GloVe, coined from Global Vectors, is a model for distributed word representation. The model is anunsupervised learning algorithm for obtainingvector representations for words. This is achieved by mapping words into a meaningful space where the distance between words is related to semantic similarity.^[1] Training is performed on aggregated global word-wordco-occurrencestatistics from a corpus, and the resulting representations showcase interesting linear substructures of theword vector space. As log-bilinear regression model for unsupervised learning of word representations, it combines the features of two model families, namely the global matrix factorization and local context window methods.

It is developed as anopen-source project atStanford^[2] and was launched in 2014. It was designed as a competitor toword2vec, and the original paper noted multiple improvements of GloVe over word2vec. As of 2022^[update], both approaches are outdated, andTransformer-based models, such asBERT, which add multiple neural-network attention layers on top of a word embedding model similar to Word2vec, have come to be regarded as the state of the art in NLP.^[3]

You shall know a word by the company it keeps (Firth, J. R. 1957:11)^[4]

The idea of GloVe is to construct, for each word${\displaystyle i}$, two vectors${\displaystyle w_i,{\tilde{w}}_i}$, such that the relative positions of the vectors capture part of the statistical regularities of the word${\displaystyle i}$. The statistical regularity is defined as the co-occurrence probabilities. Words that resemble each other in meaning should also resemble each other in co-occurrence probabilities.

Let thevocabulary be${\displaystyle V}$, the set of all possible words (aka "tokens"). Punctuation is either ignored, or treated as vocabulary, and similarly for capitalization and other typographical details.^[1]

If two words occur close to each other, then we say that they occur in thecontext of each other. For example, if the context length is 3, then we say that in the following sentence

GloVe₁, coined₂ from₃ Global₄ Vectors₅, is₆ a₇ model₈ for₉ distributed₁₀ word₁₁ representation₁₂

the word "model₈" is in the context of "word₁₁" but not the context of "representation₁₂".

A word is not in the context of itself, so "model₈" is not in the context of the word "model₈", although, if a word appears again in the same context, then it does count.

Let${\displaystyle X_{ij}}$ be the number of times that the word${\displaystyle j}$ appears in the context of the word${\displaystyle i}$ over the entire corpus. For example, if the corpus is just "I don't think that that is a problem." we have${\displaystyle X_{\text{that},\text{that}}=2}$ since the first "that" appears in the second one's context, and vice versa.

Let${\displaystyle X_i=\sum _{j\in V}{X}_{ij}}$ be the number of words in the context of all instances of word${\displaystyle i}$. By counting, we have$${\displaystyle X_i=2\times (\text{context size})\times \mathrm{\#}(\text{occurrences of word }i)}$$(except for words occurring right at the start and end of the corpus)

Let$${\displaystyle P_{ik}:=P(k|i):=\frac{X_{ik}}{X_i}}$$be theco-occurrence probability. That is, if one samples a random occurrence of the word${\displaystyle i}$ in the entire document, and a random word within its context, that word is${\displaystyle k}$ with probability${\displaystyle P_{ik}}$. Note that${\displaystyle P_{ik}\ne P_{ki}}$ in general. For example, in a typical modern English corpus,${\displaystyle P_{\text{ado},\text{much}}}$ is close to one, but${\displaystyle P_{\text{much},\text{ado}}}$ is close to zero. This is because the word "ado" is almost only used in the context of the archaic phrase "much ado about", but the word "much" occurs in all kinds of contexts.

For example, in a 6 billion token corpus, we have

Table 1 of^[1]

Probability and Ratio	${\displaystyle k=\text{ solid }}$	${\displaystyle k=\text{ gas }}$	${\displaystyle k=\text{ water }}$	${\displaystyle k=\text{ fashion }}$
${\displaystyle P(k\mid \text{ ice })}$	${\displaystyle 1.9\times {10}^{-4}}$	${\displaystyle 6.6\times {10}^{-5}}$	${\displaystyle 3.0\times {10}^{-3}}$	${\displaystyle 1.7\times {10}^{-5}}$
${\displaystyle P(k\mid \text{ steam })}$	${\displaystyle 2.2\times {10}^{-5}}$	${\displaystyle 7.8\times {10}^{-4}}$	${\displaystyle 2.2\times {10}^{-3}}$	${\displaystyle 1.8\times {10}^{-5}}$
${\displaystyle P(k\mid \text{ ice })/P(k\mid \text{ steam })}$	${\displaystyle 8.9}$	${\displaystyle 8.5\times {10}^{-2}}$	${\displaystyle 1.36}$	${\displaystyle 0.96}$

Inspecting the table, we see that the words "ice" and "steam" are indistinguishable along the "water" (often co-occurring with both) and "fashion" (rarely co-occurring with either), but distinguishable along the "solid" (co-occurring more with ice) and "gas" (co-occurring more with "steam").

The idea is to learn two vectors${\displaystyle w_i,{\tilde{w}}_i}$ for each word${\displaystyle i}$, such that we have amultinomial logistic regression:$${\displaystyle w_i^T{\tilde{w}}_j+b_i+{\tilde{b}}_j\approx \ln P_{ij}}$$and the terms${\displaystyle b_i,{\tilde{b}}_j}$ are unimportant parameters.

This means that if the words${\displaystyle i,j}$ have similar co-occurrence probabilities${\displaystyle (P_{ik}{)}_{k\in V}\approx (P_{jk}{)}_{k\in V}}$, then their vectors should also be similar:${\displaystyle w_i\approx w_j}$.

Naively, logistic regression can be run by minimizing the squared loss:$${\displaystyle L=\sum _{i,j\in V}(w_i^T{\tilde{w}}_j+b_i+{\tilde{b}}_j-\ln P_{ij}{)}^2}$$However, this would be noisy for rare co-occurrences. To fix the issue, the squared loss is weighted so that the loss is slowly ramped-up as the absolute number of co-occurrences${\displaystyle X_{ij}}$ increases:$${\displaystyle L=\sum _{i,j\in V}f(X_{ij})(w_i^T{\tilde{w}}_j+b_i+{\tilde{b}}_j-\ln P_{ij}{)}^2}$$whereand${\displaystyle x_{max},\alpha }$ arehyperparameters. In the original paper, the authors found that${\displaystyle x_{max}=100,\alpha =3/4}$ seem to work well in practice.

Once a model is trained, we have 4 trained parameters for each word:${\displaystyle w_i,{\tilde{w}}_i,b_i,{\tilde{b}}_i}$. The parameters${\displaystyle b_i,{\tilde{b}}_i}$ are irrelevant, and only${\displaystyle w_i,{\tilde{w}}_i}$ are relevant.

The authors recommended using${\displaystyle w_i+{\tilde{w}}_i}$ as the final representation vector for word${\displaystyle i}$, because empirically it worked better than${\displaystyle w_i}$ or${\displaystyle {\tilde{w}}_i}$ alone.

GloVe can be used to find relations between words like synonyms, company-product relations, zip codes and cities, etc. However, the unsupervised learning algorithm is not effective in identifying homographs, i.e., words with the same spelling and different meanings. This is as the unsupervised learning algorithm calculates a single set of vectors for words with the same morphological structure.^[5] The algorithm is also used by theSpaCy library to build semantic word embedding features, while computing the top list words that match with distance measures such ascosine similarity andEuclidean distance approach.^[6] GloVe was also used as the word representation framework for the online and offline systems designed to detect psychological distress in patient interviews.^[7]

• ELMo
• BERT
• Word2vec
• fastText
• Natural language processing

• GloVeArchived 2016-12-19 at theWayback Machine
• Deeplearning4j GloVeArchived 2019-02-02 at theWayback Machine

• Computational linguistics
• Natural language processing toolkits

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