As a semi-computer scientist, I always dream that we, humans, can make the computers understand what we say. Instead of writing sophisticated code or using other input devices (a mouse and a keyboard) to give instructions to computers, we can directly talk to a computer and give instructions. The first step to accomplish this science fiction scene is to let the computer understand what we say -- natural languages, which is the ultimate target of natural language processing(NLP) research. The first step to making computers understand natural languages is to represent the fundamental element of natural language, words, as a form that computers can understand. This raises a big research direction in NLP: word representations. This is the sub-area I am interested most in NLP. In this series post, I am going to present some vital research work on this topic.

In this very first post, I will first explain why do we need a different representation for computers and what we have done in this path. I want to present a "map" in this area to understand where we are on the road to our ultimate target: giving instructions to computers by talking.

# Why Representing Words¶

Although talking to a computer is a very appealing idea, in reality, it is still a hard problem. Why? Because computers "think" differently from humans. Language is full of ambiguity, which is somehow an advantage because it enables us to use a finite set of symbols to describe this infinite world. However, this ambiguity does not work for computers. Computers can not understand this ambiguity because it only deals with numbers, which is deterministic. For example, computers can perform adding or multiplying operations, but computers can not understand the difference between the fruit "Apple" and the company "Apple". To computers, these two words are the same symbol and thus represent the same meaning.

Apple v.s. Apple

To let computers understand the ambiguity of natural language, we need to "translate" natural language into some representations that computers enjoy. The primary element of this translation is to translate words because words are the smallest element that contains semantic meaning. Over the years, researchers developed many different representing methods. These representing methods evolved through various stages. Following is a summary of all these different representing methods.

# Representing Methods¶

In the field of word representation, researchers have gone a long way. Here, I try to divide the representing history into different stages. Be note, and this is only my perspective and not a standard division.

• Prehistory: Dictionary lookup
• Middle Age: one-hot encoding, bag-of-words
• The Enlightenment: Vector space model and distributed representations
• Industrial Age: Type vector(word2vec, Fasttext)
• Modern Age: Token vector(ELMo and BERT)

In this post, I will briefly talk about these different methods. More details will be presented in the following posts.

# Prehistory: Dictionary Lookup¶

Dictionary lookup is a straightforward idea that may exist long before computers (that's why I call it prehistory). One sentence can describe this method: Map each word to a unique number. This unique number is used as the representation of the corresponding word.

I am groot

Suppose we have a small language, which only consists of three words: I, am, and groot. Now, we need to create a representation of these three words. By assigning each word a unique number, we can create a lookup dictionary shown below:

Words ID
I 0
am 1
groot 2

By creating such a mapping relation (i$$\rightarrow 0$$, am$$\rightarrow 1$$, groot$$\rightarrow 2$$), we successfully represent the whole language into numbers, which can be understood by computers. For each given word, we can return its representation by looking it up in the dictionary. Although this is a simple idea, it builds the fundamentals for all other "modern" methods.

A straightforward example is showed in the following figure:

Morse Code is a simple dictionary lookup

This figure is a table of morse code. Here, each letter is mapped to dots and dashes. This figure composes a simple dictionary. Morese code exists long before the creation of computers. This is why I call the dictionary lookup a prehistory representation method.

Since we call it prehistory, it must have many problems. Mapping to numbers is the only advantage of this dictionary lookup method. There are many drawbacks to this method.

• Impose the ordering of words. By mapping each word into an integer, this representation imposes an ordering of words that do not exist. For example, consider I $$\rightarrow 0$$ and am $$\rightarrow 1$$, computers think am is more important than I because $$1$$ is greater than $$0$$. This is a wrong assumption.
• Integers do not contain information. Although we can map each word into an integer, an integer is merely another symbol. It does not carry any semantic meaning.
• The dictionary will grow to infinite. In our small language, we only have three words. In reality, we face unlimited word vocabulary (we are creating new words every day), which means the dictionary keeps growing forever.

To overcome all these drawbacks, researchers keep trying to develop new representation methods, which leads us to the next stage: Middle Age.

# Middle Age: One-hot and Bag-of-Words¶

Now, we are entering the middle age of word representation. In this age, one-hot encoding, along with its variants, Bag-of-words, becomes the most commonly used method.

## One-hot Represention¶

The idea of one-hot representation is also simple: Create a vector with filled zeros except one that you want to represent. Following the example language of I am groot, we can have three vectors with a size of $$4$$:

I am groot UNKNOWN
I 1 0 0 0
am 0 1 0 0
groot 0 0 1 0

As we can see here, each dimension represents one word. Only the word that needs to be represented is set to $$1$$. For example, word I is represented as $$[1, 0, 0, 0]$$. The extra dimension is used for out of vocabulary words.

The most important advantage of this representation is it can eliminate the wrong ordering assumption of Dictionary Lookup. Each word is represented equally. However, this representation still suffers the other two drawbacks of Dictionary Lookup:

• Each vector hardly carray any semantic informtion;
• when the vocabulary becomes large, this representation requires large space of memory.

## Bag-of-Words¶

Although there are drawbacks to one-hot representation, it was widely used years ago. One important extension is Bag-of-Words representation. Instead of representing a single word, Bag-of-Words usually is used to represent a sentence or a document. One can see the Bag-of-Words as the summation of one-hot representations of each word in one sentence. Following are two example sentences composed by our example I am groot language:

• I am groot:

$$[1,1,1,0]=[1,0,0,0]_{\text{I}}+[0,1,0,0]_{\text{am}}+[0,0,1,0]_{\text{groot}}$$.

• I am not groot:

$$[1,1,1,1]=[1,0,0,0]_{\text{I}}+[0,1,0,0]_{\text{am}}+[0,0,0,1]_{\text{not}}+[0,0,1,0]_{\text{groot}}$$

Because not does not belong to the language vocabulary, we have to use the UNKNOWN dimension to represent it.

Bag-of-Words suffers several drawbacks:

• It ignores the position information in the sentence. For example, we can not differentiate two sentences: "I am groot not" and "I am not groot" using Bag-of-Words.
• It needs a large memory space because the dimension of these vectors equals vocabulary size, which is very large in practice.

# The Enlightenment: Word Embeddings¶

The next stage is the enlightenment age, in which the two most important ideas of representing words were proposed. These two ideas make a significant impact on the research history of natural language processing.

The first idea is a famous assumption:

You shall know a word by the company it keeps

This assumption is proposed by John Rupert Firth. I can not find the exact source of this quotation. But I can find a similar one in Firth (1935):

... .the complete meaning of a word is always contextual, and no study of meaning apart from a complete context can be taken seriously.

This assumption lay the foundation of all following learning models that produce word embeddings. What does this assumption mean? It means that its context decides the meaning of a word. For example, suppose we have the following sentence:

$$\text{The fluffy __ barked as it chased a cat.}$$

Which word should we fill in this blank? A simple guess is dog. Why can we guess the meaning without knowing the word? Because the context (other words in the sentence) decides the meaning of this blank word. I think this sentence can well explain the context assumption Firth proposed.

The other important idea is the proposition of using a low dimension dense vector to represent words. Using a feature learning model, each word is represented by a dense vector with a fixed and lower dimension (compared to the size of the dictionary). A critical property of this dense vector is: words with the same meaning will have a similar vector. We usually call this dense vector word emebedding or distributed representation. In the following of this post, I will use these two terms interchangeably.

Let us see an example of what does a dense vector mean. Recall that in the One-hot representation, we represent the word groot as a binary vector:

$$\text{groot} \rightarrow [0, 0, 1, 0]$$

In a dense vector, groot represents as:

$$\text{groot} \rightarrow [2.56, -0.55, 5.30, -4.06, 0.82]$$

The difference is in each dimension. We have real numbers instead of all zeros. The dimension of this dense vector is fixed. The size of vocabulary does not change the dimension.

The earliest detailed analysis of distributed representation I can find is in Chapter 3 in Parallel Distributed Processing (Rumelhart and McClelland, 1987). In this book, distributed representations are analyzed thoroughly. I suggest any who are interested in word embeddings should read chapter 3 of Parallel Distributed Processing.

However, although two insightful ideas have been made, distributed representations have not become popular because, at that time, no good techniques were available to produce high-quality word embeddings. This situation continues until the year of 2003. In this year, Yoshua Bengio published the paper: A neural probabilistic language model (Bengio et al., 2003). In this paper, Bengio puts the idea of word embeddings into the context of neural networks. By training a neural network, the model can naturally produce a vector for each word. Starting from this paper, people began to review the idea of distributed representation.

# Industrial Age: Type Vector¶

Although Yoshua Bengio pointed a bright way to produce word embeddings, it is costly to train word embeddings because the neural network involves a lot of computations. The word embedding model was still not a hot topic in the NLP field for about ten years.

In 2013, a team at Google led by Tomas Mikolov published a word embedding toolkit word2vec, which can train word embeddings faster than previous approaches. It is this word2vec model that makes the word embedding idea take off. Mikolov's famous paper: "Efficient estimation of word representations in vector space" (Mikolov et al., 2013) received more than $$10,000$$ citations in just a few years. Word2vec provides a simple algorithm to produce word embeddings from the unlabelled text. These embeddings have several important properties that attract people. The most impressive property is the similarities between words. One famous example is:

$$\vec{\text{king}} - \vec{\text{man}} + \vec{\text{woman}} \approx \vec{\text{queen}}$$

This example shows that word embedding produced by word2vec at least captures some semantic meanings of words. Our representation finally is not just some meaningless symbols. It can carry meanings of words.

Word2vec toolkit

I call this Industrial Age because it is similar to the Industrial Age in human history, significant improvements have been made for productive forces. Since the publication of word2vec, more research has been done following the direction of distributed representations. In the next year of the creation of word2vec, almost every NLP task has been integrated with word embeddings.

However, although word2vec can achieve the best performance on many NLP tasks at that time, people find some drawbacks of the word2vec-style models.

• First, if one word does not show in the training set, word2vec can not produce representation for it, known as out-of-vocabulary(OOV) problem.
• Words with multiple meanings can not be represented correctly.

To overcome the OOV problem, Facebook's AI Research (FAIR) lab created another famous embedding model in 2017: fastText(Bojanowski et al., 2017). One advantage of fastText is it can produce embeddings for out-of-vocabulary words. Now, fastText has replaced word2vec to become the baseline for other embedding models.

Before entering the next age, we need to understand the difference between two concepts: type vector and token vector.

Type Vector
Type vector means context-independent. The same word in different sentences (contexts) has the same representation. For example, the word "bank" in the sentence "I need to deposit some money to the bank" and "I am walking along the river bank" has the same representation.
Token Vector
Token vector means context-dependent. The same word in the different sentence (contexts) has different representations. For example, the word "bank" in the sentence "I need to deposit some money to the bank" and "I am walking along the river bank" have entirely different representations because the word "bank" represents different meanings in these two sentences.

Clearly, word2vec produces the type vector. We will talk about the token vector in the next age.

# Modern Age: Token Vector¶

If the creation of type vector (word2vec model) marks the age of industry, then the creation of BERT marks the modern era. In 2018, Google published another important paper in word representation history: "BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding"(Devlin et al., 2019). In less than two years, it already received more than $$7,000$$ citations from the NLP community.

BERT almost improves every single NLP task. The authors of BERT call it the new era of NLP. Instead of creating an embedding for each type word, BERT creates embeddings for tokens. It generalizes word2vec-style models from type vector to token vector. For example, the word "Bank" in sentences "I need to deposit some money to the bank" and "I am walking along the river bank" have completely different representations.

Also, BERT creates a new scheme of using word embeddings. Previously, we train our embedding learning models on some unlabelled text and apply these embeddings to a specific task without updating the embedding models. By using BERT, we train BERT on large unlabelled text corpus, then fine-tune on the specific task to adjust (update) the BERT model to a specific task to achieve better performance. After fine-tuning, the model is applied to the test set.

Like the creation of word2vec, after the creation of BERT, there are many other related models and works proposed. BERT becomes a hot topic in recent years. Although BERT may create a new representation era for us, there are still many unknown to us.

# Summary¶

In this post, I summarize the development history of word representations straightforwardly. I did not mention a lot of excellent work in this post (I will talk about them in other posts) because I want to make this post compact enough to deliver the whole picture of the research of word representations. I also ignore all the details of the models I mentioned in this post. This post is not about explanations of models but clears the development history. In each age, I strengthen the improvement point to show why models in the new era can mark a new era.

Starting from this post, I will keep writing research work about the word representation field. I hope you enjoy this series of posts.

## Bibliography

Yoshua Bengio, Réjean Ducharme, Pascal Vincent, and Christian Jauvin. A neural probabilistic language model. Journal of machine learning research, 3(Feb):1137–1155, 2003.

Piotr Bojanowski, Edouard Grave, Armand Joulin, and Tomas Mikolov. Enriching word vectors with subword information. Transactions of the Association for Computational Linguistics, 5:135–146, 2017.

Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding. In Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers), 4171–4186. 2019.

John Rupert Firth. The Technique of Semantics. Transactions of the philological society, 34(1):36–73, 1935.

Tomas Mikolov, Kai Chen, Greg Corrado, and Jeffrey Dean. Efficient estimation of word representations in vector space. arXiv preprint arXiv:1301.3781, 2013.

David E Rumelhart and James L McClelland. Parallel distributed processing, explotation in the microstructure of cognition-Vol. 1: Foundations. pdpe, 1987.

Yichu Zhou is the owner of this blog.

So what do you think? Did I miss something? Is any part unclear? Leave your comments below