AutoExtend: Extending Word Embeddings to Embeddings for Synsets and Lexemes
We present AutoExtend, a system to learn embeddings for synsets and lexemes. It is flexible in that it can take any word embeddings as input and does not need an additional training corpus. The synset/lexeme embeddings obtained live in the same vector space as the word embeddings. A sparse tensor formalization guarantees efficiency and parallelizability. We use WordNet as a lexical resource, but AutoExtend can be easily applied to other resources like Freebase. AutoExtend achieves state-of-the-art performance on word similarity and word sense disambiguation tasks.
Unsupervised methods for word embeddings (also called “distributed word representations”) have become popular in natural language processing (NLP). These methods only need very large corpora as input to create sparse representations (e.g., based on local collocations) and project them into a lower dimensional dense vector space. Examples for word embeddings are SENNA [\citenameCollobert and Weston2008], the hierarchical log-bilinear model [\citenameMnih and Hinton2009], word2vec [\citenameMikolov et al.2013c] and GloVe [\citenamePennington et al.2014]. However, there are many other resources that are undoubtedly useful in NLP, including lexical resources like WordNet and Wiktionary and knowledge bases like Wikipedia and Freebase. We will simply call these resources in the rest of the paper. Our goal is to enrich these valuable resources with embeddings for those data types that are not words; e.g., we want to enrich WordNet with embeddings for synsets and lexemes. A synset is a set of synonyms that are interchangeable in some context. A lexeme pairs a particular spelling or pronunciation with a particular meaning, i.e., a lexeme is a conjunction of a word and a synset. Our premise is that many NLP applications will benefit if the non-word data types of resources – e.g., synsets in WordNet – are also available as embeddings. For example, in machine translation, enriching and improving translation dictionaries (cf. \newcitemikolov2013exploiting) would benefit from these embeddings because they would enable us to create an enriched dictionary for word senses. Generally, our premise is that the arguments for the utility of embeddings for word forms should carry over to the utility of embeddings for other data types like synsets in WordNet.
The insight underlying the method we propose is that the constraints of a resource can be formalized as constraints on embeddings and then allow us to extend word embeddings to embeddings of other data types like synsets. For example, the hyponymy relation in WordNet can be formalized as such a constraint.
The advantage of our approach is that it decouples embedding learning from the extension of embeddings to non-word data types in a resource. If somebody comes up with a better way of learning embeddings, these embeddings become immediately usable for resources. And we do not rely on any specific properties of embeddings that make them usable in some resources, but not in others.
An alternative to our approach is to train embeddings on annotated text, e.g., to train synset embeddings on corpora annotated with synsets. However, successful embedding learning generally requires very large corpora and sense labeling is too expensive to produce corpora of such a size.
Another alternative to our approach is to add up all word embedding vectors related to a particular node in a resource; e.g., to create the synset vector of lawsuit in WordNet, we can add the word vectors of the three words that are part of the synset (lawsuit, suit, case). We will call this approach naive and use it as a baseline (S in Table 3).
We will focus on WordNet [\citenameFellbaum1998] in this paper, but our method – based on a formalization that exploits the constraints of a resource for extending embeddings from words to other data types – is broadly applicable to other resources including Wikipedia and Freebase.
A word in WordNet can be viewed as a composition of several lexemes. Lexemes from different words together can form a synset. When a synset is given, it can be decomposed into its lexemes. And these lexemes then join to form words. These observations are the basis for the formalization of the constraints encoded in WordNet that will be presented in the next section: we view words as the sum of their lexemes and, analogously, synsets as the sum of their lexemes.
Another motivation for our formalization stems from the analogy calculus developed by \newcitemikolov2013efficient, which can be viewed as a group theory formalization of word relations: we have a set of elements (our vectors) and an operation (addition) satisfying the properties of a mathematical group, in particular, associativity and invertibility. For example, you can take the vector of king, subtract the vector of man and add the vector of woman to get a vector near queen. In other words, you remove the properties of man and add the properties of woman. We can also see the vector of king as the sum of the vector of man and the vector of a gender-neutral ruler. The next thing to notice is that this does not only work for words that combine several properties, but also for words that combine several senses. The vector of suit can be seen as the sum of a vector representing lawsuit and a vector representing business suit. AutoExtend is designed to take word vectors as input and unravel the word vectors to the vectors of their lexemes. The lexeme vectors will then give us the synset vectors.
The main contributions of this paper are: (i) We present AutoExtend, a flexible method that extends word embeddings to embeddings of synsets and lexemes. AutoExtend is completely general in that it can be used for any set of embeddings and for any resource that imposes constraints of a certain type on the relationship between words and other data types. (ii) We show that AutoExtend achieves state-of-the-art word similarity and word sense disambiguation (WSD) performance. (iii) We publish the AutoExtend code for extending word embeddings to other data types, the lexeme and synset embeddings and the software to replicate our WSD evaluation.
This paper is structured as follows. Section 2 introduces the model, first as a general tensor formulation then as a matrix formulation making additional assumptions. In Section 3, we describe data, experiments and evaluation. We analyze AutoExtend in Section 4 and give a short summary on how to extend our method to other resources in Section 5. Section 6 discusses related work.
We are looking for a model that extends standard embeddings for words to embeddings for the other two data types in WordNet: synsets and lexemes. We want all three data types – words, lexemes, synsets – to live in the same embedding space.
The basic premise of our model is: (i) words are sums of their lexemes and (ii) synsets are sums of their lexemes. We refer to these two premises as synset constraints. For example, the embedding of the word bloom is a sum of the embeddings of its two lexemes bloom(organ) and bloom(period); and the embedding of the synset flower-bloom-blossom(organ) is a sum of the embeddings of its three lexemes flower(organ), bloom(organ) and blossom(organ).
The synset constraints can be argued to be the simplest possible relationship between the three WordNet data types. They can also be motivated by the way many embeddings are learned from corpora – for example, the counts in vector space models are additive, supporting the view of words as the sum of their senses. The same assumption is frequently made; for example, it underlies the group theory formalization of analogy discussed in Section 1.
We denote word vectors as , synset vectors as , and lexeme vectors as . is that lexeme of word that is a member of synset . We set lexeme vectors that do not exist to zero. For example, the non-existing lexeme flower(truck) is set to zero. We can then formalize our premise that the two constraints (i) and (ii) hold as follows:
These two equations are underspecified. We therefore introduce the matrix :
We make the assumption that the dimensions in Eq. 3 are independent of each other, i.e., is a diagonal matrix. Our motivation for this assumption is: (i) This makes the computation technically feasible by significantly reducing the number of parameters and by supporting parallelism. (ii) Treating word embeddings on a per-dimension basis is a frequent design choice (e.g., \newciteKalchbrennerACL2014). Note that we allow and in general the distribution weights for each dimension (diagonal entries of ) will be different. Our assumption can be interpreted as word distributing its embedding activations to its lexemes on each dimension separately. Therefore, Eqs. 1-2 can be written as follows:
Note that from Eq. 4 it directly follows that:
with being the identity matrix.
Let be a matrix where is the dimensionality of the embedding space, is the number of words and each row is a word embedding; and let be a matrix where is the number of synsets and each row is a synset embedding. and can be interpreted as linear maps and a mapping between them is given by the rank 4 tensor . We can then write Eq. 5 as a tensor product:
while Eq. 6 states, that
Additionally, there is no interaction between different dimensions, so if . In other words, we are creating the tensor by stacking the diagonal matrices over and . Another sparsity arises from the fact that many lexemes do not exist: if ; i.e., only if word has a lexeme that is a member of synset . To summarize the sparsity:
We adopt an autoencoding framework to learn embeddings for lexemes and synsets. To this end, we view the tensor equation as the encoding part of the autoencoder: the synsets are the encoding of the words. We define a corresponding decoding part that decodes the synsets into words as follows:
In analogy to , we introduce the diagonal matrix :
In this case, it is the synset that distributes itself to its lexemes. We can then rewrite Eq. 10 to:
and we also get the equivalent of Eq. 6 for :
and in tensor notation:
Normalization and sparseness properties for the decoding part are analogous to the encoding part:
We can state the learning objective of the autoencoder as follows:
Now we have an autoencoder where input and output layers are the word embeddings and the hidden layer represents the synset vectors. A simplified version is shown in Figure 1. The tensors and have to be learned. They are rank 4 tensors of size . However, we already discussed that they are very sparse, for two reasons: (i) We make the assumption that there is no interaction between dimensions. (ii) There are only few interactions between words and synsets (only when a lexeme exists). In practice, there are only elements to learn, which is technically feasible.
2.2 Matrix formalization
Based on the assumption that each dimension is fully independent from other dimensions, a separate autoencoder for each dimension can be created and trained in parallel. Let be a matrix where each row is a word embedding and the -th column of , i.e., a vector that holds the -th dimension of each word vector. In the same way, holds the -th dimension of each synset vector and . We can write as:
with if . The decoding equation takes this form:
where and if . So and are symmetric in terms of non-zero elements. The learning objective becomes:
2.3 Lexeme embeddings
The hidden layer of the autoencoder gives us synset embeddings. The lexeme embeddings are defined when transitioning from to , or more explicitly by:
However, there is also a second lexeme embedding in AutoExtend when transitioning form to :
Aligning these two representations seems natural, so we impose the following lexeme constraints:
This can also be expressed dimension-wise. The matrix formulation is given by:
with being a square matrix having on the main diagonal and vector defined by Eq. 18. While we try to align the embeddings, there are still two different lexeme embeddings. In all experiments reported in Section 4 we will use the average of both embeddings and in Section 4 we will analyze the weighting in more detail.
2.4 WN relations
Some WordNet synsets contain only a single word (lexeme). The autoencoder learns based on the synset constraints, i.e., lexemes being shared by different synsets (and also words); thus, it is difficult to learn good embeddings for single-lexeme synsets. To remedy this problem, we impose the constraint that synsets related by WordNet (WN) relations should have similar embeddings. Table 1 shows relations we used. WN relations are entered in a new matrix , where is the number of WN relation tuples. For each relation tuple, i.e., row in , we set the columns corresponding to the first and second synset to and , respectively. The values of are not updated during training. We use a squared error function and as target value. This forces the system to find similar values for related synsets. Formally, the WN relation constraints are:
The training objective cannot be solved analytically because it is subject to constraints Eq. 8, Eq. 9, Eq. 15 and Eq. 16. We therefore use backpropagation. We do not use regularization since we found that all learned weights are in .
AutoExtend is implemented in MATLAB. We run iterations of gradient descent. On an Intel Xeon CPU E7-8857 v2 3.00GHz, one iteration on one dimension takes less than a minute because the gradient computation ignores zero entries in the matrix.
2.6 Column normalization
Our model is based on the premise that a word is the sum of its lexemes (Eq. 1). From the definition of , we derived that is normalized over the first dimension (Eq. 8). So is also normalized over the first dimension. In other words, is a column normalized matrix. Another premise of the model is that a synset is the sum of its lexemes. Therefore, is also column normalized. A simple way to implement this is to start the computation with column normalized matrices and normalize them again after each iteration as long as the error function still decreases. When the error function starts increasing, we stop normalizing the matrices and continue with a normal gradient descent. This respects that while and should be column normalized in theory, there are a lot of practical issues that prevent this, e.g., OOV words.
3 Data, experiments and evaluation
We downloaded 300-dimensional embeddings for 3,000,000 words and phrases trained on Google News, a corpus of tokens, using word2vec CBOW [\citenameMikolov et al.2013c]. Many words in the word2vec vocabulary are not in WordNet, e.g., inflected forms (cars) and proper nouns (Tony Blair). Conversely, many WordNet lemmas are not in the word2vec vocabulary, e.g., 42 (digits were converted to 0). This results in a number of empty synsets (see Table 2). Note however that AutoExtend can produce embeddings for empty synsets because we use WN relation constraints in addition to synset and lexeme constraints.
We run AutoExtend on the word2vec vectors. As we do not know anything about a suitable weighting for the three different constraints, we set . Our main goal is to produce compatible embeddings for lexemes and synsets. Thus, we can compute nearest neighbors across all three data types as shown in Figure 2.
|nearest neighbors of W/suit|
|S/suit (businessman), L/suit (businessman), L/accomodate, S/suit (be acceptable), L/suit (be acceptable), L/lawsuit, W/lawsuit, S/suit (playing card), L/suit (playing card), S/suit (petition), S/lawsuit, W/countersuit, W/complaint, W/counterclaim|
|nearest neighbors of W/lawsuit|
|L/lawsuit, S/lawsuit, S/countersuit, L/countersuit, W/countersuit, W/suit, W/counterclaim, S/counterclaim (n), L/counterclaim (n), S/counterclaim (v), L/counterclaim (v), W/sue, S/sue (n), L/sue (n)|
|nearest neighbors of S/suit-of-clothes|
|L/suit-of-clothes, S/zoot-suit, L/zoot-suit, W/zoot-suit, S/garment, L/garment, S/dress, S/trousers, L/pinstripe, L/shirt, W/tuxedo, W/gabardine, W/tux, W/pinstripe|
We evaluate the embeddings on WSD and on similarity performance. Our results depend directly on the quality of the underlying word embeddings, in our case word2vec embeddings. We would expect even better evaluation results as word representation learning methods improve. Using a new and improved set of underlying embeddings is simple: it is a simple switch of the input file that contains the word embeddings.
3.1 Word Sense Disambiguation
For WSD we use the shared tasks of Senseval-2 [\citenameKilgarriff2001] and Senseval-3 [\citenameMihalcea et al.2004] and a system named IMS [\citenameZhong and Ng2010]. Senseval-2 contains 139, Senseval-3 57 different words. They provide 8,611, respectively 8,022 training instances and 4,328, respectively 3,944 test instances. For the system, we use the same setting as in the original paper. Preprocessing consists of sentence splitting, tokenization, POS tagging and lemmatization; the classifier is a linear SVM. In our experiments (Table 3), we run IMS with each feature set by itself to assess the relative strengths of feature sets (lines 1–7) and on feature set combinations to determine which combination is best for WSD (lines 8, 12–15).
IMS implements three standard WSD feature sets: part of speech (POS), surrounding word and local collocation (lines 1–3).
Let be an ambiguous word with senses. The three feature sets on lines 5–7 are based on the AutoExtend embeddings , , of the synsets of and the centroid of the sentence in which occurs. The centroid is simply the sum of all word2vec vectors of the words in the sentence, excluding stop words.
The S-cosine feature set consists of the cosines of centroid and synset vectors:
The S-product feature set consists of the element-wise products of centroid and synset vectors:
where (resp. ) is element of (resp. ). The idea is that we let the SVM estimate how important each dimension is for WSD instead of giving all equal weight as in S-cosine.
The S-raw feature set simply consists of the elements of centroid and synset vectors:
Our main goal is to determine if AutoExtend features improve WSD performance when added to standard WSD features. To make sure that improvements we get are not solely due to the power of word2vec, we also investigate a simple word2vec baseline. For S-product, the AutoExtend feature set that performs best in the experiment (cf. lines 6 and 14), we test the alternative word2vec-based S-product feature set. It has the same definition as S-product except that we replace the synset vectors with naive synset vectors , defined as the sum of the word2vec vectors of the words that are members of synset .
Lines 1–7 in Table 3 show the performance of each feature set by itself. We see that the synset feature sets (lines 5–7) have a comparable performance to standard feature sets. S-product is the strongest of them.
Lines 8–16 show the performance of different feature set
combinations. MFS (line 8) is
the most frequent sense baseline. Lines 9&10 are the winners of Senseval. The standard configuration of IMS (line 11)
uses the three feature sets on lines 1–3 (POS, surrounding
word, local collocation) and achieves an accuracy of
on the English lexical sample task of Senseval-2
and on Senseval-3.
We do a grid search (step size .1) for optimal values of and , optimizing the average score of Senseval-2 and Senseval-3. The best performing feature set combination is S-product with and , with only a small improvement (line 16).
The main result of this experiment is that we achieve an improvement of more than 1% in WSD performance when using AutoExtend.
|IMS feature sets||1||POS||53.6||58.0|
|9||Rank 1 system||64.2||72.9|
|10||Rank 2 system||63.8||72.6|
|12||IMS + Snaive-prod.||62.6||69.4|
|13||IMS + S-cosine||65.1||72.4|
|14||IMS + S-product||66.5||73.6|
|15||IMS + S-raw||62.1||66.8|
|16||IMS + Soptimized-prod.||66.6||73.6|
3.2 Synset and lexeme similarity
We use SCWS [\citenameHuang et al.2012] for the similarity evaluation. SCWS provides not only isolated words and corresponding similarity scores, but also a context for each word. SCWS is based on WordNet, but the information as to which synset a word in context came from is not available. However, the dataset is the closest we could find for sense similarity. Synset and lexeme embeddings are obtained by running AutoExtend. Based on the results of the WSD task, we set and . Lexeme embeddings are the natural choice for this task as human subjects are provided with two words and a context for each and then have to assign a similarity score. But for completeness, we also run experiments for synsets.
For each word, we compute a context vector by adding all word vectors of the context, excluding the test word itself. Following \newcitereisinger2010multi, we compute the lexeme (resp. synset) vector either as the simple average of the lexeme (resp. synset) vectors (method AvgSim, no dependence on in this case) or as the average of the lexeme (resp. synset) vectors weighted by cosine similarity to (method AvgSimC).
Table 4 shows that AutoExtend lexeme embeddings (line 7) perform better than previous work, including [\citenameHuang et al.2012] and [\citenameTian et al.2014]. Lexeme embeddings perform better than synset embeddings (lines 7 vs. 6), presumably because using a representation that is specific to the actual word being judged is more precise than using a representation that also includes synonyms.
A simple baseline is to use the underlying word2vec embeddings directly (line 5). In this case, there is only one embedding, so there is no difference between AvgSim and AvgSimC. It is interesting that even if we do not take the context into account (method AvgSim) the lexeme embeddings outperform the original word embeddings. As AvgSim simply adds up all lexemes of a word, this is equivalent to the constraint we proposed in the beginning of the paper (Eq. 1). Thus, replacing a word’s embedding by the sum of the embeddings of its senses could generally improve the quality of embeddings (cf. \newcitehuang2012improving for a similar point). We will leave a deeper evaluation of this topic for future work.
We first look at the impact of the parameters , (Section 2.5) that control the weighting of synset constraints vs lexeme constraints vs WN relation constraints. We investigate the impact for three different tasks. WSD-alone: accuracy of IMS (average of Senseval-2 and Senseval-3) if only S-product is used as a feature set (line 6 in Table 3). WSD-additional: accuracy of IMS (average of Senseval-2 and Senseval-3) if S-product is used together with the feature sets POS, surrounding word and local collocation (line 14 in Table 3). SCWS: Spearman correlation on SCWS (line 7 in Table 4).
For WSD-alone (Figure 3, center), the best performing weightings (red) all have high weights for WN relations and are therefore at the top of triangle. Thus, WN relations are very important for WSD-alone and adding more weight to the synset and lexeme constraints does not help. However, all three constraints are important in WSD-additional: the red area is in the middle (corresponding to nonzero weights for all three constraints) in the left panel of Figure 3. Apparently, strongly weighted lexeme and synset constraints enable learning of representations that in their interaction with standard WSD feature sets like local collocation increase WSD performance. For SCWS (right panel), we should not put too much weight on WN relations as they artificially bring related, but not similar lexemes together. So the maximum for this task is located in the lower part of the triangle.
The main result of this analysis is that AutoExtend never achieves its maximum performance when using only one set of constraints. All three constraints are important – synset, lexeme and WN relation constraints – with different weights for different applications.
We also analyzed the impact of the four different WN relations (see Table 1) on performance. In Table 3 and Table 4, all four WN relations are used together. We found that any combination of three relation types performs worse than using all four together. A comparison of different relations must be done carefully as they differ in the POS they affect and in quantity (see Table 1). In general, relation types with more relations outperformed relation types with fewer relations.
Finally, the relative weighting of and when computing lexeme embeddings is also a parameter that can be tuned. We use simple averaging () for all experiments reported in this paper. We found only small changes in performance for .
5 Resources other than WordNet
AutoExtend is broadly applicable to lexical and knowledge resources that have certain properties. While we only run experiments with WordNet in this paper, we will briefly address other resources. For Freebase [\citenameBollacker et al.2008], we could replace the synsets with Freebase entities. Each entity has several aliases, e.g. Barack Obama, President Obama, Obama. The role of words in WordNet would correspond to these aliases in Freebase. This will give us the synset constraint, as well as the lexeme constraint of the system. Relations are given by Freebase types; e.g., we can add a constraint that entity embeddings of the type ”President of the US” should be similar.
To explorer multilingual word embeddings we require the word embeddings of different languages to live in the same vector space, which can easily be achieved by training a transformation matrix between two languages using known translations [\citenameMikolov et al.2013b]. Let be a matrix where each row is a word embedding in language 1 and a matrix where each row is a word embedding in language 2. For each row the words of and are a translation of each other. We then want to minimize the following objective:
We can use a gradient descent to solve this but a matrix inversion will run faster. The matrix is given by:
The matrix can be used to transform unknown embeddings into the new vector space, which enables us to use a multilingual WordNet like BabelNet [\citenameNavigli and Ponzetto2010] to compute synset embeddings. We can add cross-linguistic relationships to our model, e.g., aligning German and English synset embeddings of the same concept.
6 Related Work\newcite
rumelhart1988learning introduced distributed word representations, usually called word embeddings today. There has been a resurgence of work on them recently (e.g., \newcitebengio2003neural \newcitemnih2007three, \newcitecollobert2011natural, \newcitemikolov2013efficient, \newcitepennington2014glove). These models produce only a single embedding for each word. All of them can be used as input for AutoExtend.
There are several approaches to finding embeddings for senses, variously called meaning, sense and multiple word embeddings. \newciteschutze1998automatic created sense representations by clustering context representations derived from co-occurrence. The representation of a sense is simply the centroid of its cluster. \newcitehuang2012improving improved this by learning single-prototype embeddings before performing word sense discrimination on them. \newcitebordes2011learning created similarity measures for relations in WordNet and Freebase to learn entity embeddings. An energy based model was proposed by \newcitebordes2012joint to create disambiguated meaning embeddings and \newciteneelakantan2014efficient and \newcitetian2014probabilistic extended the Skip-gram model [\citenameMikolov et al.2013a] to learn multiple word embeddings. While these embeddings can correspond to different word senses, there is no clear mapping between them and a lexical resource like WordNet. \newcitechen2014unified also modified word2vec to learn sense embeddings, each corresponding to a WordNet synset. They use glosses to initialize sense embedding, which in turn can be used for WSD. The sense disambiguated data can again be used to improve sense embeddings.
This prior work needs a training step to learn embeddings. In contrast, we can “AutoExtend” any set of given word embeddings – without (re)training them.
There is only little work on taking existing word embeddings and producing embeddings in the same space. \newcitelabutov2013re tuned existing word embeddings in supervised training, not to create new embeddings for senses or entities, but to get better predictive performance on a task while not changing the space of embeddings.
Lexical resources have also been used to improve word embeddings. In the Relation Constrained Model, \newciteyu2014 use word2vec to learn embeddings that are optimized to predict a related word in the resource, with good evaluation results. \newcitebian2014knowledge used not only semantic, but also morphological and syntactic knowledge to compute more effective word embeddings.
Another interesting approach to create sense specific word embeddings uses bilingual resources [\citenameGuo et al.2014]. The downside of this approach is that parallel data is needed.
And while we use cosine to compute similarity between synsets, there are also a lot of similarity measures that only rely on a given resource, mostly WordNet. These measures are often functions that depend on the provided information like gloss or the topology like shortest-path. Examples include [\citenameWu and Palmer1994] and [\citenameLeacock and Chodorow1998]; \newciteblanchard2005typology give a good overview.
We presented AutoExtend, a flexible method to learn synset and lexeme
embeddings from word embeddings. It is completely general
and can be used for any other set of embeddings and for any
other resource that imposes constraints of a certain type on
the relationship between words and other data types. Our
experimental results show that AutoExtend achieves
state-of-the-art performance on word similarity and
word sense disambiguation.
Along with this paper, we will publish
AutoExtend for extending word embeddings to other data
types; the lexeme and synset embeddings used in the
experiments; and the code needed to
replicate our WSD evaluation
This work was partially funded by Deutsche Forschungsgemeinschaft (DFG SCHU 2246/2-2). We are grateful to Christiane Fellbaum for discussions leading up to this paper and to the anonymous reviewers for their comments.
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