One Model to Rule them all
Multitask and Multilingual Modelling for Lexical Analysis
Abstract—\abstracttextfontDeep Neural Networks are at the forefront of many state-of-the art approaches to Natural Language Processing (NLP). The field of NLP is currently awash with papers building on this method, to the extent that it has quite aptly been described as a tsunami (Manning, 2015). While a large part of the field is familiar with this family of learning architectures, it is the intention of this thesis to be available for a larger audience. Hence, although the rest of this thesis assumes familiarity with neural networks, this chapter is meant to be a foundational introduction for those with limited experience in this area. The reader is assumed to have some familiarity with machine learning and NLP, but not much beyond that.
We begin by exploring the basics of neural networks, and look at the three most commonly used general architectures for neural networks in NLP: Feed-forward Neural Networks, Recurrent Neural Networks, and Convolutional Neural Networks. Some common NLP scenarios are then outlined together with suggestions for suitable architectures.
Abstract—\abstracttextfontIn this chapter, we build upon the background knowledge of neural networks presented in the previous chapter. We will focus on different, but highly related, paradigms – multitask learning, and multilingual model transfer. Multitask learning is first presented in a general context, and then in the context of neural networks, which is the primary focus of this thesis. We will then look at multilingual approaches in NLP, again first in a general context, and then in the context of model transfer with multilingual word representations, which is the secondary focus of this thesis. In this thesis, we consider the first setting in Part II, the second setting in Part III, and include an outlook for a combined multilingual/multitask paradigm in Part IV.
Abstract—\abstracttextfontIn this chapter, a semantic tag set is presented, which is tailored for multilingual semantic parsing. As a first step towards exploring multitask learning, we will look at the effects of jointly learning this task, together with POS tagging, compared to learning the two tasks separately. Furthermore, we will see a deep neural network tagger, which is the first tagger to use deep residual networks (ResNets). The tagger uses both word and character representations, and includes a novel residual bypass architecture. We evaluate the tagger separately on the semantic tagging task, on POS tagging, and in the multitask learning setting. In the multitask setting, the tagger significantly outperforms prior results on English Universal Dependencies POS tagging reaching 95.71% accuracy on UD v1.2 and 95.67% accuracy on UD v1.3.
Abstract—\abstracttextfontIn the previous chapter, we saw that multitask learning improved the performance on POS tagging, when using semantic tagging as an auxiliary task. In fact, multitask learning often improves system performance for various tasks in ML in general, and NLP in particular. However, the question of when and why this is the case has yet to be answered satisfactorily. Although previous work has hypothesised that this is linked to the label distributions of the auxiliary task, it can be argued that this is not sufficient. In this chapter, we will see that information-theoretic measures which consider the joint label distributions of the main and auxiliary tasks offer far more explanatory value. The findings in this chapter are empirically supported by experiments on morphosyntactic tasks on 39 languages, and by experiments on several semantic tasks for English.
Abstract—\abstracttextfontUp until now, we have seen parameter sharing between tasks, in the context of multitask learning. Another possibility is to share parameters between languages, in a sense casting model multilinguality as a type of multitask learning. As a first example of multilingual learning, we look at cross-lingual semantic textual similarity. This task can be approached by leveraging multilingual distributional word representations, in which similar words in different languages are close to each other in semantic space. The availability of parallel data allows us to train such representations for a large number of languages. Such representations have the added advantage of allowing for leveraging semantic similarity data for languages for which no such data exists. In this chapter, the focus is on to what extent such an approach allows for enabling zero-shot learning for the task at hand. We also investigate whether language relatedness has an effect on how successful this is. We train and evaluate on six language pairs for semantic textual similarity, including English, Spanish, Arabic, and Turkish.
Abstract—\abstracttextfontThe fact that languages tend to share certain properties can be exploited by, e.g., sharing parameters between languages. This type of model multilinguality is relatively common, as taking advantage of language similarities can be beneficial. However, the question of when multilinguality is a useful addition in terms of monolingual model performance is left unanswered. In this chapter, we explore this issue by experimenting with a sample of languages on a selection of tasks: semantic tagging, part-of-speech tagging, dependency relation tagging, and morphological inflection. We compare results under various multilingual model transfer conditions, and finally observe correlations between model effectivity and two measures of language similarity.
Abstract—\abstracttextfontMultitask learning and multilingual learning share many similarities, and partially build on the same assumptions. One such assumption is that similarities between tasks, or between languages, can be exploited with beneficial effects. A natural extension of these two separate paradigms is to combine them, in order to take advantage of such similarities across both modalities simultaneously. In this chapter, such a combined paradigm is explored, with the goal of building One Model to rule them all. The pilot experiments presented here take a first step in this direction, by looking at Part-of-Speech tagging and dependency relation labelling for a large selection of source languages. We restrict ourselves to looking at three target languages representing some typological variety: Finnish, Italian, and Slovene. Furthermore, we run experiments with a relatively simple model, using simple hard parameter sharing, and multilingual input representations. In spite of this simplicity, promising results are obtained for these three languages. For instance, a model which has not seen a single target language PoS tag performs almost equally to a model trained on target language PoS tagging only.
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The work in this thesis has been carried out under the auspices of the Center for Language
and Cognition Groningen (CLCG) of the Faculty of Arts of the University of Groningen.
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One Model to Rule them all
Multitask and Multilingual Modelling
for Lexical Analysis
ter verkrijging van de graad van doctor aan de
op gezag van de
rector magnificus prof. dr. E. Sterken
en volgens besluit van het College voor Promoties.
De openbare verdediging zal plaatsvinden op
donderdag 7 december 2017 om 14.30 uur
geboren op 21 maart 1990
te Oslo, Noorwegen
Prof. dr. ing. J. Bos
Dr. B. Plank
Prof. dr. A. Søgaard
Prof. dr. J. Tiedemann
Prof. dr. L. R. B. Schomaker
This has been a bumpy ride, to say the least, and having reached the end of this four-year journey, I owe a debt of gratitude to all of my friends, family, and colleagues. Your support and guidance has certainly helped smooth out most of the ups and downs I’ve experienced.
First of all, I would like to thank my PhD supervisors. Johan, the freedom you allowed me during the past four years has been one of the things I’ve appreciated the most in the whole experience. This meant that I could pursue the track of research I felt was the most interesting, without which writing a whole book would have been much more arduous – thank you! Barbara, thank you for agreeing to join as co-supervisor so late in my project, and for putting in so much time during the last couple of months of my PhD. The thesis would likely have looked quite different if you hadn’t started in Groningen when you did. I owe you a huge thanks, especially for the final weeks – reading and commenting on the whole thesis in less than 24 hours during your vacation. Just, wow!
Next, I would like to thank Anders Søgaard, Jörg Tiedemann, and Lambert Schomaker for agreeing to form my thesis assessment committee. I feel honoured that you took the time to read this thesis, and that you deemed it scientifically sound. I also want to thank everyone who I have collaborated with throughout these years, both in Groningen and in Stockholm. Thanks Calle for agreeing to work with a sign language novice such as myself. Raf, it was an enlightening experience to work with you and see the world of ‘real’ humanities research. Robert, we should definitely continue with our one-week shared task submissions (with various degrees of success).
Most of the last few years were spent at the computational linguistics group in Groningen. I would especially like to thank all of my fellow PhD students throughout the years. Thanks Kilian, Noortje, Valerio, and Harm for welcoming me with open arms when I joined the group. Special thanks to Kilian for being so helpful with answering all of my billions and billions of questions involved in finishing this thesis. Also, a special thanks to both Noortje and Harm for the times we shared when I had just moved here (especially that first New Year’s eve!). Hessel, thanks for all the help with administrative matters while I was abroad, especially for sending a gazillion of travel declarations for me. Rik and Anna, it was great getting to know you both better during the last few months – hopefully you find the bookmark to be sufficiently sloth-y. Dieke and Rob, thanks for being such great laid back drinking buddies and travel companions. To all of you, and Pauline – I hope we will continue the tradition of going all out whenever I come to visit Groningen! A big thanks to the rest of the computational linguistics group, especially Gertjan, Malvina, Gosse, John, Leonie, and Martijn. Also thanks to all other PhD students who started with me: Luis, Simon, Raf, Ruben, Aynur, Jonne, and everyone else whose name I’ve failed to mention. A special thanks to Ben and Kaja - I hope we keep up our board-game centred visits to one another, no matter where we happen to pursue our careers.
I spent most of my final year in Stockholm, and it was great being in that relaxed atmosphere during one of the more intense periods of the past few years. Most of all, I am sincerely grateful to Calle, to Johan (and Klara, Iris, and Vive), and to Bruno. Your support is truly invaluable, and by my lights, there is not much more to say than ¡dank¿:(since a pal’s always needed). I’d also like to thank Johan and Calle especially for agreeing to observing weird Dutch traditions by being my paranymphs. Josefina, Elísabet, and David, thank you all for being there for me during the past year. Thanks to the computational linguistics group for hosting me during this period, especially Mats, Robert, Kina, and Gintarė. Finally, thanks to everyone else at the Department of Linguistics at Stockholm University.
Having moved to Copenhagen this autumn has been an extremely pleasant experience. I would like to thank the entire CoAStal NLP group for simply being the coolest research group there is. Especially, I’d like to thank Isabelle for making the whole process of moving to Denmark so easy. Thanks to Anders, Maria, Mareike, Joachim, Dirk, and Ana for being so welcoming. I’d also like to thank everyone else at the image section at DIKU, especially the running buddies at the department, and most especially Kristoffer and Niels.
Finally, I would like to thank my family. This bumpy ride would have been challenging to get through without their support through everything. Kiitos, mamma! Takk/tack Aksel, Paulina, Julian, och Lucas! Takk Olav, og takk Amanda!
Let’s see where the journey goes next!
Copenhagen, November 2017
- \thechapter Introduction
\thechapter An Introduction to Neural Networks
- 3 Introduction
- 4 Representation of NNs, terminology, and notation
- 5 Feed-forward Neural Networks
- 6 Recurrent Neural Networks
- 7 Convolutional Neural Networks
- 8 Residual Networks
- 9 Neural Networks and the Human Brain
- 10 Summary
\thechapter Multitask Learning and Multilingual Learning
- 11 Multitask Learning
- 12 Multilingual Learning
- 13 Outlook
- \thechapter An Introduction to Neural Networks
II Multitask Learning
\thechapter Multitask Semantic Tagging
- 14 Introduction
- 15 Semantic Tagging
- 16 Method
- 17 Evaluation
- 18 Discussion
- 19 Conclusions
\thechapter Information-theoretic Perspectives on Multitask Learning
- 20 Introduction
- 21 Information-theoretic Measures
- 22 Data
- 23 Method
- 24 Results and Analysis
- 25 Conclusions
- \thechapter Multitask Semantic Tagging
III Multilingual Learning
\thechapter Multilingual Semantic Textual Similarity
- 26 Introduction
- 27 Cross-lingual Semantic Textual Similarity
- 28 Method
- 29 Experiments and Results
- 30 Conclusions
\thechapter Comparing Multilinguality and Monolinguality
- 31 Introduction
- 32 Semantic Tagging
- 33 Tagging Tasks in the Universal Dependencies
- 34 Morphological Inflection
- 35 Estimating Language Similarities
- 36 Conclusions
- \thechapter Multilingual Semantic Textual Similarity
- IV Combining Multitask and Multilingual Learning
- V Conclusions
- \thechapter Summary
- \thechapter Samenvatting
Chapter \thechapter Introduction
When learning a new skill, you take advantage of your preexisting skills and knowledge. For instance, if you are a skilled violinist, you will likely have an easier time learning to play cello. Similarly, when learning a new language you take advantage of the languages you already speak. For instance, if your native language is Norwegian and you decide to learn Dutch, the lexical overlap between these two languages will likely benefit your rate of language acquisition. This thesis deals with the intersection of learning multiple tasks and learning multiple languages in the context of Natural Language Processing (NLP), which can be defined as the study of computational processing of human language. Although these two types of learning may seem different on the surface, we will see that they share many similarities.
Traditionally, NLP practitioners have looked at solving a single problem for a single task at a time. For instance, considerable time and effort might be put into engineering a system for part-of-speech (PoS) tagging for English. However, although the focus has been on considering a single task at a time, fact is that many NLP tasks are highly related. For instance, different lexical tag sets will likely exhibit high correlations with each other. As an example, consider the following sentence annotated with Universal Dependencies (UD) PoS tags (Nivre et al., 2016a), and semantic tags (Bjerva et al., 2016b).111PMB 01/3421. Original source: Tatoeba. UD tags obtained using UD-Pipe (Straka et al., 2016)222The semantic tag set consists of 72 tags, and is developed for multilingual semantic parsing. The tag set is described further in Chapter \thechapter.
We must draw attention to the distribution of this form in those dialects . PRON AUX VERB NOUN ADP DET NOUN ADP DET NOUN ADP DET NOUN PUNCT \gln\glend
We must draw attention to the distribution of this form in those dialects . PRO NEC EXS CON REL DEF CON AND PRX CON REL DST CON NIL \gln\glend
While these tag sets are certainly different, the distinctions they make compared to one another in this example are few, as there are only two apparent systematic differences. Firstly, the semantic tags offer a difference between definite (DEF), proximal (PRX), and distal determiners (DST), whereas UD lumps these together as DET (highlighted in green). Secondly, the semantic tags also differentiate between relations (REL) and conjunctions (AND), which are both represented by the ADP PoS tag, highlighted in blue. Hence, although these tasks are undoubtedly different, there are considerable correlations between the two, as the rest of the tags exhibit a one-to-one mapping in this example. This raises the question of how this fact can be exploited, as it seems like a colossal waste to not take advantage of such inter-task correlations. In this thesis I approach this by exploring multitask learning (MTL, Caruana, 1993; 1997), which has been beneficial for many NLP tasks. In spite of such successes, however, it is not clear when or why MTL is beneficial.
Similarly to how different tag sets correlate with each other, languages also share many commonalities with one another. These resemblances can occur on various levels, with languages sharing, for instance, syntactic, morphological, or lexical features. Such similarities can have many different causes, such as common language ancestry, loan words, or being a result of universals and constraints in the properties of natural language itself (see, e.g., Chomsky,2005, and Hauser et al., 2002). Consider, for instance, the following German translation of the previous English example, annotated with semantic tags.333PMB 01/3421. Original source: Tatoeba.
Wir müssen die Verbreitung dieser Form in diesen Dialekten beachten . PRO NEC DEF CON PRX CON REL PRX CON EXS NIL \glt\glend
Comparing the English and German annotations, there is a high overlap between the semantic tags used, and a high lexical overlap. As in the case of related NLP tasks, this begs the question of how multilinguality can be exploited, as it seems like an equally colossal waste to not consider using, e.g., Norwegian PoS data when training a Swedish PoS tagger. There are several approaches to exploiting multilingual data, such as annotation projection and model transfer, as detailed in Chapter \thechapter. The approach in this thesis is a type of model transfer, in which such inter-language relations are exploited by exploring multilingual word representations, which have also been beneficial for many NLP tasks. As with MTL, in spite of the fact that such approaches have been successful for many NLP tasks, it is not clear in which cases it is an advantage to go multilingual.
Given the large amount of data available for many languages in different annotations, it is tempting to investigate possibilities of combining the paradigms of multitask learning and multilingual learning in order to take full advantage of this data. Hence, as the title of the thesis suggests, the final effort in this thesis is to arrive at One Model to rule them all.
This thesis approaches these two related aspects of NLP by experimenting with deep neural networks, which represent a family of learning architectures which are exceptionally well suited for the aforementioned purposes (described in Chapter \thechapter). For one, it is fairly straightforward to implement the sharing of parameters between tasks, thus enabling multitask learning (discussed in Chapter \thechapter). Additionally, providing such an architecture with multilingual input representations is also straightforward (discussed in Chapter \thechapter). Experiments in this thesis are run on a large collection of tasks, both semantic and morphosyntactic in nature, and a total of 60 languages are considered, depending on the task at hand.
1 Chapter guide
The thesis is divided into five parts, totalling 9 chapters, aiming to provide answers to the following general research questions (RQs):
To what extent can a semantic tagging task be informative for other NLP tasks?
How can multitask learning effectivity in NLP be quantified?
To what extent can multilingual word representations be used to enable zero-shot learning in semantic textual similarity?
In which way can language similarities be quantified, and what correlations can we find between multilingual model performance and language similarities?
Can a multitask and multilingual approach be combined to generalise across languages and tasks simultaneously?
Part I – Background
The goal of Part I is to provide the reader with sufficient background knowledge to understand the material in this thesis. Chapter \thechapter contains a crash-course in neural networks, introducing the main concepts and architectures used in NLP. Chapter \thechapter provides an introduction to multitask learning and multilingual learning, which are the two central topics of this work.
Part II – Multitask Learning
In Part II, the goal is to investigate multitask learning (MTL), in particular by looking at the effects of this paradigm in NLP sequence prediction tasks. In Chapter \thechapter we present a semantic tag set tailored for multilingual semantic parsing. We attempt to use this tag set as an auxiliary task for PoS tagging, observing what effects this yields, answering RQ 1. Chapter \thechapter then delves deeper into MTL, attempting to find when MTL is effective, and how this effectiveness can be predicted by using information-theoretic measures (RQ 1).
Part III – Multilingual Learning
Having looked at similarities between tasks, we turn to similarities between languages in Part III. In Chapter \thechapter, we attempt to make a language-agnostic solution for semantic textual similarity, by exploiting multilingual word representations, thus answering RQ 1. Having seen the results of combining related languages in this task, we try to quantify these effects in Chapter \thechapter, aiming to answer RQ 1.
Part IV – Combining Multitask and Multilingual Learning
In Part IV we want to combine the paradigms of multitask learning and multilingual learning in order to make One Model to rule them all. Chapter \thechapter presents a pilot study taking a step in this direction, looking at predicting labels for an unseen task–language combination while exploiting other task–language combinations.
Part V – Conclusions
Finally, Chapter \thechapter contains an overview of the conclusions from this thesis. In addition to this, we provide an outlook for future work in this direction, in particular focussing on the combined multitask–multilingual paradigm.
This thesis is based on the following publications:
Some parts of the thesis may also refer to the following peer-reviewed publications completed in the course of the PhD:
Part I Background
to Neural Networks
The term deep learning is used to refer to a family of learning models, which represent some of the most powerful learning models available today. The power of this type of model lies in part in its intrinsic hierarchical processing of input features, which allows for learning representations at multiple levels of abstraction (LeCun et al., 2015). This type of model is commonly referred to by several umbrella terms, such as deep learning, and (deep) neural networks.444While some make a distinction between deep and non-deep neural networks (NNs) depending on the amount of layers used, there is no real consensus on where the line between these models should be. For the sake of consistency, I attempt to refer to this family of models as NNs, or some specification thereof, as consistently as possible. In this chapter, I aim to introduce the basic concepts of NNs, at a level sufficient to understand the work in this thesis. The following sections are meant to cover the most basic workings in an intuitive, and theoretically supported, manner. In addition to this background, I give an overview of the scenarios in which different recurrent NN architectures might be suitable in NLP (Section 6.2).
Neural networks have a long history, and have been popular in three main waves.555Only a very brief overview of the history is given here. For more details, the reader is referred to, e.g., Wang et al., 2017, or Goodfellow et al., 2016. In the first wave, roughly between the , they appeared under the moniker of cybernetics (e.g., Wiener, 1948), inspired by the Hebbian learning rule (Hebb, 1949). In this wave, the perceptron was first outlined (Rosenblatt, 1957), which is still relatively popular today (see Section 5). Next, in the and , connectionism was on the rise. In this wave, the algorithm for backwards propagation of errors (Rumelhart et al., 1985) was described, which is at the core of how neural networks are trained (see Section 5.3). After an AI winter lasting roughly from to , we finally arrive at the current wave (or tsunami), in which the term deep learning is favoured. This wave was initiated by works on deep belief networks (Hinton et al., 2006), and has been the subject of much attention after successes in, e.g., reducing error rates in some tasks by more than 50% (LeCun et al., 2015). The recent advances made in the current wave further include breakthroughs in both recognition (He et al., 2016) and generation (Goodfellow et al., 2014) of images, in NLP tasks such as machine translation (Bahdanau et al., 2015; Wu et al., 2016) and parsing (Chen and Manning, 2014), as well as in the strategic board game Go (Silver et al., 2016), and the first-person shooter Doom (Lample and Chaplot, 2017).
4 Representation of NNs, terminology, and notation
Before embarking upon this journey and exploring the wondrous world of NNs, it is necessary to equip ourselves with some common ground in terms of terminology, notation, and how NNs are generally represented in this thesis. Figure 1 contains a NN, which we will go through in detail.
First, note that the network is divided into three vertical slices. Each such slice represents a layer, marked by a light grey field. Each layer contains one or more white circles, each representing a unit, or neuron.666In this thesis, the term unit is preferred. While this is conventional in much of NLP, it is also debatable whether borrowing terminology for neural networks from neuroscience is motivated at all (this is discussed further in Section 9). In this network, each unit has a connection to every unit in the following layer. These connections are represented by arrows, which denote some weighting of the output of the unit at the start of the arrow, for the input of the unit at the end of the arrow. Each layer can be described mathematically as a vector of activations. In the case of the first layer (the input layer), these activations are equal to the input (i.e. ). The final layer encodes the output of the network, which is denoted by . Each layer up until the final layer also contains a special unit, marked by , which is called the bias unit.777Although this can be discussed at length, suffice it to say that including bias units facilitates learning. The collection of all arrows between two layers, can be described mathematically as a matrix of weights (e.g., ).888We will cover ways in which to learn these weights later in this chapter (Section 5.3). The application of the weight matrix to the input of the network can be described in linear algebraic notation as
where is the vector (i.e. a series of numbers) resulting from this linear transformation. The -vectors can be referred to as pre-activation vectors. Each hidden layer thus first encodes the sum of the multiplications of each of the activations in the previous layer by some weight. For instance, if we set to be matrix of ones, then the pre-activation value of the first unit in the first hidden layer . The final piece of the puzzle is to calculate the output of each unit in the layer, by applying an activation function to the pre-activation vector,
where is some non-linear activation function.999Traditionally the activation function () used is some sigmoidal function, such as the logistic function. However, many functions are suitable, given that they satisfy certain properties (see Section 5.2). Essentially, this is all that a basic FFNN is – a series of matrix-vector multiplications, with non-linearities applied to it. Now, how can this be used to solve problems, and how does the network learn to do this? The answers to these questions will be made clear in the course of the following few pages.
Before we continue, a brief note on the notation used in this thesis. Scalars are represented with lower case letters (), vectors are represented with lower case letters with arrows (), and matrices are represented with blackboard upper case letters (). Subscripts are used to denote the layer number, and where necessary, a superscript is used to denote indexation, to indicate the unit number in the case of deep networks. For instance, indicates the activation of unit in layer , and indicates the weight matrix for layer . Activation functions (Section 5.2) are denoted with , occasionally subscripted with the actual function used ().
5 Feed-forward Neural Networks
A Feed-forward Neural Network (FFNN), also known as a multilayer perceptron, is perhaps the most basic variant of neural networks, and is the kind depicted in the previous figure. As mentioned, a neural network can be seen as a collection of non-linear functions applied to a collection of matrices and vectors, thus mapping from one domain (e.g., words) to another (e.g., PoS tags). Let us consider a concrete example, in which contains information about the current weather, and denotes human-annotated labels denoting whether or not the weather is considered good. In this case, contains several variables, each representing a certain type of weather (e.g. = calm weather, and = sunny weather).101010Note that we begin numbering of features with , as the index is reserved for the bias terms. Table 1 represents the weather judgements of this example, where indicates good weather, and indicates not-so-good weather.
|Calm ()||Sunny ()||Label ()|
The table shows the judgements of someone who considers weather to be good (i.e. ) only when it is both calm and sunny (i.e. the logical and function). Let us now consider our second neural network, which can solve the problem of determining whether the weather is good, based on this person’s judgements, in Figure 2.
|Calm ()||Sunny ()||Label ()|
Applying the calculations detailed in the previous section to this network yields the results shown in Table 2. If only one of is active, the activation is approximately , while the activation is if both and are active. We get these values, by applying the perhaps most commonly used activation function to . This is the logistic function, defined as
where is Euler’s number. Plotting this function, yields the graph in Figure 3. Hence, the value of approaches 0 when , and approaches 1 when .
The simple neural network considered here, is what is also referred to as a perceptron, although, technically, a perceptron uses the step function as its activation function – in other words, if where is some threshold, then , and if , then (Rosenblatt, 1957). This is a very simple and useful architecture, but there are many problems which can not be easily solved by a perceptron, such as those in which the decision boundary to be learned is non-linear. Take, for instance, the problem given in Table 3.
|Snowy ()||Sunny ()||Label ()|
This table shows the labels provided by some annotator who considers weather to be good (i.e. ) if it is either snowy or sunny – but not both (i.e. the logical xor function). As mentioned, a single unit (i.e. a perceptron) is not able to learn this decision boundary (Minsky and Papert, 1988).111111This is frequently cited as a potential catalyst for the the AI winter, in which funding and interest in artificial intelligence was at a low. Nonetheless, it was known at the time that the xor problem could be solved by a neural network with more hidden units (Rumelhart et al., 1985). Let us now have a look at a neural network which encodes this function. This is depicted in Figure 4. For the sake of clarity, all weights between and are set to , but only one of these weights is shown.
Applying the calculations detailed in the previous section to this network yields the results shown in Table 4. If both or none of are active, then the network will output , whereas if one and only one of are active, the network will output . Exactly what we want!
|Calm ()||Sunny ()|
The last two examples have shown how neural networks can encode certain simple functions. It turns out that neural networks can do much more than this, and are in fact universal function approximators (Cybenko, 1989; Hornik et al., 1989). What this means, is that no matter the function, there is guaranteed to be a neural network with a single layer and a finite number of hidden units, such that for each potential input , (a close approximation of) the value is output from the network.
The class of networks discussed here is useful for many tasks in NLP, and can be used as a simple replacement for other classifiers. Furthermore, they can be expanded by adding more units to each layer, or by adding more layers. This allows such networks to learn to solve interesting NLP problems, like language modelling (Bengio et al., 2003; Vaswani et al., 2013), and sentiment classification (Iyyer et al., 2015).
Before going into other NN architectures, we will first consider some of the inner workings of NNs. This includes how we represent our input, how weights are obtained, and finally some limitations which motivate the use of more complex architectures than FFNNs.
5.1 Feature representations
In many NLP problems, we are interested in mapping from some textual language representation () to some label (). This textual representation can take many forms, both depending on the problem at hand, and on the choices made when approaching the problem. As an example, say we are interested in doing sentiment analysis, i.e., given a text (), predict whether the text is positive or negative in sentiment (). The perhaps simplest way of representing the text is to count the occurrences of each word in the text. The intuition behind this is that if a text contains many negative words (horrible, bad, appalling), it is more likely to be negative in sentiment than if it contains many positive words (wonderful, good, exquisite). Since these features (i.e. counts of each word) need to be passed to an FFNN, they need to be represented as a single fixed-length vector . What one might then do, is to assign an index to each unique word, and assign the count of each word to that index in the vector. This can be referred to as a bag-of-words model.
Although this type of feature representation is sufficient for some problems, and is traditionally used extensively, more recent developments include using other types of representations based on distributional semantics. This is covered in more detail in the next chapter, in Section 12.5.
5.2 Activation Functions
As stated in Section 5, each hidden unit applies an activation function to the sum of its weighted inputs. While many functions might be used, an activation function should have certain properties. One such property is that the function needs to be non-linear. It is for this kind of function that it has been proven that a two-layer neural network is a universal function approximator (Cybenko, 1989). Additionally, the function should be monotonic, as the error surface associated with a single-layer model will then be convex (Wu, 2009).121212A monotonic function is either non-increasing or non-decreasing in its entirety. There are several other important properties, which are not covered here. Some of the more commonly used activation functions are listed in Table 5.
|Logistic (aka. sigmoid)|
|Hyperbolic Tangent (tanh)|
|Rectified Linear Unit (ReLU)|
The traditionally popular logistic function was already described in Figure 3. We will now consider some other commonly used activation functions. Activation functions turn out to be one of the areas in which biological inspiration has been directly applicable to the development of neural networks. The Rectified Linear Unit (ReLU) is in fact remarkably similar to what happens in a biological neuron (Hahnloser et al., 2000; Hahnloser and Seung, 2001). That is to say, when the input is below a certain threshold, the neuron does not fire, and when the input is above this threshold, the neuron fires with a current proportional to its input. ReLUs have been found to make it substantially easier to train deep networks (Nair and Hinton, 2010), and are currently very widely used. One disadvantage of ReLUs is that they can wind up in a state in which they are inactive for almost all inputs, meaning that no gradients flow backward through the unit. This, in turn, means that the unit is perpetually stuck in an inactive state, which at a large scale can decrease the network’s overall capacity. This is mitigated by using leaky ReLUs, for which even input leads to some activity, allowing for error propagation given any input value.
The softmax function is generally only used at the final layer in classification problems, as it yields a probability distribution based on its input.
Learning in an FFNN happens in two phases. First, in the forward propagation pass, the network sends a given input through the network, and produces some output. Then, the error of this output is calculated, as compared to some target label, and this error is sent back through the network, updating the weights of the network so as to make a more accurate prediction given the input in the next forward pass.131313This is referred to as backward propagation of errors, and is covered later in this section.
We have already seen the largest part of the forward pass, as in the examples with the and and xor functions in Section 5. The only remaining part of the forward pass, is how the error of the network is calculated – for this, a loss function is necessary.
The loss functions used in NNs, generally fall into two classes – those used for classification problems (i.e. when attempting to predict some discrete class label, out of a finite set of labels), and those used for regression problems (i.e. when attempting to predict some continuous score). Classification is one of the most common cases in NLP (e.g. in POS tagging, NER, language identification, and so on). In such cases, the activation function of the final layer is the softmax function, which allows for interpreting the layer’s activations as a probability distribution over the labels under consideration. Most often, the cross-entropy between this predicted probability distribution and the target probability distribution is used to calculate the error, or loss , such that
where denotes the loss function, is the target probability distribution over labels, is the model’s predicted model distribution given an input . A high error thus indicates that the predicted probability distribution is not consistent with the target probability distribution, and therefore changes should be made accordingly in the backward propagation pass.
Another loss function, common in regression, is the squared error function, defined as
where is the predicted label, and is the true label. This function is commonly used in regression, and is especially handy for explaining backpropagation, as in the next section.
Backward propagation of errors, or backprop (Rumelhart et al., 1985; LeCun et al., 1998b), is an algorithm for calculating the gradient of the loss function, for each weight. The gradient can, in turn, be used to update the weights by using an optimisation algorithm, such as gradient descent (discussed further in Section 5.3). Intuitively seen, gradient-based methods operate by viewing the errors as a geometric area, and use the slope of the area in which they are (i.e., the gradient) in order to shift weights towards obtaining an error in a minimum of this area, as in Figure 5.
Backprop relies on the fact that the partial derivative of the error of a certain weight , with respect to the loss function, can be easily calculated if we know the partial derivative of the outputs in the layer following that weight. It turns out that this is, indeed, the case, as the derivative of the output layer is quite easily obtained. The output error of a given unit, , is calculated as
where is the activation of the current unit, is the target output, is the collection of all units receiving input from the current unit, and is the weight from the current unit to unit . Let us consider a concrete example, and go through the forward pass, calculation of the error, and the backward pass. The network in Figure 6 shows a neural network with its weights.
Assuming that the activation function used is the logistic function, the following calculations hold:
Assuming that the target output is , we can now calculate the error. Applying equation 6, we can obtain the error of the output, namely
The errors of the two hidden units can also be calculated, yielding
We now need to update the weights used, via gradient descent. This can be done by shifting the weights with some constant with respect to the error obtained,
where is the amount with which to change (i.e., the weight between the firing and receiving unit), is some learning rate, is the activation of the firing unit, and and is the error of the receiving unit. Hence, if we set , the changes of the weights are calculated as
Using the new weights yields the following activations in the next forward pass, given the same input:
and the output error
which is smaller than the previous error where . This process is repeated with other training examples, until some criterion is reached, such as a sufficiently low average loss.
Backpropagation, as described in the previous section, can provide us with the derivatives of the error surface. This can be used in a variety of ways to update the weights. What we just saw, in Equation 11, is known as gradient descent. One of the most commonly used optimisation methods is Stochastic Gradient Descent (SGD). In SGD, a minibatch of samples is drawn from the training set, the gradient is calculated based on this batch, and the weights are then updated accordingly (Bottou, 1998). Other algorithms, such as AdaGrad (Duchi et al., 2011) and RMSProp (Hinton, 2012), learn and adapt the learning rate () for each weight. Modifying the learning rate in this manner can both increase the rate at which the error decreases, and lead to lower overall errors. A recent and increasingly popular optimisation method is Adam, which is similar to RMSProp and yields better results on a many problems (Kingma and Ba, 2014). The choice of optimisation method is not all that straightforward, and no real consensus exists for how this should be done (Schaul et al., 2014). Hence, commonly, trial-and-error is applied in order to make this choice, by experimentally investigating performance on a development set.
Finding the global minimum
The goal of an optimisation algorithm is to find the global minimum, as shown in Figure 5. What so-called gradient-based optimisation algorithms do, is to calculate the derivative with respect to this error surface, and shift the weights so as to move towards the closest of all local minima. Such local minima can, however, be the source of a host of problems, if the loss is high compared to the global minimum. This is a frequently occurring issue, and it is possible to construct small neural networks in which this scenario appears (Sontag and Sussmann, 1989; Brady et al., 1989; Gori and Tesi, 1992). It turns out, however, that practically speaking, when considering larger neural networks, it is not particularly important to find the global minimum. This has to do with the fact that, in the case of supervised learning with deep neural networks, most local minima appear to have a low loss function value, roughly equivalent to that of the true global minimum (Saxe et al., 2013; Dauphin et al., 2014; Goodfellow et al., 2015; Choromanska et al., 2015).
There are several methods for initialising the weights in a neural network. Naively, one might think to set the all weight matrices , however due to how backpropagation works, this will result in all hidden units representing the same function, and receiving the exact same weight updates. Therefore, some random process is required. Common methods include those introduced by Glorot and Bengio (2010), and Saxe et al. (2013). When employing the ReLU activation function, He et al. (2015b) show that weights should be initialised based on a Gaussian distribution with standard deviation , where is the input dimensionality. In the case of recurrent neural networks, which are covered in Section 6, particular care needs to be taken, and weight initialisation is often done using orthogonal matrices (cf. Goodfellow et al.[p.404], 2016).
Regularisation in Neural Networks
One of the most common problems when training an ML system in general, is that of overfitting – and neural networks are no exception. Overfitting occurs when the network does not generalise to data outside of the training set, while having a low loss on the training set itself. Generalisation is one of the most important parts of learning, as learning without generalisation is simply the memorisation of a training set. A model which has only memorised the training set is of little practical value, as it will most likely fail miserably on unseen examples. In order to avoid overfitting, regularisation techniques are typically employed. The probably most common regularisation technique used today, is dropout (Srivastava et al., 2014). In dropout, every activation has a probability of not being included in the forward and backward passes, during training. This procedure leads to significantly lower generalisation error, as the network needs to be more robust, and less reliant on specific units. In the case of recurrent neural networks, which are covered next, specific variants of dropout exist. such as recurrent dropout (Semeniuta et al., 2016), or variational dropout (Gal and Ghahramani, 2016) in which the same dropout mask is used for each time step. Another commonly used manner of regularisation is weight decay, in which the magnitudes of weights are decreased according to some criterion (Krogh and Hertz, 1992).
6 Recurrent Neural Networks
Although FFNNs are suitable for many problems, they do not take the structure of the input into account. Although it is possible to attempt to enforce this in such a network, this has several disadvantages, such as the fact that the amount of parameters which need to be tuned can become prohibitively large. Luckily, there are architectures for dealing with structure, as this is not entirely unimportant when considering natural language. Two such approaches are covered in the following sections.
Recurrent Neural Networks (RNNs) are an extension of feed-forward neural networks, which are designed for sequential data (Elman, 1990). They can be thought of as a sequence of copies of the same FFNN, each with a connection to the following time step in the sequence, sharing parameters between time steps. RNNs take a sequence of arbitrary length as input (), and return another sequence (). Each in the input sequence is a vector representation of element in the sequence. Each in the output sequence can take advantage of information in the sequence up to step in the input sequence. This is illustrated in Figure 7. Each layer is shown as containing only one unit, which is here meant as an abstraction depicting the entire internal representation of the RNN. The left side of the figure depicts an FFNN with a loop, whereas the right side shows the unrolled version of the network. The output of the hidden layer is passed as an input to the hidden layer in the next time step.
An RNN is essentially a group of FFNNs with connections to one another. This connection is a sort of loop, going from the hidden layer of the network at time to the hidden layer at . In other words, is calculated as
where is the matrix of weights for the current time step’s input (), is a weight matrix for the connections from the previous time step, is a state vector representing the history of the sequence, is the index of the current time step, is the matrix of weights for the output, and the rest is defined as for FFNNs. This is what is also referred to as an Elman net, or a Simple RNN (Elman, 1990). The advantage of having access to , is that the network can take advantage of preceding information when outputting . For instance, in the case of POS tagging, if the current input is fly, and the state vector shows that the previous word was to, we most likely want to output the tag verb. Hence, in this way, the prediction at each time step is conditioned on the inputs in the entire preceding sequence. There are also variants of this, in which the net’s outputs are used to calculate the state vector, as in the case of Jordan nets (Jordan, 1997), which is defined such that
Although RNNs, in theory, can learn long dependencies (i.e. that an output at a certain time step is dependant on the state at a time step far back in the history), and can handle input sequences of arbitrary length, they are in practice heavily biased to the most recent items in the given sequence, and thus difficult to train on long sequences with long dependencies (Bengio et al., 1994). For instance, in the case of language modelling, given a sentence such as My mother is from Finland, so I speak fluent , it is quite likely that the omitted word should be Finnish. However, as the distance between such dependencies grows, it becomes increasingly difficult for an RNN to make use of such contextual information. In general, this is because deep neural networks suffer from having unstable gradients, as the gradients calculated by backprop (Section 5.3) are dependant on the output of the network, which can be quite far away from the first layers in the network. One problem with this is that this can lead to vanishing gradients (i.e. the gradient becomes very small). This happens since the gradient in early layers of the network are the result of a large number of multiplication operators on numbers . One might consider the fact that, since these multiplications involve the weights in the network, we might just set the weights to be really large. Although this might seem like a good idea, this will likely lead to the converse of the issue one is trying to avoid, namely that of exploding gradients. Since most common optimisation methods are gradient-based, this is problematic (see Section 5.3 for optimisation details).
6.1 Long Short-Term Memory
Previous work has attempted to solve this problem by adapting the optimisation method used (Bengio et al., 2013; Pascanu et al., 2013; Sutskever et al., 2014), however the more successful approach has been to modify the neural network architecture itself. Because of such efforts, there are several types of RNNs specifically designed to cope with this issue, essentially by enforcing a type of protection of the memory of the history of the input sequence, storing and maintaining important features, while neglecting and forgetting unimportant features. One such method, namely Long Short-Term Memory (LSTM), was described in Hochreiter and Schmidhuber (1997), and saw an explosion in popularity around 2014, following several influential papers (e.g. Sundermeyer et al. (2012); Sutskever et al. (2014); Dyer et al. (2015)). An LSTM is an extension of RNNs, with memory cells, engineered to cope with the issue of unstable gradients, and have been shown to be able to capture long-range dependencies (Hochreiter and Schmidhuber, 1997; Cho, 2015). For an overview of the many variations of LSTMs which appear in the literature, see Greff et al. (2016).
Whereas an RNN only has a single internal layer (Figure 9), typically with a tanh (hyperbolic tangent) activation, an LSTM is somewhat more complicated (Figure 9). An LSTM contains gates, denoted in the figure by the layers, which are used to modify the extent to which old information is remembered or forgotten. Part of the explanation for LSTMs involves the observation that they, on the surface, can be seen as a combination of Elman nets and Jordan nets, in that both the cell state and the hypothesis are passed between states. In detail, an LSTM is implemented as follows
where represents the output of the forget gate, represents the output of the input gate, represents the output of the output gate, represents the cell state, represents the output vector, and represent the weight matrices, represents the current input, and represents bias units. Each of these parts are covered in detail in the following sections.
The cell state, , is the line coded in blue in Figure 9. It is similar to the state vector, , in a simple RNN, but its content is maintained and protected by three gates. The forget gate’s output determines to which extent each feature in the cell state should be kept. This is done by observing the current input , and the previous time step’s output .
For instance, say we have a POS tagger which at time observes a word which could be either a noun or a verb (e.g. fly). If the previous word was to, this would be useful to keep in mind in order to better predict the next tag. Following this time step, however, we might want to forget about this word, when predicting the next tag.
Adding information to the cell state happens in two steps. We first decide on which values in the cell state to update again observing and , again deciding for each dimension the extent to which we will add information. This is denoted by the input gate . The vector which is added to the cell state, is calculated by passing and through a non-linearity, marked by tanh in the figure. In the POS tagging example, we want to add the information regarding the preceding determiner. These two vectors are then summed, resulting in our new cell state .
Finally, we need to output a value from the current time step. This output is based on the cell state, , which is first run through a non-linearity (usually tanh), and filtered again by , which also observes and , when deciding on which dimensions to keep, and to what extent.
Gated Recurrent Units
In addition to the many LSTM variants (Greff et al., 2016), Gated Recurrent Units (GRUs) represent a different variant of gated RNNs which was independently developed to LSTMs and similar in both purpose and implementation (Cho et al., 2014). The main difference between LSTMs and GRUs is the fact that GRUs do not have separate memory cells, and only include two gates – an update gate, and a reset gate (Chung et al., 2014). This in turn means that GRUs are computationally somewhat more efficient than LSTMs. In practice, both LSTMs and GRUs have been found to yield comparable results (Chung et al., 2014; Jozefowicz et al., 2015). On a general level, the performance of various gated RNN architectures is, at least in the case of large amounts of data, closely tied to the number of parameters (Collins et al., 2017; Melis et al., 2017).
Many properties of language depend on both preceding and proceeding contexts, so it is useful to have knowledge of both of these contexts simultaneously. This can be done by using a bi-directional RNN variant, which makes both forward and backward passes over sequences, allowing it to use both contexts simultaneously for the task at hand (Schuster and Paliwal, 1997; Graves and Schmidhuber, 2005; Goldberg, 2015). Bi-directional GRUs and LSTMs have been shown to yield high performance on several NLP tasks, such as POS tagging, named entity tagging, and chunking (Wang et al., 2015; Yang et al., 2016; Plank et al., 2016).
6.2 Common use-cases of RNNs in NLP
In NLP, there are four general scenarios for producing some sort of analysis for a given text. Consider that we have the following sentence as input:
I’m not fussy.141414PMB 76/2032, Original source: Tatoeba
We might want to analyse this unit as a whole, for instance in order to judge that the text is in English, and not in some other language, or to determine the native language of the person writing it, or the sentiment of the text itself. This can be referred to as a many-to-one scenario, since we have several smaller units (e.g. words or characters), which we want to translate into a single score or class, depending on the task at hand.
On the other hand, we might want to analyse the sentence word by word, by assigning, e.g., a part-of-speech (POS) tag or a semantic tag to each word in the sentence. This can be referred to as a one-to-one scenario, since every single unit in the text (e.g. each word token) has a direct correspondence to a single tag.151515The term ’one-to-one’ is also used for simple classification cases where there is no sentential context available. We see this as simply being a special case in which the sequence length . This is equivalent to the relation between FFNNs and RNNs, in which an FFNN can be seen as a special case of RNNs (or vice versa).
We might also want to carry out some task in which the sentence should be translated to some other form, for instance translating the sentence to German, or some other language. If the sentence was written in some non-standard form of English, we might want to produce a normalised version of the sentence, or in a different setting we might want to generate an inflected form of some word in the same language. This can be referred to as a many-to-many scenario, as there is no structural one-to-one correspondence between the input and the output .
A final logically possible case, is the one-to-many scenario. This is a highly uncommon scenario, as it is not generally the case that one tries to predict several things from an atomic unit. Although one could argue that some tasks fit this scenario, such as caption generation, this is not really a one-to-many scenario, as the image is not an atomic unit, but is read by the NN as a matrix of pixels.
A schematic overview of the three relevant scenarios is given in Figure 10. The versatility of these three scenarios is evident when observing the current NLP scene, in which common practise is to cast a problem to fit one of these scenarios, and to then throw a Bi-LSTM at the problem.
Many NLP tasks deal with going from several smaller units to a single prediction. This essentially means that these units need to be compressed into a single vector, onto which a softmax layer can be applied in order to arrive at a probability distribution over the classes at hand (e.g. a set of languages to identify). For this type of problem, a number of possibilities exist, such as
Averaging the vectors representing each unit in the sentence (i.e. average pooling);
Applying an RNN and using the final state output vector as a representation of the sentence (depicted in Figure 10);
Applying convolutions in order to arrive at a condensed representation.161616Convolutional Neural Networks are described in Section 7.
Approach 1) is the most simplistic of these, and has been successfully applied in previous work (e.g. Socher et al. (2013a); Zhang et al. (2015a)). The main advantage of this approach is indeed its simplicity, as calculating the mean of the vectorial representations of a sentence is both a very cheap operation, as well as an operation which allows for the application of a simple FFNN on top of this vector. With this approach, however, the structure inherent in the natural language signal is left unexploited.
Approaches 2) and 3) both offer more expressive power as compared to approach 1), as they both take advantage of the structure inherent in the input signal. This is not the case when summing the vectors, which is in a way analogous to a bag-of-words approach. Structure is naturally of paramount importance in natural language, so taking advantage of this is good. Although structure in natural language is generally hierarchical, even using the sequential structure is better than assuming no structure at all. There are, however, some recent architectures which do encode the hierarchical structure of language, such as tree LSTMs (Tai et al., 2015), and RNN-Grammars (Dyer et al., 2016).
These three approaches are meant to give an overview of some straight-forward manners of obtaining such representations. Other, more sophisticated approaches, include skip-thought vectors, in which sentence-level representations are learned with the objective of being able to predict surrounding sentences in a document (Kiros et al., 2015). A systematic overview of such methods is given by Hill et al. (2016), who conclude that the best suited approach depends on the intended application of such representations.
Another use case for this approach is when building hierarchical models, in the sense that one, e.g., may want to have word representations which are aware of what is going on on a sub-word level. For this, one might apply a many-to-one RNN, and use the final state output vector as a word vector (Ballesteros et al., 2015; Plank et al., 2016). Alternatively, one can use convolutions to arrive at this type of word vector, as in dos Santos and Zadrozny (2014).
The one-to-one case is perhaps one of the most common scenarios in NLP. This covers tagging task scenarios, as well as simple classification scenarios. Many NLP tagging tasks have seen relatively large improvements when applying variants of RNNs similarly to what is depicted in Figure 10. Recently, gated variants such as LSTMs and GRUs, often in a bi-directional incarnation are applied (Wang et al., 2015; Huang et al., 2015; Yang et al., 2016; Plank et al., 2016). Such RNNs are highly suited for this type of task, as it is highly informative for, e.g., POS tagging to know which words occur both before and after the word at hand. Such dependencies might also have quite large spans, which both LSTMs and GRUs are able to capture well. To contrast with older feature-based models, it would require a fair bit of feature engineering to decide on what types of spans to include in feature representations, lest one wishes to suffer from the sparsity of simply using -gram features with large values of .
This paradigm is also what is frequently referred to as an encoder-decoder architecture in the literature, or sequence-to-sequence learning problems (Bahdanau et al., 2015; Sutskever et al., 2014).
A frequent approach here, for instance in machine translation, is to apply an RNN from which one takes the final time step’s output to be a representation of the entire sentence, as represented in Figure 10, which may seem like a bold thing to do.171717You can’t cram the meaning of a whole sentence into a single vector!
–Ray Mooney, as communicated by Kyunghyun Cho in his NoDaLiDa 2017 keynote (https://play.gu.se/media/1_xt08m5je) It turns out that this is in fact often not sufficient, although one can obtain surprisingly good translations this way. However, results improve dramatically when going a step further by incorporating an attentional mechanisms. This is not focussed upon in this thesis, and will not be explained in full detail. Essentially, an attention mechanism can learn which parts of the source sentence to attend to, when producing the target sentence translation. For instance, such a mechanism might learn an implicit weighted word-alignment between the source and target sentences, thus facilitating translation.
Many NLP tasks can be solved with a many-to-many approach. Machine translation has already been mentioned, and has in no small degree been the driving force behind research in this direction. Apart from this, the approach has been applied to morphological inflection (Kann and Schütze, 2016; Cotterell et al., 2016; Östling and Bjerva, 2017; Cotterell et al., 2017), AMR parsing (Barzdins and Gosko, 2016; Konstas et al., 2017; van Noord and Bos, 2017b, a), language modelling (e.g. Vinyals et al., 2015), generation of Chinese poetry (Yi et al., 2016), historical text normalisation (Korchagina, 2017), and a whole host of other tasks.
7 Convolutional Neural Networks
Certain machine learning problems, such as image recognition, deal with input data in which spatial relationships are of utmost importance. While simpler image recognition problems, such as handwritten digit recognition, can be carried out relatively successfully with simple FFNNs, this is often not sufficient. Recall that the input for an FFNN is simply a single vector , meaning that the network has no notion of adjacency between, e.g., two pixels. A Convolutional Neural Network (CNN) is a type of network explicitly designed to take advantage of the spatial structure of its input. The origins of CNNs go back to the 1970s, but the seminal paper for modern CNNs is considered to be LeCun et al. (1998a), although other work exists in the same direction (e.g., LeCun et al. (1989); Waibel et al. (1989)). CNNs have been used extensively in NLP, and can in many cases be used instead of an RNN (contrast, e.g., dos Santos and Zadrozny (2014) who use CNNs for character-based word representations, and Plank et al. (2016) who use RNNs for the same purpose).
Although NLP is the focus of this thesis, we will approach CNNs from an image recognition perspective, as this is somewhat more intuitive. This is in part due to the fact that image recognition was the intended application of CNNs upon their conception. On a general level, convolutions can be carried out on input of arbitrary dimensionality. As mentioned, two-dimensional input (e.g. images) were the original target for CNNs. More recent work has extended this to three-dimensional input (e.g. videos). In the case of NLP, it is often the case that one-dimensional input is used, for instance applying a CNN to a text string. There are three basic notions which CNNs rely upon: local receptive fields, weight sharing, and pooling.
7.1 Local receptive fields
In the case of image recognition, an image of pixels can be coded as an input layer of units.181818This is assuming greyscale, i.e., one value per pixel. In a CNN, this input is processed by sliding a window of size across this image. This window, or patch, is known as a local receptive field. After passing this window over the input image, the following layer contains a representation based on sized slices of the input image. Intuitively, this can be seen as blurring the input image somewhat, as the spatial dimensions of the image are generally reduced through this process.
The length with which this window moves is referred to as its stride, and is most often set to , meaning that the window simply shifts by one pixel at a time. Although stride lengths of 2 and 3 are encountered in the literature, it is fairly uncommon to see larger stride lengths than this. Figure 12 shows a convolution, where , , a stride of is used, which yields a new layer with size .
7.2 Weight sharing
A key notion of CNNs is the fact that weights are shared between each such local receptive field, and the units to which they are attached. Hence, in our example, rather than having to learn weights (where is the total number of units in the first hidden layer), as in an FFNN, only parameters need to be learned. Therefore, all units in the first hidden layer capture the same type of features from the input image in various locations. For instance, imagine you want to identify whether a picture contains cats (as in Figure 12). In this figure, units in the first hidden layer might encode some sort of cat detector. The fact that weights are shared in this manner, results in CNNs being robust to translation invariance. This means that a feature is free to occur in different regions in the input image. Intuitively, taking our cat detector as an example, it is naturally the case that a cat is a cat, regardless of where in the image it happens to hide.
Each such cat detector, is referred to as a feature map, or a channel.191919The channel terminology makes sense when considering an input image in, e.g., RGB formatting, in which the intensities of each colour is represented in a separate colour channel. For a CNN to be useful, normally more than one feature map is learnt. That is to say, while the figures shown so far only show a single feature map, an input image is normally mapped to several smaller images. As an example, another feature map in Figure 12 might learn a dog detector. A more realistic example can be found in facial recognition, in which one feature map might learn to detect eyes, while another learns to detect ears, and yet another learns to detect mouths. Local receptive fields generally speaking look at all feature maps of the previous layers, hence the combination of eyes, ears, and mouths might be used to learn a feature map representing an entire face.
The fact that we generally map to several feature maps means that, at each layer, the spatial size of the image shrinks (i.e. ), while the depth of the image increases, as shown in Figure 13. Finally, following a series of convolutional layers, it is common practise to attach an FFNN prior to outputting predictions.
In NLP, the situation is somewhat different, as we normally do not have an image as input, but rather some sort of textual representation. Commonly, this will either be a string of words, characters, or bytes. An intuition for how this works, is that something resembling an n-gram feature detector is learnt given a window. This type of approach has been applied successfully in various tasks, for instance to obtain word-level representations which take advantage of sub-word information (dos Santos and Zadrozny, 2014; Bjerva et al., 2016b), and for sentence classification (Kim, 2014).
A pooling layer takes a feature map and condenses this into a smaller feature map. Each unit in a pooling layer summarises a region in the previous layer, generally using a simple arithmetic operation. Frequently, operations like maximum pooling (max pooling) or average pooling are used (Zhou and Chellappa, 1988). These operations take, e.g., the maximum of some region to be a representation of that entire region, thus reducing dimensionality by essentially applying simple non-linear downsampling. Max pooling can thus be seen as a way for each max pooling unit to encode whether or not a feature from the previous layer was found anywhere in the region which the unit covers. The intuition is that the downsampled version of the feature map, which yields feature locations which are rough, rather than precise, is sufficient in combination with the relative location to other such downsampled features. Importantly, this operation reduces the dimensionality of feature maps, thus reducing the number of parameters needed in later layers.
8 Residual Networks
Residual Networks (ResNets) define a special class of networks with skip connections between layers, as depicted in Figure 14. This facilitates the training of deeper networks, as these skip connections ease the propagation of errors back to earlier layers in the network.
Such skip connections are referred to as residual connections, and can be expressed as
where and are the input and output of the -th layer, is the weights for the -th layer, and is a residual function (He et al., 2016) such as the identity function (He et al., 2015a), which we also use in our experiments. Although ResNets were developed for the use in CNNs, the skip connections are currently being used, e.g., in LSTMs (Wu et al., 2016). ResNets can be intuitively understood by thinking of residual functions as paths through which information can propagate easily. This means that, in every layer, a ResNet learns more complex feature combinations, which it combines with the shallower representation from the previous layer. This architecture allows for the construction of much deeper networks. ResNets have recently been found to yield impressive performance in image recognition tasks, with networks as deep as 1001 layers (He et al., 2015a, 2016), and are thus an interesting and effective alternative to simply stacking layers. Another useful feature of ResNets is that they act as ensembles of relatively shallow networks, which may help to explain why they are relatively robust to overfitting in spite of their large number of parameters (Veit et al., 2016).
ResNets have recently been applied in NLP to morphological re-inflection (Östling, 2016), language identification (Bjerva, 2016), sentiment analysis and text categorisation (Conneau et al., 2016), semantic tagging (Bjerva et al., 2016b), as well as machine translation (Wu et al., 2016). Recently proposed variants include wide residual networks, with relatively wide convolutional blocks, showing that resnets do not necessarily need to be as deep as the 1001 layers used in previous work (Zagoruyko and Komodakis, 2016).
9 Neural Networks and the Human Brain
While there are numerous reasons to use neural networks, there are camps which might argue for applying NNs because they are ’biologically motivated’. While it can be tempting to use the conceptual metaphor (Lakoff and Johnson, 1980) of neural networks are the brain, this can be rather misleading. While usage of misleading metaphors can seem innocent, it has been shown that they do affect reasoning (Thibodeau and Boroditsky, 2013). Therefore, a misleading metaphor should certainly not be used as an argument for the usage of neural networks – there are plenty of other reasons for that.
Now, you might ask, is this metaphor really as misleading as it seems? At best, neural networks (as used in NLP) are a mere caricature of the human brain. On a physiological level, there is evidence that neurons do more than simply outputting some activation value based on a weighting of its inputs. For instance, recent research has shown that a single neuron can encode temporal response patterns, without relying on temporal information in input signals. Hence, the nature of how neurons work is quite different from what is encoded in a neural network, for instance in terms of information storage capacity (Jirenhed et al., 2017). There is in fact compelling evidence that memory is not coded in (sets of) synapses, but rather internally in neurons (cf. Gallistel and King, 2011, and Gallistel, 2016 and references therein, notably Johansson et al. (2014)). Additionally, backpropagation is not biologically plausible, although there is work on making biologically plausible neural networks (Bengio et al., 2015).
Convolutional Neural Networks and the Brain
Similarly to the ReLUs discussed in Section 5.2, CNNs are biologically inspired. When CNNs were invented (LeCun et al., 1998a), this was inspired by work which proposed an explanation for how the world is visually perceived by mammals (Hubel and Wiesel, 1959, 1962, 1968). The attempts to reverse-engineer a similar mechanism, as in CNNs, have proven fruitful, as CNNs are indeed highly suitable for image recognition. Furthermore, recent research has found some correlations between the representations used by a CNN, and those encoded in the brain in a study where the CNN could identify which image a human participant was looking at roughly 20% of the time (Seeliger et al., 2017). However, it remains to be seen whether anything similar to this is even plausible for natural language.
In this chapter, an intuitive and theoretically supported overview of neural networks was given, including a practical overview NLP. We have seen that many common NLP problems can be classified into three categories: one-to-one, one-to-many, and many-to-many. Appropriate deep learning architectures suitable for each of these categories were suggested.
While this chapter is meant to be a sufficient introduction to neural networks to understand this thesis, it is by no means a complete account of the topic. For a more in-depth description of neural networks in general, I refer the readers to Goodfellow et al. (2016). For a primer which is more geared towards NLP, see Goldberg (2015).
and Multilingual Learning
11 Multitask Learning
In Natural Language Processing (NLP), and machine learning (ML) in general, the focus is generally on solving a single task at a time. For instance, one might invest significant amounts of time in making a Part-of-Speech tagger or a parser. However, fact is that many tasks are related to one another. The aim of multitask learning (MTL) is to take advantage of this fact, by attempting to solve several tasks simultaneously, while taking advantage of the overlapping information in the training signals of related tasks (Caruana, 1993, 1997). When the tasks are related to each other, this approach can improve generalisation, partially since it provides a source of inductive bias, and since it allows for leveraging larger amounts of more diverse data.202020Generally speaking, it is beneficial to have access to more data when training an ML model. Additionally, since related tasks can often make use of similar representations, this can lead to the tasks being learnt even better than when training on a single task in isolation.
The use of MTL is skyrocketing in NLP, and has been applied successfully to a wide range of tasks, for instance sequence labelling such as POS tagging (Collobert and Weston, 2008; Plank et al., 2016), semantic tagging (Bjerva et al., 2016b), as well as chunking and supertagging (Søgaard and Goldberg, 2016). In addition to this, it is the primary focus of this thesis, and having some background knowledge on this will be useful for the following chapters. The first part of this chapter is an attempt at providing an understanding of what MTL is and how it is applied. While some general MTL scenarios are covered, the focus will be on MTL in the context of neural networks, and in the context of NLP.
11.1 Non-neural Multitask Learning
Before going into MTL in neural networks (NNs), we first take a look at the usage of this paradigm in other frameworks. Generally speaking, we seek to exploit the fact that there are many tasks which are somehow related to one another (Caruana, 1993, 1997; Thrun and Pratt, 1998). For instance, MTL can have the role of being a distant supervision signal, in the sense that the tasks used might be fairly distantly related. Additionally, since MTL plays the role as a regulariser (see Chapter \thechapter), and lowers the risk of overfitting (Baxter, 1997; Baxter et al., 2000), MTL often improves generalisation. This is in part because MTL reduces Rademacher complexity (Baxter et al., 2000; Maurer, 2006).212121A lower Rademacher complexity essentially indicates that a class of functions is easier to learn. Furthermore, MTL will push the weights of a model towards representations which are useful for more than one task. Finally, MTL can be seen as a method of dataset augmentation, as it allows for using more data than when only considering a single task at a time.
A commonly made assumption in MTL is that only a handful of parameters or weights (see Chapter \thechapter) ought to be shared between tasks, and conversely that most parameters should not be shared (Argyriou et al., 2007). This can intuitively be understood by considering that only a few features useful for a task might be useful for another task . For instance, imagine that we are building a joint POS tagger and language identification system. A feature capturing capitalised words preceded by a determiner will both be a decent indicator of the language being, e.g., German, as well as that the capitalised word is a noun. Other features, on the other hand, such as one indicating that the language is likely to be Norwegian or Danish if the letter ø is encountered, is not likely to be beneficial for POS tagging at all. In other words, this type of parameter sparsity can be phrased as that most parameters should not be shared, as many parameters are task specific. In this type of approach, all shared parameters are generally considered by all tasks involved. This puts the system at a relatively large risk of negative transfer, if one tries to combine this approach with tasks which are only slightly related. In NLP we are often interested in exploiting even relatively weak training signals, which makes this particularly problematic.
Another approach is to learn clusters of tasks, which allows for letting related tasks share certain parameters, and relatively unrelated tasks perhaps only a few. Such approaches have in common that they assume that the parameters which are beneficial for each other are geometrically close to one another in -dimensional space (Evgeniou and Pontil, 2004; Kang et al., 2011). Other work has come up with other definitions of task similarities. For instance, Thrun and O’Sullivan (1995) consider two tasks to be similar simply if one improves performance on the other. While other approaches to MTL have been used in the past, such as Daumé III (2009) who approach MTL from a Bayesian perspective, and Toutanova et al. (2005) who train a joint classifier for semantic role labelling with automatically generated auxiliary tasks, the perhaps most popular approach in NLP is parameter sharing in NNs.
11.2 Neural Multitask Learning
We now turn to the main method used in this thesis, namely neural MTL. There are two main approaches to this, differing in the manner in which parameters are shared – hard and soft parameter sharing. Currently, the less popular variant of the two in NLP is soft parameter sharing, and will not be covered in detail. Briefly put, in this setting, parameters are constrained in a similar manner to the parameter sparsity approach. That is to say, the parameters between tasks are encouraged to be similar to one another, which allows for some transfer between tasks, or between languages (Duong et al., 2015). However, as parameters are not explicitly shared between tasks, the risks of negative transfer are relatively low in this setting. This approach is not explored in this thesis as hard parameter sharing offers several advantages, including ease of implementation, and computational effectivity, as the amount of parameters is kept almost constant as compared to having a single task.
Hard parameter sharing is currently more common, perhaps mainly due to the ease with which a neural MTL system with several tasks can be created. This is the type of MTL discussed in the seminal works by Caruana (1993, 1997). In this thesis we consider research questions tied to this type of MTL in the context of NLP, partially due to the versatility of the paradigm. Apart from allowing for considering data from several tasks simultaneously, even corpora in different languages might be used in this approach, given some sort of unified input representations.222222This is covered further in the second half of this chapter. Then, if the output labels between tasks correlate with one another to some extent, it seems quite intuitive that this approach should be beneficial.
In NLP, MTL is generally approached from the perspective that there is some main task, i.e., the task in which we are interested, and some auxiliary task, which should improve the main task. It is important to note, however, that these labels are quite arbitrary.232323The exception being cases in which the performance on the auxiliary task is disregarded in favour of the main task performance. There is not necessarily anything to distinguish a main task from an auxiliary task in an NN. One might lower the weighting of the auxiliary task (i.e. multiply the loss for each batch by some ), but this strategy appears to be relatively rare in the literature.
A common way of implementing hard parameter sharing, is to have a stack of layers for which weights are updated with respect to all tasks, with at least two output layers, each with task-specific weights (see Figure 15). Concretely, consider that we have corpora with different annotations, each containing pairs of input and output sequences () for a single task. While the inputs will largely be part of the same vocabulary, and can be shared across tasks, the tag sets used, and therefore the labels () differ. Note that the vocabularies in the tasks at hand do not necessarily need to overlap, but when considering a single natural language, this tends to be the case. A common approach when training is to randomly sample such sequence pairs, predict a label distribution , and update model parameters as calculated by the loss relative to the true label distribution with backpropagation (see Chapter \thechapter for an overview of this). Each task has a task-specific classifier () with its own weight matrix (). The output of the task-specific layer is then calculated using the softmax function (cf. Section 5.2), such that
where denotes the activations of the layer before the output layer.
This architecture is common in NLP, with weights typically shared between the main and auxiliary task at all layers, up to the task-specific classification layer (i.e. the output layer). A multitude of other possibilities do exist, as the task-specific output layers can be attached anywhere in the network. This can be advantageous, as Søgaard and Goldberg (2016) found that including the lower-level task supervision at lower levels in the network was useful, in the case of using the low-level task of POS tagging in combination with CCG supertagging (i.e. assigning CCG lexical categories). Most related work, including the experiments in this thesis, apply multitask learning akin to what is shown in Figure 15.
Neural Multitask Learning in Natural Language Processing
Hard parameter sharing in NNs is the target of considerable attention in the recent NLP literature. Practically speaking, there appear to be two main approaches to MTL in the NLP literature. Some work, such as Ando and Zhang (2005), Collobert and Weston (2008), Søgaard and Goldberg (2016), Plank et al. (2016), Bjerva et al. (2016b), and Augenstein and Søgaard (2017) take the approach of exploiting seemingly related NLP tasks, based on some linguistic annotation. Other work, e.g., Plank (2016), and Klerke et al. (2016), take the approach of exploiting data from non-linguistic sources (keystroke data and eye gaze data, respectively). While these approaches are both useful and interesting, the focus of this thesis is the first approach, specifically in which an NLP sequence prediction task is used as an auxiliary task for some other NLP sequence prediction task. This is partially motivated by the fact that using a word-level input for all tasks, allows for a one-to-one mapping between labels in different tag sets (given a specific token in context), which in turn opens up for the information-theoretic approach considered in Chapter \thechapter.
11.3 Effectivity of Multitask Learning
Plenty of studies demonstrate the success of MTL, such as in computer vision (Torralba et al., 2007; Loeff and Farhadi, 2008; Quattoni et al., 2008), genomics (Obozinski et al., 2010), and the aforementioned NLP studies. Apart from relatively straight-forward results showing that MTL is often beneficial, efforts have been put into experimentally investigating when and why MTL is advantageous in NLP. Martínez Alonso and Plank (2017) look at a collection of semantic main tasks while using morphosyntactic and frequency-based tasks as auxiliary tasks. They find that the success of an auxiliary tasks depends on the distribution of the auxiliary task labels, e.g., the distribution’s entropy and kurtosis.242424The kurtosis of a distribution is essentially a measure of its tailedness. Bingel and Søgaard (2017) present a large systematic study of MTL in a collection of NLP tasks. They find that certain dataset characteristics are predictors of auxiliary task effectivity, corroborating the findings of Martínez Alonso and Plank (2017), and also show that MTL can help target tasks out of local minima in the optimisation process. In Bjerva (2017b), it is argued that entropy is not sufficient for explaining auxiliary task effectivity, and that measures which take the joint distribution between tasks into account offer more explanatory value (this is elaborated in Chapter \thechapter).
In terms of data sizes Benton et al. (2017) suggest that MTL is effective given limited training data for the main task. Luong et al. (2015), however, highlight that the auxiliary task data should not outsize the main task data – this is contradicted by Augenstein and Søgaard (2017), who highlight the usefulness of an auxiliary task when abundant data is available for such a task, and little for the main task. Finally, Mou et al. (2016) investigate transferability of neural network parameters, by attempting to initialise a network for a main task with weights which are pre-trained on an auxiliary task, and highlight the importance of similarities between tasks in such a setting. Finally, a promising recent innovation is that of sluice networks, in which a NN learns which parts of hidden layers to share between tasks, and to what extent (Ruder et al., 2017).
11.4 When MTL fails
The cases in which MTL does not work are also deserving of attention. While up until now we have assumed that applying MTL is a piece of cake, there are times when one adds an auxiliary task, causing the system to collapse like a house of cards. This type of performance loss is referred to as negative transfer, and can occur when two unrelated tasks share parameters. This is generally something to avoid, as there are few, if any, advantages to worsening the generalisation ability of the network. However, such results are rarely shared in the community, in part due to the file drawer problem (Rosenthal, 1979). In short, the problem is that it is impossible to access, or even know of, studies which have been conducted and not published. In the case of MTL, this issue might be alleviated by publishing results on all auxiliary tasks experimented with, even if only one or two such tasks improved performance.
12 Multilingual Learning
In the second half of this chapter, we turn to multilingual approaches. Many languages are similar to each other in some respect, and similarly to related tasks, this fact can also be exploited in order to improve model performance with respect to, e.g., a given language. While there are many approaches to multilingual NLP, with various use cases, the focus in this thesis is on model transfer, in which a single model is shared between languages. We will nonetheless begin with an overview of the most common approaches.
As an example, consider NLP tagging tasks, which can be summed up as learning to assign a sequence of tags from a tag set to a sequence of tokens in language . In cross-lingual multitask NLP settings, there are many / pairs which do not have any annotated data. For instance, there is (at the time of writing) no annotated data for Welsh in the Universal Dependencies (Nivre et al., 2017). However, many NLP systems require input data from specific tag sets. For instance, the Stanford Neural Network Dependency parser requires POS tags in its input (Chen and Manning, 2014), whereas the semantic parser Boxer requires semantic tags in its input (Bos, 2008; Abzianidze et al., 2017). Hence, for such tools to be applicable in multilingual settings, the tags they rely on need to be available for other languages as well, which highlights the importance of approaches which deal with this. There are three frequently used approaches to solving this problem:
Although serious efforts have gone into furthering these approaches, they all have considerable drawbacks. In brief, human annotation is time consuming and expensive, annotation projection is only applicable to texts which are both translated and aligned, and model transfer is generally only used in mono-lingual or mono-task settings.
12.1 Human Annotation
Generally speaking, annotating data manually is a very expensive and time-consuming manner of, e.g., producing some sort of linguistic labels for a sentence. Although the process can be alleviated with gamification (Venhuizen et al., 2013; Chamberlain, 2014; Jurgens and Navigli, 2014; Bos and Nissim, 2015), considerable time and effort still needs to be invested into creating such crowd-sourcing systems.
12.2 Annotation Projection
Given an annotated sentence in a source language and a translation of that sentence in a target language, it is possible to transfer, or project, the annotation from the source language to the target language. This approach is known as annotation projection, and relies on having access to parallel text for which at least one source language is annotated (Yarowsky et al., 2001; Hwa et al., 2005). Usually, word alignments are used in order to project linguistic labels from source to target. The resulting annotations can then be used to train a new monolingual system for the target language(s). This approach has been applied successfully to various tasks, primarily syntactic parsing (Hwa et al., 2005; Tiedemann, 2014; Rasooli and Collins, 2015; Agić et al., 2016), POS tagging (Yarowsky et al., 2001), and recently also semantic parsing (Evang and Bos, 2016; Evang, 2016).
Annotation projection has two main drawbacks. Primarily, it is only applicable to texts which are both translated and aligned, whereas the majority of available texts are monolingual. Furthermore, this approach relies heavily on the quality of the automatic word alignments. Word-aligning parallel text is not always successful, for instance with very dissimilar languages, insufficient statistics, or bad translations (Östling, 2014, 2015). Another approach for annotation projection relies on automatic translation. This works by applying a machine translation (MT) system to generate a parallel text for which source language annotation exists (Tiedemann et al., 2014). In other words, in addition to the difficulties of the annotation projection approach, this method places high requirements on availability of parallel texts for training an MT model. In addition to these prerequisites, the involvement of a fully-fledged MT system in an annotation pipeline, will in itself increase its complexity severely.
12.3 Model Transfer
Model transfer deals with learning a single model which is shared between several languages (Zeman and Resnik, 2008; McDonald et al., 2011a).252525Note the similarities to multitask learning with hard parameter sharing. This type of approach has been explored extensively in previous work. Multilingual model transfer has been successfully applied to, e.g., POS tagging (Täckström et al., 2013), and syntactic parsing (Täckström, 2013; Ammar et al., 2016). This is commonly done by using delexicalised input representations, as in the case of parsing (Zeman and Resnik, 2008; McDonald et al., 2011a; Täckström et al., 2012, 2013). A related situation, is the case of exploiting language similarities in order to train models for low-resource languages (see, e.g., Georgi et al. (2010)).
In this thesis, model transfer is framed as a special case of MTL. That is to say, each language in the model can be seen analogously to a task. This means that we are also free to choose whether we want to code tag predictions jointly as a single output layer, or have one separate output layer per language. As with MTL with multiple tasks, we consider the same specific type of MTL across languages, namely hard parameter sharing in neural networks.
A common approach in parsing is to delexicalise the input representations in order to enforce uniformity across languages, by training a parser on sequences of PoS tags rather than sequences of words (Zeman and Resnik, 2008; McDonald et al., 2011a). However, as we are looking at predicting such tags, we approach this by using input representations which are shared across languages. This allows for training a neural network for several languages simultaneously in a language-agnostic manner, while still taking lexical semantics into account. Apart from this advantage, implementing a system in this manner is straightforward. Additionally, this approach offers the possibility of out-of-the-box zero-shot learning, as simply adding input representations for a different language is sufficient to enable this.
Zero-shot learning is the problem of learning to predict labels which have not been seen during training. This is especially relevant in cases such as MT, in which, e.g., many of the target forms which need to be produced for languages with rich morphology have not been seen. In recent years, zero-shot learning has become increasingly popular, for instance in image recognition (Palatucci et al., 2009; Socher et al., 2013b). Recently, it has also been applied to MT, resulting in a model which even allows for translation into unseen languages (Johnson et al., 2016). One way of enabling zero-shot learning, is to use shared input representations. For instance, in the case of character-based models, we can simply use the same alphabet in the inputs and outputs of each system, as in Östling and Bjerva (2017) and Bjerva (2017a). In the case of word level input representations, one can employ word embeddings living in the same space, regardless of language.
12.4 Model Transfer with Multilingual Input Representations
Looking further at the problem of model transfer across languages, consider the following example, of an English sentence and its translation, as two separate input sequences to a neural network, with their corresponding annotated output sequences.262626PMB 01/3421. Original source: Tatoeba.
We must draw attention to the distribution of this form in those dialects . PRON VERB VERB NOUN ADP DET NOUN ADP DET NOUN ADP DET NOUN PUNCT \glt\glend
Wir müssen die Verbreitung dieser Form in diesen Dialekten beachten . PRON VERB DET NOUN DET NOUN ADP DET NOUN VERB PUNCT \glt\glend
Although the surface forms of these two sentences differ, as one is in English and one in German, multilingual word representations for the corresponding words in these two sentences ought to be close to one another. Hence, if the NN only sees the English sentence in training, and the German sentence during test time, it ought to be fairly successful in tagging this ’unseen’ sentence with suitable tags.272727Considering that the semantic content of the two sentences ought to be highly similar, one could regard the translated sentence to be ’seen’ if the original sentence was in the training data. This has the further implication that one, in this type of experiments, must take care not to allow corresponding sentences to occur in both training and evaluation data. However, one question is whether having access to the same sentence in a typologically more distance language such as Japanese also would be useful (this is approached in Chapter \thechapter).
In order for such an approach to work, it is necessary that words with similar meanings in different languages are represented in a fairly similar way. How do we arrive at word representations with such properties? In the next few sections we will look at this, beginning at simple monolingual representations, and leading up to bilingual and multilingual representations.
12.5 Continuous Space Word Representations
In many NLP problems, we are concerned with processing some word-like unit, in order to arrive at some linguistically motivated and appropriate label. In Section 5.1, we considered bag-of-words models for tasks such as this. To recap, in this type of model we assign an index to each unique word. Each word is then represented by a vector , with a dimensionality equal to the size of the vocabulary, since each word requires its own index. As an example, consider a vocabulary size of five words, with three of those words being cat, dog, and coastal, with their corresponding vector representations, such that
In NLP, we are often interested in comparing words with one another, either simply in order to have some measure of their similarity, or because we are interested in the fact that similar words tend to have similar properties in down-stream tasks. For instance, the words cat and dog are likely to have the same or similar linguistic analyses in many cases, such as both being tagged with the PoS tag NOUN. A commonly used similarity measure between vectors is the cosine distance. In this setting, a word representation as presented above is somewhat problematic, as the distances between the three words are equal, although we want a higher similarity between cat and dog.
The representation we have seen so far is known as a sparse feature representation, as each word is represented by a vector of zeroes with one element set to one, also known as a one-hot vector. Apart from the drawback of similarity, this type of input representation can run into other problems, such as the dimensionality of the representations becoming too large to handle as vocabulary size grows. This can be remedied in many ways, for instance by applying dimensionality reduction algorithms. Commonly used algorithms include singular value decomposition (SVD), and random indexing (Kanerva et al., 2000; Sahlgren, 2005). This does not help with the problem of similarities, however.
It turns out that one can arrive at word representations with nice properties of similarity by taking advantage of the distributional hypothesis:
’Semantics is partly a function of the statistical distribution of words.’
’You shall know a word by the company it keeps.’
–Firth (1957, p.11)
This means that the semantic content of a given word is related to other words occurring in similar contexts. Furthermore, Harris (1954) claims that the strength of this relation is proportional to the similarity between two words, such that if two words and are more similar in meaning than and , then the relative distribution of the first pair will be more similar than that of the second pair. One way of implementing this type of distributional semantics is to count word co-occurrences in a large corpus. Let us now assign the two remaining indices in the five-dimensional representation used above to the words pet and water, such that
These five vectors can then be used to generate new distributional vectors, , by representing each word by the sum of the vectors of the words with which it co-occurs. If cat and dog frequently co-occur with each other, and with pet, whereas coastal mainly co-occurs with water, the resulting representations may be similar to
In this representation, cat and dog are more similar to one another than they are to coastal, which is exactly what we want. A visualisation of such a word space is given in Figure 16.
The type of word representation discussed up until now is also known as a count-based representation, as opposed to a prediction-based representation (Baroni et al., 2014).282828Whereas Baroni et al. (2014) suggest that prediction-based methods outperform count-based ones, Levy and Goldberg (2014b) show that the underlying differences between the approaches are small. Whereas a count-based representation can be seen as counting the words in a given context, a prediction-based representation can be made by attempting to predict that context. Doing this with a neural network, the error obtained when attempting to make such predictions is used to update the representations, until a low error is obtained (see Chapter \thechapter for details on neural networks). With the entry of the deep learning tsunami on the NLP scene (Manning, 2015), this type of dense word representations has become increasingly popular. The availability of tools implementing such algorithms, such as word2vec, undoubtedly helped push the popularity of this approach further. This trend was introduced by Collobert and Weston (2008), Turian et al. (2010), and Collobert et al. (2011), and was further spearheaded by papers such as Mikolov et al. (2013c), which showed that a simple neural model would encapsulate linguistic regularities in its embedded vector space. The now infamous example of this property is shown in a figure in Mikolov et al. (2013c), replicated in Figure 17, where the following relation holds
In other words, the distance between man and woman is similar to that between king and queen, so adding this difference to the vector of king results in a vector close to queen.
In a prediction-based approach, the terminology used is that a word is embedded into -dimensional space. Typically, this dimensionality is much lower (e.g. around ) than what is generally used in count-based approaches (e.g. around ). In the case of neural networks, these embeddings can be trained together with the rest of the network. This results in a matrix of word vectors in which words with similar properties (under the task at hand) are close to one another.
Distributional vs. Distributed representations
An useful distinction to make is that of distributed vs. distributional representations. A distributional word representation is based on a co-occurrence matrix, taking advantage of the distributional hypothesis. Similarities between the resulting distributional word representations thus represent the extent to which they co-occur, and therefore also their semantic similarity. A distributed representation, on the other hand, is simply one that is continuous. That is to say, a word is represented by a dense, real-valued, and usually low-dimensional vector. Such representations are generally known as word embeddings, with each dimension representing some latent feature of the word at hand. One way to remember this is that such representations are distributed across some -dimensional space. The first representations we saw were therefore distributional, but not distributed (Turian et al., 2010). The word embeddings, on the other hand, can be said to be both.
Bilingual and Multilingual Word Representations
Going from monolingual to bilingual word representations has been the subject of much attention in recent years. One of the first approaches to bilingual word representations was shown by Klementiev et al. (2012), followed by work such as Wolf et al. (2014), and Coulmance et al. (2015). Parallel to approaches which aim at making good multilingual embeddings, are attempts at producing better monolingual embeddings by exploiting bilingual contexts, as in Guo et al. (2014), Šuster et al. (2016), and Šuster (2016).
In essence, the approaches to building such representations can be divided up into several categories. Cross-lingual mapping can be done by first learning monolingual embeddings for separate languages, and then using a bilingual lexicon to map representations from one space to the other (Mikolov et al., 2013b). Another approach is to mix contexts from different languages, and training pre-existing systems, such as word2vec, on this mixed data (Gouws and Søgaard, 2015). The approach under consideration in this thesis is based on exploiting parallel texts, by jointly optimising a loss function when predicting multilingual contexts (Guo et al., 2016).
The true power of multilinguality is not unlocked until we can consider an arbitrary number of languages at a time. Whereas bilingual word representations only encode two languages, a multilingual word space contains representations from several languages in the same space. As before, we here also have the property that words with similar meanings are close to one another irrespective of the language (see Figure 18).
One such is the multilingual skip-gram model, as outlined by Guo et al. (2016).292929The skip-gram method to create word embeddings, in which a neural network attempts to predict the context of a word, is not to be confused with skip-grams in the sense of -grams which are not necessarily consecutive. In the second sense, we can define a k-skip-n-gram as a sequence of length n, in which words occur at distance k from each other. In this thesis, only the first sense is of importance. As a variant of this model is used in Part III and Part IV, we will now cover this in more detail.
The skip-gram model has become one of the most popular manners of learning word representations in NLP (Mikolov et al., 2013a). This is in part owed to its speed and simplicity, as well as the performance gains observed when incorporating the resulting word embeddings into almost any NLP system. The model takes a word as its input, and predicts the surrou