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[Page no. 11] "results irrespective of speed. 5 Conclusion Recently, considerable attention has been focused on the question of whether distributional word representations are best learned from count-based 9In contrast, noise-contrastive estimation is an approxi- mation which improves with more negative samples. In Ta- ble 1 of (Mnih et al., 2013), accuracy on the analogy task is a non-decreasing function of the number of negative samples. methods or from prediction-based methods. Cur- rently, prediction-based models garner substantial support; for example, Baroni et al. (2014) argue that these models perform better across a range of tasks. In this work we argue that the two classes of methods are not dramatically different at a fun- damental level since they both probe the under- lying co-occurrence statistics of the corpus, but the efﬁciency with which the count-based meth- ods capture global statistics can be advantageous. We construct a model that utilizes this main ben- eﬁt of count data while simultaneously capturing the meaningful linear substructures prevalent in recent log-bilinear prediction-based methods like word2vec. The result, GloVe, is a new global log-bilinear regression model for the unsupervised learning of word representations that outperforms other models on word analogy, word similarity, and named entity recognition tasks. Acknowledgments We thank the anonymous reviewers for their valu- able comments. Stanford University gratefully acknowledges the support of the Defense Threat Reduction Agency (DTRA) under Air Force Re- search Laboratory (AFRL) contract no. FA8650- 10-C-7020 and the Defense Advanced Research Projects Agency (DARPA) Deep Exploration and Filtering of Text (DEFT) Program under AFRL contract no. FA8750-13-2-0040. Any opinions, ﬁndings, and conclusion or recommendations ex- pressed in this material are those of the authors and do not necessarily reﬂect the view of the DTRA, AFRL, DEFT, or the US government.  References Tom M. Apostol. 1976. Introduction to Analytic Number Theory. Introduction to"

[Page no. 4] "viewed as a continuous function, it should vanish as x → 0 fast enough that the limx→0 f (x) log2 x is ﬁnite. 2. f (x) should be non-decreasing so that rare co-occurrences are not overweighted. 3. f (x) should be relatively small for large val- ues of x, so that frequent co-occurrences are not overweighted. Of course a large number of functions satisfy these properties, but one class of functions that we found to work well can be parameterized as, f (x) = � (x/xmax)α if x < xmax 1 otherwise . (9) 0.2 0.4 0.6 0.8 1.0 0.0 Figure 1: Weighting function f with α = 3/4. The performance of the model depends weakly on the cutoff, which we ﬁx to xmax = 100 for all our experiments. We found that α = 3/4 gives a mod- est improvement over a linear version with α = 1. Although we offer only empirical motivation for choosing the value 3/4, it is interesting that a sim- ilar fractional power scaling was found to give the best performance in (Mikolov et al., 2013a). 3.1 Relationship to Other Models Because all unsupervised methods for learning word vectors are ultimately based on the occur- rence statistics of a corpus, there should be com- monalities between the models. Nevertheless, cer- tain models remain somewhat opaque in this re- gard, particularly the recent window-based meth- ods like skip-gram and ivLBL. Therefore, in this subsection we show how these models are related to our proposed model, as deﬁned in Eqn. (8). The starting point for the skip-gram or ivLBL methods is a model Qi j for the probability that word j appears in the context of word i. For con- creteness, let us assume that Qi j is a softmax, Qi j = exp(wT i ˜wj)"

[Page no. 11] "Analytic Num- ber Theory. Marco Baroni, Georgiana Dinu, and Germ´an Kruszewski. 2014. Don’t count, predict! A systematic comparison of context-counting vs. context-predicting semantic vectors. In ACL. Yoshua Bengio. 2009. Learning deep architectures for AI. Foundations and Trends in Machine Learning. Yoshua Bengio, R´ejean Ducharme, Pascal Vin- cent, and Christian Janvin. 2003. A neural prob- abilistic language model. JMLR, 3:1137–1155. John A. Bullinaria and Joseph P. Levy. 2007. Ex- tracting semantic representations from word co- occurrence statistics: A computational study. Behavior Research Methods, 39(3):510–526. Dan C. Ciresan, Alessandro Giusti, Luca M. Gam- bardella, and J¨urgen Schmidhuber. 2012. Deep neural networks segment neuronal membranes in electron microscopy images. In NIPS, pages 2852–2860. Ronan Collobert and Jason Weston. 2008. A uni- ﬁed architecture for natural language process- ing: deep neural networks with multitask learn- ing. In Proceedings of ICML, pages 160–167. Ronan Collobert, Jason Weston, L´eon Bottou, Michael Karlen, Koray Kavukcuoglu, and Pavel Kuksa. 2011. Natural Language Processing (Al- most) from Scratch. JMLR, 12:2493–2537. Scott Deerwester, Susan T. Dumais, George W. Furnas, Thomas K. Landauer, and Richard Harshman. 1990. Indexing by latent semantic analysis. Journal of the American Society for Information Science, 41. John Duchi, Elad Hazan, and Yoram Singer. 2011. Adaptive subgradient methods for online learn- ing and stochastic optimization. JMLR, 12. Lev Finkelstein, Evgenly Gabrilovich, Yossi Ma- tias, Ehud Rivlin, Zach Solan, Gadi Wolfman, and Eytan Ruppin. 2001. Placing search in con- text: The concept revisited. In Proceedings of the 10th international conference on World Wide Web, pages 406–414. ACM. Eric H. Huang, Richard Socher, Christopher D. Manning, and Andrew Y. Ng. 2012. Improving Word Representations via Global Context and Multiple Word Prototypes. In ACL. R´emi Lebret and Ronan Collobert. 2014. Word embeddings through Hellinger PCA. In EACL. Omer Levy, Yoav Goldberg, and Israel Ramat- Gan. 2014. Linguistic regularities in sparse"

[Page no. 3] "can be extracted directly from co-occurrence probabilities. Con- sider two words i and j that exhibit a particular as- pect of interest; for concreteness, suppose we are interested in the concept of thermodynamic phase, for which we might take i = ice and j = steam. The relationship of these words can be examined by studying the ratio of their co-occurrence prob- abilities with various probe words, k. For words k related to ice but not steam, say k = solid, we expect the ratio Pik/Pjk will be large. Similarly, for words k related to steam but not ice, say k = gas, the ratio should be small. For words k like water or fashion, that are either related to both ice and steam, or to neither, the ratio should be close to one. Table 1 shows these probabilities and their ratios for a large corpus, and the numbers conﬁrm these expectations. Compared to the raw probabil- ities, the ratio is better able to distinguish relevant words (solid and gas) from irrelevant words (water and fashion) and it is also better able to discrimi- nate between the two relevant words. The above argument suggests that the appropri- ate starting point for word vector learning should be with ratios of co-occurrence probabilities rather than the probabilities themselves. Noting that the ratio Pik/Pjk depends on three words i, j, and k, the most general model takes the form, F(wi,wj, ˜wk) = Pik Pjk , (1) where w ∈ Rd are word vectors and ˜w ∈ Rd are separate context word vectors whose role will be discussed in Section 4.2. In this equation, the right-hand side is extracted from the corpus, and F may depend on some as-of-yet unspeciﬁed pa- rameters. The number of possibilities for F is vast, but by enforcing a"

[Page no. 7] "on test on three datasets: 1) ConLL-03 testing data, 2) ACE Phase 2 (2001-02) and ACE-2003 data, and 3) MUC7 Formal Run test set. We adopt the BIO2 annota- tion standard, as well as all the preprocessing steps described in (Wang and Manning, 2013). We use a comprehensive set of discrete features that comes with the standard distribution of the Stanford NER model (Finkel et al., 2005). A total of 437,905 discrete features were generated for the CoNLL- 2003 training dataset. In addition, 50-dimensional vectors for each word of a ﬁve-word context are added and used as continuous features. With these features as input, we trained a conditional random ﬁeld (CRF) with exactly the same setup as the CRFjoin model of (Wang and Manning, 2013). 4.2 Corpora and training details We trained our model on ﬁve corpora of varying sizes: a 2010 Wikipedia dump with 1 billion to- kens; a 2014 Wikipedia dump with 1.6 billion to- kens; Gigaword 5 which has 4.3 billion tokens; the combination Gigaword5 + Wikipedia2014, which the analogy task. This number is evaluated on a subset of the dataset so it is not included in Table 2. 3COSMUL performed worse than cosine similarity in almost all of our experiments. has 6 billion tokens; and on 42 billion tokens of web data, from Common Crawl5. We tokenize and lowercase each corpus with the Stanford to- kenizer, build a vocabulary of the 400,000 most frequent words6, and then construct a matrix of co- occurrence counts X. In constructing X, we must choose how large the context window should be and whether to distinguish left context from right context. We explore the effect of these choices be- low. In all cases we use a decreasing weighting function, so that word pairs that are d words apart contribute 1/d"

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