Imparting Interpretability to Word Embeddings while Preserving Semantic Structure

Abstract: As an ubiquitous method in natural language processing, word embeddings are extensively employed to map semantic properties of words into a dense vector representation. They capture semantic and syntactic relations among words but the vector corresponding to the words are only meaningful relative to each other. Neither the vector nor its dimensions have any absolute, interpretable meaning. We introduce an additive modification to the objective function of the embedding learning algorithm that encourages the embedding vectors of words that are semantically related to a predefined concept to take larger values along a specified dimension, while leaving the original semantic learning mechanism mostly unaffected. In other words, we align words that are already determined to be related, along predefined concepts. Therefore, we impart interpretability to the word embedding by assigning meaning to its vector dimensions. The predefined concepts are derived from an external lexical resource, which in this paper is chosen as Roget's Thesaurus. We observe that alignment along the chosen concepts is not limited to words in the Thesaurus and extends to other related words as well. We quantify the extent of interpretability and assignment of meaning from our experimental results. We also demonstrate the preservation of semantic coherence of the resulting vector space by using word-analogy and word-similarity tests. These tests show that the interpretability-imparted word embeddings that are obtained by the proposed framework do not sacrifice performances in common benchmark tests.

Distributed word representations, commonly referred to as word embeddings BIBREF0 , BIBREF1 , BIBREF2 , BIBREF3 , serve as elementary building blocks in the course of algorithm design for an expanding range of applications in natural language processing (NLP), including named entity recognition BIBREF4 , BIBREF5 , parsing BIBREF6 , sentiment analysis BIBREF7 , BIBREF8 , and word-sense disambiguation BIBREF9 . Although the empirical utility of word embeddings as an unsupervised method for capturing the semantic or syntactic features of a certain word as it is used in a given lexical resource is well-established BIBREF10 , BIBREF11 , BIBREF12 , an understanding of what these features mean remains an open problem BIBREF13 , BIBREF14 and as such word embeddings mostly remain a black box. It is desirable to be able to develop insight into this black box and be able to interpret what it means, while retaining the utility of word embeddings as semantically-rich intermediate representations. Other than the intrinsic value of this insight, this would not only allow us to explain and understand how algorithms work BIBREF15 , but also set a ground that would facilitate the design of new algorithms in a more deliberate way.
Recent approaches to generating word embeddings (e.g. BIBREF0 , BIBREF2 ) are rooted linguistically in the field of distributed semantics BIBREF16 , where words are taken to assume meaning mainly by their degree of interaction (or lack thereof) with other words in the lexicon BIBREF17 , BIBREF18 . Under this paradigm, dense, continuous vector representations are learned in an unsupervised manner from a large corpus, using the word cooccurrence statistics directly or indirectly, and such an approach is shown to result in vector representations that mathematically capture various semantic and syntactic relations between words BIBREF0 , BIBREF2 , BIBREF3 . However, the dense nature of the learned embeddings obfuscate the distinct concepts encoded in the different dimensions, which renders the resulting vectors virtually uninterpretable. The learned embeddings make sense only in relation to each other and their specific dimensions do not carry explicit information that can be interpreted. However, being able to interpret a word embedding would illuminate the semantic concepts implicitly represented along the various dimensions of the embedding, and reveal its hidden semantic structures.
In the literature, researchers tackled interpretability problem of the word embeddings using different approaches. Several researchers BIBREF19 , BIBREF20 , BIBREF21 proposed algorithms based on non-negative matrix factorization (NMF) applied to cooccurrence variant matrices. Other researchers suggested to obtain interpretable word vectors from existing uninterpretable word vectors by applying sparse coding BIBREF22 , BIBREF23 , by training a sparse auto-encoder to transform the embedding space BIBREF24 , by rotating the original embeddings BIBREF25 , BIBREF26 or by applying transformations based on external semantic datasets BIBREF27 .
Although the above-mentioned approaches provide better interpretability that is measured using a particular method such as word intrusion test, usually the improved interpretability comes with a cost of performance in the benchmark tests such as word similarity or word analogy. One possible explanation for this performance decrease is that the proposed transformations from the original embedding space distort the underlying semantic structure constructed by the original embedding algorithm. Therefore, it can be claimed that a method that learns dense and interpretable word embeddings without inflicting any damage to the underlying semantic learning mechanism is the key to achieve both high performing and interpretable word embeddings.
Especially after the introduction of the word2vec algorithm by Mikolov BIBREF0 , BIBREF1 , there has been a growing interest in algorithms that generate improved word representations under some performance metric. Significant effort is spent on appropriately modifying the objective functions of the algorithms in order to incorporate knowledge from external resources, with the purpose of increasing the performance of the resulting word representations BIBREF28 , BIBREF29 , BIBREF30 , BIBREF31 , BIBREF32 , BIBREF33 , BIBREF34 , BIBREF35 , BIBREF36 , BIBREF37 . Inspired by the line of work reported in these studies, we propose to use modified objective functions for a different purpose: learning more interpretable dense word embeddings. By doing this, we aim to incorporate semantic information from an external lexical resource into the word embedding so that the embedding dimensions are aligned along predefined concepts. This alignment is achieved by introducing a modification to the embedding learning process. In our proposed method, which is built on top of the GloVe algorithm BIBREF2 , the cost function for any one of the words of concept word-groups is modified by the introduction of an additive term to the cost function. Each embedding vector dimension is first associated with a concept. For a word belonging to any one of the word-groups representing these concepts, the modified cost term favors an increase for the value of this word's embedding vector dimension corresponding to the concept that the particular word belongs to. For words that do not belong to any one of the word-groups, the cost term is left untouched. Specifically, Roget's Thesaurus BIBREF38 , BIBREF39 is used to derive the concepts and concept word-groups to be used as the external lexical resource for our proposed method. We quantitatively demonstrate the increase in interpretability by using the measure given in BIBREF27 , BIBREF40 as well as demonstrating qualitative results. We also show that the semantic structure of the original embedding has not been harmed in the process since there is no performance loss with standard word-similarity or word-analogy tests.
The paper is organized as follows. In Section SECREF2 , we discuss previous studies related to our work under two main categories: interpretability of word embeddings and joint-learning frameworks where the objective function is modified. In Section SECREF3 , we present the problem framework and provide the formulation within the GloVe BIBREF2 algorithm setting. In Section SECREF4 where our approach is proposed, we motivate and develop a modification to the original objective function with the aim of increasing representation interpretability. In Section SECREF5 , experimental results are provided and the proposed method is quantitatively and qualitatively evaluated. Additionally, in Section SECREF5 , results demonstrating the extent to which the original semantic structure of the embedding space is affected are presented by using word-analogy and word-similarity tests. We conclude the paper in Section SECREF6 .
Methodologically, our work is related to prior studies that aim to obtain “improved” word embeddings using external lexical resources, under some performance metric. Previous work in this area can be divided into two main categories: works that i) modify the word embedding learning algorithm to incorporate lexical information, ii) operate on pre-trained embeddings with a post-processing step.
Among works that follow the first approach, BIBREF28 extend the Skip-Gram model by incorporating the word similarity relations extracted from the Paraphrase Database (PPDB) and WordNet BIBREF29 , into the Skip-Gram predictive model as an additional cost term. In BIBREF30 , the authors extend the CBOW model by considering two types of semantic information, termed relational and categorical, to be incorporated into the embeddings during training. For the former type of semantic information, the authors propose the learning of explicit vectors for the different relations extracted from a semantic lexicon such that the word pairs that satisfy the same relation are distributed more homogeneously. For the latter, the authors modify the learning objective such that some weighted average distance is minimized for words under the same semantic category. In BIBREF31 , the authors represent the synonymy and hypernymy-hyponymy relations in terms of inequality constraints, where the pairwise similarity rankings over word triplets are forced to follow an order extracted from a lexical resource. Following their extraction from WordNet, the authors impose these constraints in the form of an additive cost term to the Skip-Gram formulation. Finally, BIBREF32 builds on top of the GloVe algorithm by introducing a regularization term to the objective function that encourages the vector representations of similar words as dictated by WordNet to be similar as well.
Turning our attention to the post-processing approach for enriching word embeddings with external lexical knowledge, BIBREF33 has introduced the retrofitting algorithm that acts on pre-trained embeddings such as Skip-Gram or GloVe. The authors propose an objective function that aims to balance out the semantic information captured in the pre-trained embeddings with the constraints derived from lexical resources such as WordNet, PPDB and FrameNet. One of the models proposed in BIBREF34 extends the retrofitting approach to incorporate the word sense information from WordNet. Similarly, BIBREF35 creates multi-sense embeddings by gathering the word sense information from a lexical resource and learning to decompose the pre-trained embeddings into a convex combination of sense embeddings. In BIBREF36 , the authors focus on improving word embeddings for capturing word similarity, as opposed to mere relatedness. To this end, they introduce the counter-fitting technique which acts on the input word vectors such that synonymous words are attracted to one another whereas antonymous words are repelled, where the synonymy-antonymy relations are extracted from a lexical resource. More recently, the ATTRACT-REPEL algorithm proposed by BIBREF37 improves on counter-fitting by a formulation which imparts the word vectors with external lexical information in mini-batches.
Most of the studies discussed above ( BIBREF30 , BIBREF31 , BIBREF32 , BIBREF33 , BIBREF34 , BIBREF36 , BIBREF37 ) report performance improvements in benchmark tests such as word similarity or word analogy, while BIBREF29 uses a different analysis method (mean reciprocal rank). In sum, the literature is rich with studies aiming to obtain word embeddings that perform better under specific performance metrics. However, less attention has been directed to the issue of interpretability of the word embeddings. In the literature, the problem of interpretability has been tackled using different approaches. BIBREF19 proposed non-negative matrix factorization (NMF) for learning sparse, interpretable word vectors from co-occurrence variant matrices where the resulting vector space is called non-negative sparse embeddigns (NNSE). However, since NMF methods require maintaining a global matrix for learning, they suffer from memory and scale issue. This problem has been addressed in BIBREF20 where an online method of learning interpretable word embeddings from corpora using a modified version of skip-gram model BIBREF0 is proposed. As a different approach, BIBREF21 combined text-based similarity information among words with brain activity based similarity information to improve interpretability using joint non-negative sparse embedding (JNNSE).
A common alternative approach for learning interpretable embeddings is to learn transformations that map pre-trained state-of-the-art embeddings to new interpretable semantic spaces. To obtain sparse, higher dimensional and more interpretable vector spaces, BIBREF22 and BIBREF23 use sparse coding on conventional dense word embeddings. However, these methods learn the projection vectors that are used for the transformation from the word embeddings without supervision. For this reason, labels describing the corresponding semantic categories cannot be provided. An alternative approach was proposed in BIBREF25 , where orthogonal transformations were utilized to increase interpretability while preserving the performance of the underlying embedding. However, BIBREF25 has also shown that total interpretability of an embedding is kept constant under any orthogonal transformation and it can only be redistributed across the dimensions. Rotation algorithms based on exploratory factor analysis (EFA) to preserve the performance of the original word embeddings while improving their interpretability was proposed in BIBREF26 . BIBREF24 proposed to deploy a sparse auto-encoder using pre-trained dense word embeddings to improve interpretability. More detailed investigation of semantic structure and interpretability of word embeddings can be found in BIBREF27 , where a metric was proposed to quantitatively measure the degree of interpretability already present in the embedding vector spaces.
Previous works on interpretability mentioned above, except BIBREF21 , BIBREF27 and our proposed method, do not need external resources, utilization of which has both advantages and disadvantages. Methods that do not use external resources require fewer resources but they also lack the aid of information extracted from these resources.
For the task of unsupervised word embedding extraction, we operate on a discrete collection of lexical units (words) INLINEFORM0 that is part of an input corpus INLINEFORM1 , with number of tokens INLINEFORM2 , sourced from a vocabulary INLINEFORM3 of size INLINEFORM4 . In the setting of distributional semantics, the objective of a word embedding algorithm is to maximize some aggregate utility over the entire corpus so that some measure of “closeness” is maximized for pairs of vector representations INLINEFORM14 for words which, on the average, appear in proximity to one another. In the GloVe algorithm BIBREF2 , which we base our improvements upon, the following objective function is considered: DISPLAYFORM0 
In ( EQREF6 ), INLINEFORM0 and INLINEFORM1 stand for word and context vector representations, respectively, for words INLINEFORM2 and INLINEFORM3 , while INLINEFORM4 represents the (possibly weighted) cooccurrence count for the word pair INLINEFORM5 . Intuitively, ( EQREF6 ) represents the requirement that if some word INLINEFORM6 occurs often enough in the context (or vicinity) of another word INLINEFORM7 , then the corresponding word representations should have a large enough inner product in keeping with their large INLINEFORM8 value, up to some bias terms INLINEFORM9 ; and vice versa. INLINEFORM10 in ( EQREF6 ) is used as a discounting factor that prohibits rare cooccurrences from disproportionately influencing the resulting embeddings.
The objective ( EQREF6 ) is minimized using stochastic gradient descent by iterating over the matrix of cooccurrence records INLINEFORM0 . In the GloVe algorithm, for a given word INLINEFORM1 , the final word representation is taken to be the average of the two intermediate vector representations obtained from ( EQREF6 ); i.e, INLINEFORM2 . In the next section, we detail the enhancements made to ( EQREF6 ) for the purposes of enhanced interpretability, using the aforementioned framework as our basis.
Our approach falls into a joint-learning framework where the distributional information extracted from the corpus is allowed to fuse with the external lexicon-based information. Word-groups extracted from Roget's Thesaurus are directly mapped to individual dimensions of word embeddings. Specifically, the vector representations of words that belong to a particular group are encouraged to have deliberately increased values in a particular dimension that corresponds to the word-group under consideration. This can be achieved by modifying the objective function of the embedding algorithm to partially influence vector representation distributions across their dimensions over an input vocabulary. To do this, we propose the following modification to the GloVe objective in ( EQREF6 ): rCl J = i,j=1V f(Xij)[ (wiTwj + bi + bj -Xij)2
 + k(l=1D INLINEFORM0 iFl g(wi,l) + l=1D INLINEFORM1 j Fl g(wj,l) ) ]. In ( SECREF4 ), INLINEFORM2 denotes the indices for the elements of the INLINEFORM3 th concept word-group which we wish to assign in the vector dimension INLINEFORM4 . The objective ( SECREF4 ) is designed as a mixture of two individual cost terms: the original GloVe cost term along with a second term that encourages embedding vectors of a given concept word-group to achieve deliberately increased values along an associated dimension INLINEFORM5 . The relative weight of the second term is controlled by the parameter INLINEFORM6 . The simultaneous minimization of both objectives ensures that words that are similar to, but not included in, one of these concept word-groups are also “nudged” towards the associated dimension INLINEFORM7 . The trained word vectors are thus encouraged to form a distribution where the individual vector dimensions align with certain semantic concepts represented by a collection of concept word-groups, one assigned to each vector dimension. To facilitate this behaviour, ( SECREF4 ) introduces a monotone decreasing function INLINEFORM8 defined as INLINEFORM9 
which serves to increase the total cost incurred if the value of the INLINEFORM0 th dimension for the two vector representations INLINEFORM1 and INLINEFORM2 for a concept word INLINEFORM3 with INLINEFORM4 fails to be large enough. INLINEFORM5 is also shown in Fig. FIGREF7 .
The objective ( SECREF4 ) is minimized using stochastic gradient descent over the cooccurrence records INLINEFORM0 . Intuitively, the terms added to ( SECREF4 ) in comparison with ( EQREF6 ) introduce the effect of selectively applying a positive step-type input to the original descent updates of ( EQREF6 ) for concept words along their respective vector dimensions, which influences the dimension value in the positive direction. The parameter INLINEFORM1 in ( SECREF4 ) allows for the adjustment of the magnitude of this influence as needed.
In the next section, we demonstrate the feasibility of this approach by experiments with an example collection of concept word-groups extracted from Roget's Thesaurus.
We first identified 300 concepts, one for each dimension of the 300-dimensional vector representation, by employing Roget's Thesaurus. This thesaurus follows a tree structure which starts with a Root node that contains all the words and phrases in the thesaurus. The root node is successively split into Classes and Sections, which are then (optionally) split into Subsections of various depths, finally ending in Categories, which constitute the smallest unit of word/phrase collections in the structure. The actual words and phrases descend from these Categories, and make up the leaves of the tree structure. We note that a given word typically appears in multiple categories corresponding to the different senses of the word. We constructed concept word-groups from Roget's Thesaurus as follows: We first filtered out the multi-word phrases and the relatively obscure terms from the thesaurus. The obscure terms were identified by checking them against a vocabulary extracted from Wikipedia. We then obtained 300 word-groups as the result of a partitioning operation applied to the subtree that ends with categories as its leaves. The partition boundaries, hence the resulting word-groups, can be chosen in many different ways. In our proposed approach, we have chosen to determine this partitioning by traversing this tree structure from the root node in breadth-first order, and by employing a parameter INLINEFORM0 for the maximum size of a node. Here, the size of a node is defined as the number of unique words that ever-descend from that node. During the traversal, if the size of a given node is less than this threshold, we designate the words that ultimately descend from that node as a concept word-group. Otherwise, if the node has children, we discard the node, and queue up all its children for further consideration. If this node does not have any children, on the other hand, the node is truncated to INLINEFORM1 elements with the highest frequency-ranks, and the resulting words are designated as a concept word-group. We note that the choice of INLINEFORM2 greatly affects the resulting collection of word-groups: Excessively large values result in few word-groups that greatly overlap with one another, while overly small values result in numerous tiny word-groups that fail to adequately represent a concept. We experimentally determined that a INLINEFORM3 value of 452 results in the most healthy number of relatively large word-groups (113 groups with size INLINEFORM4 100), while yielding a preferably small overlap amongst the resulting word-groups (with average overlap size not exceeding 3 words). A total of 566 word-groups were thus obtained. 259 smallest word-groups (with size INLINEFORM5 38) were discarded to bring down the number of word-groups to 307. Out of these, 7 groups with the lowest median frequency-rank were further discarded, which yields the final 300 concept word-groups used in the experiments. We present some of the resulting word-groups in Table TABREF9 .
By using the concept word-groups, we have trained the GloVe algorithm with the proposed modification given in Section SECREF4 on a snapshot of English Wikipedia measuring 8GB in size, with the stop-words filtered out. Using the parameters given in Table TABREF10 , this resulted in a vocabulary size of 287,847. For the weighting parameter in Eq. SECREF4 , we used a value of INLINEFORM0 . The algorithm was trained over 20 iterations. The GloVe algorithm without any modifications was also trained as a baseline with the same parameters. In addition to the original GloVe algorithm, we compare our proposed method with previous studies that aim to obtain interpretable word vectors. We train the improved projected gradient model proposed in BIBREF20 to obtain word vectors (called OIWE-IPG) using the same corpus we use to train GloVe and our proposed method. Using the methods proposed in BIBREF23 , BIBREF26 , BIBREF24 on our baseline GloVe embeddings, we obtain SOV, SPINE and Parsimax (orthogonal) word representations, respectively. We train all the models with the proposed parameters. However, in BIBREF26 , the authors show results for a relatively small vocabulary of 15,000 words. When we trained their model on our baseline GloVe embeddings with a large vocabulary of size 287,847, the resulting vectors performed significantly poor on word similarity tasks compared to the results presented in their paper. In addition, Parsimax (orthogonal) word vectors obtained using method in BIBREF26 are nearly identical to the baseline vectors (i.e. learned orthogonal transformation matrix is very close to identity). Therefore, Parsimax (orthogonal) yields almost same results with baseline vectors in all evaluations. We evaluate the interpretability of the resulting embeddings qualitatively and quantitatively. We also test the performance of the embeddings on word similarity and word analogy tests.
In our experiments, vocabulary size is close to 300,000 while only 16,242 unique words of the vocabulary are present in the concept groups. Furthermore, only dimensions that correspond to the concept group of the word will be updated due to the additional cost term. Given that these concept words can belong to multiple concept groups (2 on average), only 33,319 parameters are updated. There are 90 million individual parameters present for the 300,000 word vectors of size 300. Of these parameters, only approximately 33,000 are updated by the additional cost term.
In Fig. FIGREF13 , we demonstrate the particular way in which the proposed algorithm ( SECREF4 ) influences the vector representation distributions. Specifically, we consider, for illustration, the 32nd dimension values for the original GloVe algorithm and our modified version, restricting the plots to the top-1000 words with respect to their frequency ranks for clarity of presentation. In Fig. FIGREF13 , the words in the horizontal axis are sorted in descending order with respect to the values at the 32nd dimension of their word embedding vectors coming from the original GloVe algorithm. The dimension values are denoted with blue and red/green markers for the original and the proposed algorithms, respectively. Additionally, the top-50 words that achieve the greatest 32nd dimension values among the considered 1000 words are emphasized with enlarged markers, along with text annotations. In the presented simulation of the proposed algorithm, the 32nd dimension values are encoded with the concept JUDGMENT, which is reflected as an increase in the dimension values for words such as committee, academy, and article. We note that these words (red) are not part of the pre-determined word-group for the concept JUDGMENT, in contrast to words such as award, review and account (green) which are. This implies that the increase in the corresponding dimension values seen for these words is attributable to the joint effect of the first term in ( SECREF4 ) which is inherited from the original GloVe algorithm, in conjunction with the remaining terms in the proposed objective expression ( SECREF4 ). This experiment illustrates that the proposed algorithm is able to impart the concept of JUDGMENT on its designated vector dimension above and beyond the supplied list of words belonging to the concept word-group for that dimension. We also present the list of words with the greatest dimension value for the dimensions 11, 13, 16, 31, 36, 39, 41, 43 and 79 in Table TABREF11 . These dimensions are aligned/imparted with the concepts that are given in the column headers. In Table TABREF11 , the words that are highlighted with green denote the words that exist in the corresponding word-group obtained from Roget's Thesaurus (and are thus explicitly forced to achieve increased dimension values), while the red words denote the words that achieve increased dimension values by virtue of their cooccurrence statistics with the thesaurus-based words (indirectly, without being explicitly forced). This again illustrates that a semantic concept can indeed be coded to a vector dimension provided that a sensible lexical resource is used to guide semantically related words to the desired vector dimension via the proposed objective function in ( SECREF4 ). Even the words that do not appear in, but are semantically related to, the word-groups that we formed using Roget's Thesaurus, are indirectly affected by the proposed algorithm. They also reflect the associated concepts at their respective dimensions even though the objective functions for their particular vectors are not modified. This point cannot be overemphasized. Although the word-groups extracted from Roget's Thesaurus impose a degree of supervision to the process, the fact that the remaining words in the entire vocabulary are also indirectly affected makes the proposed method a semi-supervised approach that can handle words that are not in these chosen word-groups. A qualitative example of this result can be seen in the last column of Table TABREF11 . It is interesting to note the appearance of words such as guerilla, insurgency, mujahideen, Wehrmacht and Luftwaffe in addition to the more obvious and straightforward army, soldiers and troops, all of which are not present in the associated word-group WARFARE.
Most of the dimensions we investigated exhibit similar behaviour to the ones presented in Table TABREF11 . Thus generally speaking, we can say that the entries in Table TABREF11 are representative of the great majority. However, we have also specifically looked for dimensions that make less sense and determined a few such dimensions which are relatively less satisfactory. These less satisfactory examples are given in Table TABREF14 . These examples are also interesting in that they shed insight into the limitations posed by polysemy and existence of very rare outlier words.
One of the main goals of this study is to improve the interpretability of dense word embeddings by aligning the dimensions with predefined concepts from a suitable lexicon. A quantitative measure is required to reliably evaluate the achieved improvement. One of the methods proposed to measure the interpretability is the word intrusion test BIBREF41 . But, this method is expensive to apply since it requires evaluations from multiple human evaluators for each embedding dimension. In this study, we use a semantic category-based approach based on the method and category dataset (SEMCAT) introduced in BIBREF27 to quantify interpretability. Specifically, we apply a modified version of the approach presented in BIBREF40 in order to consider possible sub-groupings within the categories in SEMCAT. Interpretability scores are calculated using Interpretability Score (IS) as given below:
 DISPLAYFORM0 
In ( EQREF17 ), INLINEFORM0 and INLINEFORM1 represents the interpretability scores in the positive and negative directions of the INLINEFORM2 dimension ( INLINEFORM3 , INLINEFORM4 number of dimensions in the embedding space) of word embedding space for the INLINEFORM5 category ( INLINEFORM6 , INLINEFORM7 is number of categories in SEMCAT, INLINEFORM8 ) in SEMCAT respectively. INLINEFORM9 is the set of words in the INLINEFORM10 category in SEMCAT and INLINEFORM11 is the number of words in INLINEFORM12 . INLINEFORM13 corresponds to the minimum number of words required to construct a semantic category (i.e. represent a concept). INLINEFORM14 represents the set of INLINEFORM15 words that have the highest ( INLINEFORM16 ) and lowest ( INLINEFORM17 ) values in INLINEFORM18 dimension of the embedding space. INLINEFORM19 is the intersection operator and INLINEFORM20 is the cardinality operator (number of elements) for the intersecting set. In ( EQREF17 ), INLINEFORM21 gives the interpretability score for the INLINEFORM22 dimension and INLINEFORM23 gives the average interpretability score of the embedding space.
Fig. FIGREF18 presents the measured average interpretability scores across dimensions for original GloVe embeddings, for the proposed method and for the other four methods we compare, along with a randomly generated embedding. Results are calculated for the parameters INLINEFORM0 and INLINEFORM1 . Our proposed method significantly improves the interpretability for all INLINEFORM2 compared to the original GloVe approach. Our proposed method is second to only SPINE in increasing interpretability. However, as we will experimentally demonstrate in the next subsection, in doing this, SPINE almost entirely destroys the underlying semantic structure of the word embeddings, which is the primary function of a word embedding.
The proposed method and interpretability measurements are both based on utilizing concepts represented by word-groups. Therefore it is expected that there will be higher interpretability scores for some of the dimensions for which the imparted concepts are also contained in SEMCAT. However, by design, word groups that they use are formed by using different sources and are independent. Interpretability measurements use SEMCAT while our proposed method utilizes Roget's Thesaurus.
It is necessary to show that the semantic structure of the original embedding has not been damaged or distorted as a result of aligning the dimensions with given concepts, and that there is no substantial sacrifice involved from the performance that can be obtained with the original GloVe. To check this, we evaluate performances of the proposed embeddings on word similarity BIBREF42 and word analogy BIBREF0 tests. We compare the results with the original embeddings and the three alternatives excluding Parsimax BIBREF26 since orthogonal transformations will not affect the performance of the original embeddings on these tests.
Word similarity test measures the correlation between word similarity scores obtained from human evaluation (i.e. true similarities) and from word embeddings (usually using cosine similarity). In other words, this test quantifies how well the embedding space reflects human judgements in terms of similarities between different words. The correlation scores for 13 different similarity test sets are reported in Table TABREF20 . We observe that, let alone a reduction in performance, the obtained scores indicate an almost uniform improvement in the correlation values for the proposed algorithm, outperforming all the alternatives in almost all test sets. Categories from Roget's thesaurus are groupings of words that are similar in some sense which the original embedding algorithm may fail to capture. These test results signify that the semantic information injected into the algorithm by the additional cost term is significant enough to result in a measurable improvement. It should also be noted that scores obtained by SPINE is unacceptably low on almost all tests indicating that it has achieved its interpretability performance at the cost of losing its semantic functions.
Word analogy test is introduced in BIBREF1 and looks for the answers of the questions that are in the form of "X is to Y, what Z is to ?" by applying simple arithmetic operations to vectors of words X, Y and Z. We present precision scores for the word analogy tests in Table TABREF21 . It can be seen that the alternative approaches that aim to improve interpretability, have poor performance on the word analogy tests. However, our proposed method has comparable performance with the original GloVe embeddings. Our method outperforms GloVe in semantic analogy test set and in overall results, while GloVe performs slightly better in syntactic test set. This comparable performance is mainly due to the cost function of our proposed method that includes the original objective of the GloVe.
To investigate the effect of the additional cost term on the performance improvement in the semantic analogy test, we present Table TABREF22 . In particular, we present results for the cases where i) all questions in the dataset are considered, ii) only the questions that contains at least one concept word are considered, iii) only the questions that consist entirely of concept words are considered. We note specifically that for the last case, only a subset of the questions under the semantic category family.txt ended up being included. We observe that for all three scenarios, our proposed algorithm results in an improvement in the precision scores. However, the greatest performance increase is seen for the last scenario, which underscores the extent to which the semantic features captured by embeddings can be improved with a reasonable selection of the lexical resource from which the concept word-groups were derived.
We presented a novel approach to impart interpretability into word embeddings. We achieved this by encouraging different dimensions of the vector representation to align with predefined concepts, through the addition of an additional cost term in the optimization objective of the GloVe algorithm that favors a selective increase for a pre-specified input of concept words along each dimension.
We demonstrated the efficacy of this approach by applying qualitative and quantitative evaluations for interpretability. We also showed via standard word-analogy and word-similarity tests that the semantic coherence of the original vector space is preserved, even slightly improved. We have also performed and reported quantitative comparisons with several other methods for both interpretabilty increase and preservation of semantic coherence. Upon inspection of Fig. FIGREF18 and Tables TABREF20 , TABREF21 , and TABREF22 altogether, it should be noted that our proposed method achieves both of the objectives simultaneously, increased interpretability and preservation of the intrinsic semantic structure.
An important point was that, while it is expected for words that are already included in the concept word-groups to be aligned together since their dimensions are directly updated with the proposed cost term, it was also observed that words not in these groups also aligned in a meaningful manner without any direct modification to their cost function. This indicates that the cost term we added works productively with the original cost function of GloVe to handle words that are not included in the original concept word-groups, but are semantically related to those word-groups. The underlying mechanism can be explained as follows. While the outside lexical resource we introduce contains a relatively small number of words compared to the total number of words, these words and the categories they represent have been carefully chosen and in a sense, "densely span" all the words in the language. By saying "span", we mean they cover most of the concepts and ideas in the language without leaving too many uncovered areas. With "densely" we mean all areas are covered with sufficient strength. In other words, this subset of words is able to constitute a sufficiently strong skeleton, or scaffold. Now remember that GloVe works to align or bring closer related groups of words, which will include words from the lexical source. So the joint action of aligning the words with the predefined categories (introduced by us) and aligning related words (handled by GloVe) allows words not in the lexical groups to also be aligned meaningfully. We may say that the non-included words are "pulled along" with the included words by virtue of the "strings" or "glue" that is provided by GloVe. In numbers, the desired effect is achieved by manipulating less than only 0.05% of parameters of the entire word vectors. Thus, while there is a degree of supervision coming from the external lexical resource, the rest of the vocabulary is also aligned indirectly in an unsupervised way. This may be the reason why, unlike earlier proposed approaches, our method is able to achieve increasing interpretability without destroying underlying semantic structure, and consequently without sacrificing performance in benchmark tests.
Upon inspecting the 2nd column of Table TABREF14 , where qualitative results for concept TASTE are presented, another insight regarding the learning mechanism of our proposed approach can be made. Here it seems understandable that our proposed approach, along with GloVe, brought together the words taste and polish, and then the words Polish and, for instance, Warsaw are brought together by GloVe. These examples are interesting in that they shed insight into how GloVe works and the limitations posed by polysemy. It should be underlined that the present approach is not totally incapable of handling polysemy, but cannot do so perfectly. Since related words are being clustered, sufficiently well-connected words that do not meaningfully belong along with others will be appropriately "pulled away" from that group by several words, against the less effective, inappropriate pull of a particular word. Even though polish with lowercase "p" belongs where it is, it is attracting Warsaw to itself through polysemy and this is not meaningful. Perhaps because Warsaw is not a sufficiently well-connected word, it ends being dragged along, although words with greater connectedness to a concept group might have better resisted such inappropriate attractions.
In this study, we used the GloVe algorithm as the underlying dense word embedding scheme to demonstrate our approach. However, we stress that it is possible for our approach to be extended to other word embedding algorithms which have a learning routine consisting of iterations over cooccurrence records, by making suitable adjustments in the objective function. Since word2vec model is also based on the coocurrences of words in a sliding window through a large corpus, we expect that our approach can also be applied to word2vec after making suitable adjustments, which can be considered as an immediate future work for our approach. Although the semantic concepts are encoded in only one direction (positive) within the embedding dimensions, it might be beneficial to pursue future work that also encodes opposite concepts, such as good and bad, in two opposite directions of the same dimension.
The proposed methodology can also be helpful in computational cross-lingual studies, where the similarities are explored across the vector spaces of different languages BIBREF43 , BIBREF44 .

Figure and table captions:
Fig. 1. Function g in the additional cost term.
TABLE I SAMPLE CONCEPTS AND THEIR ASSOCIATED WORD-GROUPS FROM ROGET’S THESAURUS
TABLE II GLOVE PARAMETERS
TABLE III WORDS WITH LARGEST DIMENSION VALUES FOR THE PROPOSED ALGORITHM
Fig. 2. Most frequent 1000 words sorted according to their values in the 32nd dimension of the original GloVe embedding are shown with blue markers. Red and green markers show the values of the same words for the 32nd dimension of the embedding obtained with the proposed method where the dimension is aligned with the concept JUDGMENT. Words with green markers are contained in the concept JUDGMENT while words with red markers are not contained.
Fig. 3. Interpretability scores averaged over 300 dimensions for the original GloVe method, the proposed method, and four alternative methods along with a randomly generated baseline embedding for λ = 5. Please note that Parsimax method yields identical results with the GloVe baseline so that their plots coincide with each other (light blue).
TABLE IV WORDS WITH LARGEST DIMENSION VALUES FOR THE PROPOSED ALGORITHM - LESS SATISFACTORY EXAMPLES
TABLE V CORRELATIONS FOR WORD SIMILARITY TESTS
TABLE VI PRECISION SCORES FOR THE ANALOGY TEST
TABLE VII PRECISION SCORES FOR THE SEMANTIC ANALOGY TEST

Questions about this paper:
What experiments do they use to quantify the extent of interpretability?
What is the additive modification to the objective function?

Answers:
Human evaluation for interpretability using the word intrusion test and automated evaluation for interpretability using a semantic category-based approach based on the method and category dataset (SEMCAT).
An additive term added to the cost function for any one of the words of concept word-groups