There are works on multiple representations, e.g., (Reisinger and Mooney, 2010) ; we focus on single representation here. generating negative examples in a fashion analogous to the NLM learning algorithm of (Collobert and Weston, 2008) and contrastive estimation (Smith and Eisner, 2005) . First, given some initial word representations and raw sentences, we compute the compositional vector with function f (in this section, we will assume that we will be using the addition operator). Second, in order to obtain the score of compositional vector, we compute the dot product with vector s \u2208 R n (n is the dimension of the word vector space): verb vector", |
| "cite_spans": [ |
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| "start": 436, |
| "end": 437, |
| "text": "3", |
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| "end": 517, |
| "text": "(Reisinger and Mooney, 2010)", |
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| }, |
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| "end": 673, |
| "text": "(Collobert and Weston, 2008)", |
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| "end": 725, |
| "text": "(Smith and Eisner, 2005)", |
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| } |
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| { |
| "start": 344, |
| "end": 352, |
| "text": "Figure 3", |
| "ref_id": "FIGREF1" |
| } |
| ], |
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| "section": "Compositional Neural Language Model", |
| "sec_num": "4.1" |
| }, |
| { |
| "text": "z = f(v, o) s score = s T z P obj P verb Co-Compositional Neural Language Model (CoC-NLM) v o y x verb obj", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Compositional Neural Language Model", |
| "sec_num": "4.1" |
| }, |
| { |
| "text": "EQUATION", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [ |
| { |
| "start": 0, |
| "end": 8, |
| "text": "EQUATION", |
| "ref_id": "EQREF", |
| "raw_str": "v = d(w v ) and object vector o = d(w o ). score(v, o) = s T f (v, o) = s T (v + o)", |
| "eq_num": "(8)" |
| } |
| ], |
| "section": "Compositional Neural Language Model", |
| "sec_num": "4.1" |
| }, |
| { |
| "text": "We also create a corrupted pair by substituting a random verb w verb \u2032 . The cost function", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Compositional Neural Language Model", |
| "sec_num": "4.1" |
| }, |
| { |
| "text": "J = max(0, 1 \u2212 score(v, o) + score(v c , o)),", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Compositional Neural Language Model", |
| "sec_num": "4.1" |
| }, |
| { |
| "text": "where v c is the word vector of w verb \u2032 , encourages that the score of correct pair is higher than the score of the corrupt pair. Let z = v + o, our model parameters are \u03b8 = (s, z, v) . The optimization is divided into two steps:", |
| "cite_spans": [], |
| "ref_spans": [ |
| { |
| "start": 175, |
| "end": 184, |
| "text": "(s, z, v)", |
| "ref_id": null |
| } |
| ], |
| "eq_spans": [], |
| "section": "Compositional Neural Language Model", |
| "sec_num": "4.1" |
| }, |
| { |
| "text": "1. Optimize s and z via SGD.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Compositional Neural Language Model", |
| "sec_num": "4.1" |
| }, |
| { |
| "text": "2. Let z new be the updated z via step 1. The new verb vector v new trained within additive compositionality is just v new = z new \u2212 o. Note that if we also want to optimize o, we may want to also corrupt the object and run SGD in step 2 as well.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Compositional Neural Language Model", |
| "sec_num": "4.1" |
| }, |
| { |
| "text": "(CoC-NLM)", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Co-Compositional Neural Language Model", |
| "sec_num": "4.2" |
| }, |
| { |
| "text": "We now add prototype projection into C-NLM, making our final model: Co-Compositional Neural Language Model (CoC-NLM). We define the score function as dot product of s and additional vector of prototype projected vectors (Figure 4 ). Let P obj = P (VerbOf,wo) and P verb = P (ObjOf,wv) ,", |
| "cite_spans": [], |
| "ref_spans": [ |
| { |
| "start": 220, |
| "end": 229, |
| "text": "(Figure 4", |
| "ref_id": "FIGREF2" |
| } |
| ], |
| "eq_spans": [], |
| "section": "Co-Compositional Neural Language Model", |
| "sec_num": "4.2" |
| }, |
| { |
| "text": "EQUATION", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [ |
| { |
| "start": 0, |
| "end": 8, |
| "text": "EQUATION", |
| "ref_id": "EQREF", |
| "raw_str": "score(v, o) = s T (P obj v + P verb o).", |
| "eq_num": "(9)" |
| } |
| ], |
| "section": "Co-Compositional Neural Language Model", |
| "sec_num": "4.2" |
| }, |
| { |
| "text": "Let x = P obj v, y = P verb o and z = x + y.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Co-Compositional Neural Language Model", |
| "sec_num": "4.2" |
| }, |
| { |
| "text": "Our model parameters are \u03b8 = (s, z, v) . The optimization algorithm of CoC-NLM is divided into three steps like C-NLM. First, we optimize s and z. Second, the projected verb vector is updated as x new = z new \u2212 y. Finally we optimize v to minimize the Euclidean distance between x new and P obj v, where \u03bb is a regularization hyper-parameter:", |
| "cite_spans": [], |
| "ref_spans": [ |
| { |
| "start": 29, |
| "end": 38, |
| "text": "(s, z, v)", |
| "ref_id": null |
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| ], |
| "eq_spans": [], |
| "section": "Co-Compositional Neural Language Model", |
| "sec_num": "4.2" |
| }, |
| { |
| "text": "EQUATION", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [ |
| { |
| "start": 0, |
| "end": 8, |
| "text": "EQUATION", |
| "ref_id": "EQREF", |
| "raw_str": "J(v) = 1 2 ||x new \u2212 P obj v|| 2 + \u03bb 2 v T v", |
| "eq_num": "(10)" |
| } |
| ], |
| "section": "Co-Compositional Neural Language Model", |
| "sec_num": "4.2" |
| }, |
| { |
| "text": "5 Evaluation", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Co-Compositional Neural Language Model", |
| "sec_num": "4.2" |
| }, |
| { |
| "text": "In order to evaluate the performance of our new co-compositional model with prototype projection and word representation learning algorithm, we make use of the disambiguation task of transitive sentences developed by Grefenstette and Sadrzadeh (2011) . This is an extension of the two words phrase similarity task defined in Mitchell and Lapata (2008), and constructed according to similar guidelines. The dataset consists of similarity judgments between a landmark verb and a triple consisting of a transitive target verb, subject and object extracted from the BNC corpus. Human judges give scores between 1 to 7, with higher scores implying higher semantic similarity. For example, Table 2 shows some examples from the data: we see that the verb meet with subject system and object criterion is judged similar to the landmark verb satisfy but not visit. The dataset contains a total of 2500 similarity judgements, provided by 25 participants. 4 The task is to have the model produce a score for each pair of landmark verb and verb-subject-object triple. Models are evaluated by computing the Spearman's \u03c1 correlation between its similarity scores and that of the human judgments. Table 2 : Examples from the disambiguation task developed by Grefenstette and Sadrzadeh (2011). Human judges give scores between 1 to 7, with higher scores implying higher semantic similarity. Verb meet with subject system and object criterion is judged similar to the landmark verb satisfy but not visit.", |
| "cite_spans": [ |
| { |
| "start": 217, |
| "end": 250, |
| "text": "Grefenstette and Sadrzadeh (2011)", |
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| }, |
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| "start": 945, |
| "end": 946, |
| "text": "4", |
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| } |
| ], |
| "ref_spans": [ |
| { |
| "start": 684, |
| "end": 691, |
| "text": "Table 2", |
| "ref_id": null |
| }, |
| { |
| "start": 1182, |
| "end": 1189, |
| "text": "Table 2", |
| "ref_id": null |
| } |
| ], |
| "eq_spans": [], |
| "section": "Dataset", |
| "sec_num": "5.1" |
| }, |
| { |
| "text": "We compare our model against multiple baselines for semantic compositionality:", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Baselines", |
| "sec_num": "5.2" |
| }, |
| { |
| "text": "1. Mitchell and Lapata's (2008) additive and element-wise multiplicative model as simplest baselines.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Baselines", |
| "sec_num": "5.2" |
| }, |
| { |
| "text": "2. Grefenstette and Sadrzadeh's (2011) model based on the abstract categorical framework (Coecke et al., 2010) . This model computes the outer product of the subject and object vector, the outer product of the verb vector with itself, and then the element-wise product of both results. 's (2008) model, which adapts the word vectors based on context and is the most similar in terms of motivation to ours. 4. Van de Cruy et al. (2013) multi-way interaction model based on matrix factorization. This achieves the best result for this task to date.", |
| "cite_spans": [ |
| { |
| "start": 89, |
| "end": 110, |
| "text": "(Coecke et al., 2010)", |
| "ref_id": "BIBREF5" |
| }, |
| { |
| "start": 286, |
| "end": 295, |
| "text": "'s (2008)", |
| "ref_id": null |
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| "section": "Baselines", |
| "sec_num": "5.2" |
| }, |
| { |
| "text": "A detailed explanation of these models will be provided in Section 7. For the underlying word representations, we experiment with sparse 2000-dim SDS and dense 50-dim NLM. These are provided by Blacoe and Lapata (2012) 5 and trained on the British National Corpus (BNC). We are interested in knowing how sensitive each model is to the underlying word representation. In general, this is a challenging task: the upper-bound of \u03c1 = 0.62 is the inter-annotator agreement.", |
| "cite_spans": [ |
| { |
| "start": 194, |
| "end": 218, |
| "text": "Blacoe and Lapata (2012)", |
| "ref_id": "BIBREF4" |
| }, |
| { |
| "start": 219, |
| "end": 220, |
| "text": "5", |
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| "eq_spans": [], |
| "section": "Erk and Pad\u00f3", |
| "sec_num": "3." |
| }, |
| { |
| "text": "In terms of implementation detail, our model and our re-implementation of Erk and Pado's model make use of the ukWaC corpus (Baroni et al., 2009) . 6 This corpus is a two billion word corpus automatically harvested from the web and parsed by the Malt-Parser (Nivre et al., 2006) . We use ukWaC corpus to collect W (VerbOf, w o ) and W (ObjOf, w v ) for prototype projections. We also extract about 5000 verb-object pairs that relevant for testdata from this corpus to train our neural network learning algorithm. In our co-compositional model, the contribution ratio of SVD is set to 80% (i.e. automatically fixing k in SVD to include 80% of the top singular values). We set the number of prototype vectors to be m = 20, where W (VerbOf, w o ) is filtered with high frequency words and W (ObjOf, w v ) is filtered with both high frequency and high similarity words. In our model, we output the scores for SVO triple sentence dataset as (subject=w s , verb=w v , object=w o , f = Addition/Multiplication):", |
| "cite_spans": [ |
| { |
| "start": 124, |
| "end": 145, |
| "text": "(Baroni et al., 2009)", |
| "ref_id": "BIBREF1" |
| }, |
| { |
| "start": 258, |
| "end": 278, |
| "text": "(Nivre et al., 2006)", |
| "ref_id": "BIBREF8" |
| } |
| ], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Implementation details", |
| "sec_num": "5.3" |
| }, |
| { |
| "text": "cocomp(w s , w v , w o ) = f (d(w s ), cocomp(w v , w o )) (11)", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Implementation details", |
| "sec_num": "5.3" |
| }, |
| { |
| "text": "6 Results and Discussion Table 3 shows the correlation scores of various models. Our observations are as follows:", |
| "cite_spans": [], |
| "ref_spans": [ |
| { |
| "start": 25, |
| "end": 32, |
| "text": "Table 3", |
| "ref_id": "TABREF5" |
| } |
| ], |
| "eq_spans": [], |
| "section": "Implementation details", |
| "sec_num": "5.3" |
| }, |
| { |
| "text": "1. The best reported result for this task (Van de Cruys et al., 2013) is \u03c1 = 0.37. Our model (with NLM as word representation and f =Addition as operator) achieves \u03c1 = 0.44, outperforming it by a large margin. To the best of our knowledge, this is now state-of-the-art result for this task. 3. The contextual model of Erk and Pad\u00f3 (SDS) also performed relatively well (\u03c1 = 0.39), in fact outperforming the Van de Cruy et al. (2013) result as well. This means that the general idea of adapting word representations based on context is a very powerful one. However, Erk and Pad\u00f3's model using the NLM representation is extremely poor (\u03c1 = 0.03). The reason is that it uses a product operation underthe-hood to adapt the vectors, which inherently assumes a sparse representation. In this sense, our projection approach is more robust.", |
| "cite_spans": [ |
| { |
| "start": 42, |
| "end": 69, |
| "text": "(Van de Cruys et al., 2013)", |
| "ref_id": "BIBREF17" |
| } |
| ], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Main Results: The Correlation", |
| "sec_num": "6.1" |
| }, |
| { |
| "text": "The state-of-the-art result for our model in Table 3 does not yet make use of the training algorithm described in Section 4. It is simply implementing the co-compositionality idea using prototype projections (Section 3.2). Next in Section 6.2 we will show additional gains using unsupervised learning.", |
| "cite_spans": [], |
| "ref_spans": [ |
| { |
| "start": 45, |
| "end": 53, |
| "text": "Table 3", |
| "ref_id": "TABREF5" |
| } |
| ], |
| "eq_spans": [], |
| "section": "Main Results: The Correlation", |
| "sec_num": "6.1" |
| }, |
| { |
| "text": "In this experiment, we examine how much gain is possible by re-training the word representation of verbs using the unsupervised algorithm described in Section 4. We focus on the additive model of Compositional NLM, both basic and prototype projection. The initial word representation is from model original representation re-trained C-NLM 0.31 0.38 CoC-NLM 0.44 0.47 Table 4 : Results of re-training the word representation for C-NLM and CoC-NLM. Learning rate \u03b1 = 0.01, regularization \u03bb = 10 \u22124 and iteration = 20. One iteration is one run through the dataset of 5000 verb-object pairs which we made from the ukWaC corpus.", |
| "cite_spans": [], |
| "ref_spans": [ |
| { |
| "start": 367, |
| "end": 374, |
| "text": "Table 4", |
| "ref_id": null |
| } |
| ], |
| "eq_spans": [], |
| "section": "Improvements from unsupervised learning", |
| "sec_num": "6.2" |
| }, |
| { |
| "text": "NLM. Table 4 shows the gains in correlation score. This result shows that our learning model successfully captures good representation within cocompositionality of additive model. In contrast to other previous compositional models, our model does not require estimating a large number of parameters for computation of compositional vectors and word representation itself is more suitable for it. Furthermore, learning is very fast, taking about 10 minutes for C-NLM on a standard machine with Intel Core i7 2.93Ghz CPU and 8GB of RAM.", |
| "cite_spans": [], |
| "ref_spans": [ |
| { |
| "start": 5, |
| "end": 12, |
| "text": "Table 4", |
| "ref_id": null |
| } |
| ], |
| "eq_spans": [], |
| "section": "Improvements from unsupervised learning", |
| "sec_num": "6.2" |
| }, |
| { |
| "text": "The number of prototype words (m in Figure 1 ) we use to generate the prototype space is one hyperparameter that our model has. Here, we analyze the effect of the choice of m. Figure 5 shows the relation of m and the performance of co-compositional model with prototype projections using either SDS or NLM representations. In general, both NLM and SDS show relatively smooth and flat curves across m, indicating the relative robustness of the approach. Nevertheless, results do degrade for large m, due to increase in noise from non-prototype words. Further, it does appear that NLM has a slower drop in correlation with increasing m compared with SDS. This suggests that NLM is more robust, which is possibly attributable to the dense and lowdimensional distributed features.", |
| "cite_spans": [], |
| "ref_spans": [ |
| { |
| "start": 36, |
| "end": 44, |
| "text": "Figure 1", |
| "ref_id": null |
| }, |
| { |
| "start": 176, |
| "end": 184, |
| "text": "Figure 5", |
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| "text": "We have presented a compositional model of the form d(w s ) + cocomp(w v , w o ), where prototype projections are performed on both w v and w o and w s is composed as is without projection. In general, we have the freedom to choose what to project and what not to project under this co-compositional framework. Here in Table 5 we show the results of Figure 5 : The relation between the number of prototype words and correlation of SDS or NLM. In general, NLM has higher correlation than SDS and is more robust across the m. these variants, using f =Addition and SDS/NLM representations without re-training. We note that our positive results mainly come from the verb projections. Subject information actually does not help. We believe this best configuration is taskdependent; in this test collection, the subjects appear to have little contribution to the landmark verb.", |
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| "text": "In recent years, several sophisticated vector space models have been proposed for computing compositional semantics. Mitchell and Lapata (2010), Erk (2012) and Baroni et al. (2013) are recommended survey papers.", |
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| "text": "One of the first approaches is the vector addition/multiplication idea of Mitchell and Lapata (2008) . The appeal of this kind of simple approach is its intuitive geometric interpretation and its robustness to various datasets. However, it may not be sufficiently expressive to represent the various factors involved in compositional semantics, such as syntax and context. To this end, Baroni and Zamparelli (2010) present a compositional model for adjectives and nouns. In their model, an adjective is a matrix operator that modifies the noun vector into an adjective-noun vector. Zanzotto et al. 2010and Guevara (2010) also proposed linear transformation models for composition and address the issue of estimating large matrices with least squares or regression techniques. Socher et al. (2012) extend this linear transformation approach with the more powerful model of Matrix-Vector Recursive Neural Networks (MV-RNN). Each node in a parse tree is assigned both a vector and a matrix. The vector captures the actual meaning of the word itself, while the matrix is modeled as a operator that modify the meaning of neighboring words and phrases. This model captures semantic change phenomenon like not bad is similar to good due to a composition of the bad vector with a meaning-flipping not matrix. But this MV-RNN also need to optimize all matrices of words from initial value (identity plus a small amount of Gaussian noise) with supervised dataset like movie reviews. Our prototype projection model is similar to these models as a matrix-vector operation, except that the matrix is not learned and computed from prototype words. In future work, we can imagine integrating the two models, using these prototype projection matrices as initial values for MV-RNN training (Socher et al., 2012) .", |
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| "text": "Another approach is exemplified by Coecke et al. (2010) . In their mathematical framework unifying categorical logic and vector space models, the sentence vector is modeled as a function of the Kronecker product of its word vectors. Grefenstette and Sadrzadeh (2011) implement this based on unsupervised learning of matrices for relational words and apply them to the vectors of their arguments. Their idea is that words with relational types, such as verbs, adjectives, and adverbs are matrices that act as a filter on their arguments. They also developed a new semantic similarity task based on transitive Composition Operator Parameter Add: Table 6 : Comparison of composition operators that combine two word vector representations, u, v \u2208 R n and their learning parameters. Our model only needs two hyper-parameters: the number of prototype words m and dimensional reduction k in SVD verbs, which is the dataset we used here. The previous state-of-the-art result for this task comes from the model of Van de Cruys et al. (2013) . They model compositionality as a multi-way interaction between latent factors, which are automatically constructed from corpus data via matrix factorization.", |
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| "text": "w 1 u + w 2 v w 1 , w 2 \u2208 R Multiply: u w1 \u2299 v w2 w 1 , w 2 \u2208 R FullAdd: W 1 u + W 2 v W 1 , W 2 \u2208 R n\u00d7n LexFunc: A u v A u \u2208 R n\u00d7n FullLex: \u03c3([W 1 A u v, W 2 A v u]) A u , A v \u2208 R n\u00d7n W 1 , W 2 \u2208 R n\u00d7n Ours (Add): P (R,v) u + P (R,u) v SVD's (m, k) Ours (Mult): P (R,v) u \u2299 P (R,u) v SVD's (m, k)", |
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| "text": "Comprehensive evaluation of various existing models are reported in (Blacoe and Lapata, 2012; Dinu et al., 2013) . Blacoe and Lapata (2012) highlight the importance of jointly examining word representations and compositionality operators. However, two out of three composition methods they evaluate are parameter-free, so that they can side-step the issue of parameter estimation. Dinu et al. (2013) describe the relation between word vector and compositionality in more detail with free parameters. Table 6 summarizes some ways to compose the meaning of two word vectors (u, v), following (Dinu et al., 2013) . These range from simple operators (e.g. Add and Multiply) to expressive models with many free parameters (e.g. LexFunc, FullLex). Many of these models need to optimize n \u00d7 n parameters, which may be large. On the other hand, our model only needs two hyper-parameters: the number of prototype words m and dimensional reduction k in SVD (Table 6) . Furthermore, our model performance with neural language model word embeddings is robust to variations in m.", |
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| "text": "Most closely related to our work is the work by Erk and Pad\u00f3 (2008; 2009) and Thater et al. (2010; , which falls under the research theme of computing word meaning in context. Both methods are characterized by the use of selectional prefer-ence information for subjects, verbs, and objects in context; our prototype word vectors are essentially equivalent to this idea. The main difference is in how we modify the target word representation v using this information: whereas we project v onto a latent subspace formed by collection of prototype vectors, Erk and Pad\u00f3 (2008; 2009) and Thater et al. (2010; use the prototype vectors to directly modify the elements of v, i.e. by elementwise product with the centroid prototype vector. Intuitively, both our method and theirs essentially delete part of a word vector representation to adapt the meaning in context. We believe the projection is more robust to the underlying word representation (and this is shown in the results for SDS vs. NLM representations), but we note that we may be able to borrow some of more sophisticated ways to find prototype vectors from Erk and Pad\u00f3 (2008; 2009) and Thater et al. (2010; .", |
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| "text": "We began this work by asking how it is possible to handle polysemy issues in compositional semantics, especially when adopting distributional semantics methods that construct only one representation per word type. After all, the different senses of the same word are all conflated into a single vector representation. We found our inspiration in Generative Lexicon Theory (Pustejovsky, 1995) , where ambiguity is resolved due to co-compositionality of the words in the sentence, i.e., the meaning of an ambiguous verb is generated by the properties the object it takes, and vice versa. We implement this idea in a novel neural network model using prototype projections. The advantages of this model is that it is robust to the underlying word representation used and that it enables an effective joint learning of word representations. The model achieves the current state-of-the-art performance (\u03c1 = 0.47) on the semantic similarity task of transitive verbs (Grefenstette and Sadrzadeh, 2011).", |
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| "section": "Conclusion and Future Work", |
| "sec_num": "8" |
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| { |
| "text": "Directions for future research include:", |
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| "sec_num": "8" |
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| "text": "\u2022 Experiments on other semantics tasks, such as paraphrase detection, word sense induction, and word meaning in context.", |
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| "section": "Conclusion and Future Work", |
| "sec_num": "8" |
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| "text": "\u2022 Extension to more holistic sentence-level com-position using a matrix-vector recursive framework like (Socher et al., 2012) .", |
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| "section": "Conclusion and Future Work", |
| "sec_num": "8" |
| }, |
| { |
| "text": "\u2022 Explore further the potential synergy between Distributional Semantics and the Generative Lexicon.", |
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| "section": "Conclusion and Future Work", |
| "sec_num": "8" |
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| { |
| "text": "ronan.collobert.com/senna/", |
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| "text": "http://homepages.inf.ed.ac.uk/ s1066731/index.php?page=resources", |
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| "text": "This work was partially supported by JSPS KAK-ENHI Grant Number 24800041, JSPS KAKENHI 2430057 and Microsoft Research CORE Project. We would like to thank Hiroyuki Shindo and anonymous reviewers for their helpful comments. ", |
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| "sec_num": null |
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| "FIGREF0": { |
| "num": null, |
| "type_str": "figure", |
| "text": "Graphical representation of SVD in our model.", |
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| }, |
| "FIGREF1": { |
| "num": null, |
| "type_str": "figure", |
| "text": "Compositional Neural Language Model (C-NLM).", |
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| "FIGREF2": { |
| "num": null, |
| "type_str": "figure", |
| "text": "Co-Compositional Neural Language Model (CoC-NLM) is C-NLM with prototype projection.", |
| "uris": null |
| }, |
| "TABREF1": { |
| "type_str": "table", |
| "content": "<table><tr><td>if w 0 =</td></tr></table>", |
| "text": "Examples of verb-object pairs. Original verb and landmark verb similarity, prototype projected verb and landmark verb similarity, as measure by cosine using Collobert and Weston's word embeddings. Meet has a abstract meaning itself, but after prototype projection with matrix constructed by word vectors of W (VerbOf, criterion), meet is more close to meaning of satisfy.", |
| "html": null, |
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| }, |
| "TABREF2": { |
| "type_str": "table", |
| "content": "<table/>", |
| "text": "shows several examples of how meanings change after prototype projection using word embeddings ofCollobert and Weston (2008).2", |
| "html": null, |
| "num": null |
| }, |
| "TABREF5": { |
| "type_str": "table", |
| "content": "<table><tr><td>: Results of the different compositionality models</td></tr><tr><td>on the similarity task. The number of prototype words</td></tr><tr><td>m = 20 in all our models. Our model (f =Addition and</td></tr><tr><td>NLM) achieves the new state-of-the-art performance for</td></tr><tr><td>this task (\u03c1 = 0.44).</td></tr></table>", |
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| "html": null, |
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| "TABREF7": { |
| "type_str": "table", |
| "content": "<table/>", |
| "text": "Variants of the full co-compositional model, based on how subject, verb, and object vector representations are included. prpj indicates that prototype projection is used. + indicates that the vector is added without projection first. Blank indicates that the vector is not used in the final compositional score.", |
| "html": null, |
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| } |
| } |
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