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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Evaluating word embeddings for computational pragmatics</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Leonardo Sanna</string-name>
          <email>leonardo.sanna@unimore.it</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>University of Modena and Reggio Emilia</institution>
          ,
          <addr-line>Modena</addr-line>
          ,
          <country country="IT">Italy</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>distant. Word embeddings are a popular set of machine learning techniques that are used in natural language processing to create a semantic model of a corpus, representing semantic relationship within a geometric space. In this space every word is mapped to a vector so that words with similar meanings are represented close to one another while words with different meanings are In this work we briefly present a novel use of word embedding for computational pragmatics in which we used word2vec Skip-Gram (henceforth SG) to explore the inferential model generated by algorithmic personalization on Facebook. We used their experiment in a recent study in which we implemented Eco's model reader as an inferential model. In a nutshell, we found that we can simulate the model reader with word embedding to create computational inferential models, that are then compared to identify a possible divergence of interpretation paths. Our experiment conducted on Facebook showed that algorithmic personalization influences model readers, differentiating inferences across different timelines. Though for pragmatic goals, word embeddings have two significant issues that are 1) accuracy 2) variability. The standard way of evaluating the accuracy of word embeddings is to use intrinsic evaluation, using predefined analogies and similarities such as (Finkelstein et al. 2002) and SimLex. However, this accuracy is quite hard to estimate while inquiring pragmatic aspects as we do not have any predefined pragmatic output. This work aims to review these methods for a computational pragmatic approach, highlighting possible limitations and adaptations. The review will cover three aspects: 1) Reproducibility of computational pragmatics 2) Reliability assessment for computational pragmatics inferences 3) Accuracy test for computational pragmatics goals Word Embedding, model reader, evaluation, computational pragmatics</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        Word embeddings are a popular set of techniques that are used in natural language processing to
create a semantic model of a corpus, representing semantic relationship within a geometric space. In
this space every word is mapped to a vector so that words with similar meanings are represented close
to one another; instead, distance within the space means that words have less semantic affinity. This
semantic representation originates in the distributional hypothesis [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ], affirming that words with similar
meanings occur in similar contexts. In mathematical terms, we can say that “The degree of semantic
similarity between two linguistic expressions A and B is a function of the similarity of the linguistic
contexts in which A and B can appear” [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ].
      </p>
      <p>
        In a nutshell, there are two main ways of doing word embeddings. On the one hand, we have
countbased models, on the other hand, predictive-probabilistic models. In the first case, embeddings are built
using a co-occurrence matrix while in the letter case machine learning is used to build a stochastic
model of the language. A renowned empirical evaluation [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ] showed that the performance of predictive
models was far superior compared to models based on counting co-occurrences.
      </p>
      <p>2020 Copyright for this paper by its authors.</p>
      <p>In this paper we are using word2vec, perhaps the most famous and used word embedding predictive
algorithm. The goal of this work is to discuss some issues in the evaluation of probabilistic word
embeddings for computational pragmatics. In the following sections we will briefly illustrate the
functioning of word2vec and how could they be used for studying pragmatics. Then, we will introduce
the evaluation problem, proposing a first outline of a quali-quantitative framework to evaluate our
embeddings while inquiring pragmatics.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Related work</title>
      <p>
        Predictive word embeddings might be performed with different algorithms such as word2vec [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ],
fastText [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ], Star Space [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ] and RAND-WALK [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ]. More recently, other approaches such as ELMO
and BERT [
        <xref ref-type="bibr" rid="ref8 ref9">8,9</xref>
        ] have gained popularity in the field of NLP. In this work we used word2vec because it
is the most used and renowned version of probabilistic word embeddings.
      </p>
      <p>
        Word2vec works on probabilistic neural networks and it might be realized in two different ways
[
        <xref ref-type="bibr" rid="ref10">10</xref>
        ]: continuous-bag-of-words models (CBOW) and skip-gram (SG). A CBOW trains the neural
network to predict a word given a context, while the SG model learns how to predict a context starting
from a target word (Figure 1).
      </p>
      <p>
        Word2Vec can work either with negative sampling or with hierarchical softmax; in the case study
presented we used SG with negative sampling because of its better performance on analogical reasoning
as explained in the paper by Mikolov et al. [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ].
      </p>
      <p>
        We can say that word2vec creates a model computing the probability of words to co-occur, meaning
that it can also capture semantic relations between words that rarely or never co-occur in the corpus
whilst being semantically related. Moreover, word2vec models can perform actual inferences based on
words’ semantics2. For this reason, we used word2vec to evaluate pragmatic inferences [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ], simulating
Eco’s model reader [
        <xref ref-type="bibr" rid="ref12">12</xref>
        ] with word embeddings.
      </p>
      <p>We can think of the model reader as the pragmatic competence needed to interpret a text with
reference to its producer’s intention, meaning that, in Umberto Eco’s semiotics, text interpretation is
always guided and limited by the text itself. On the other hand, what we call "producer intention",
although partially embedded in the text instance, has to be guessed by the empirical reader who has to
formulate a hypothesis on the producer intention. To sum up, in Eco’s theory the interpretation process
is successful only when the interpretation matches the author intention by following the instructions of
the model reader, meaning that the reader understood what the producer wanted to communicate. A
crucial component of the model reader is what Eco called encyclopedic competence, namely the shared
2 The renowned example is that given the words “king” and “man”, the word2vec model can infer the word "queen", given the word woman,
cultural context between the reader and the author. For instance, to understand the sentence "word
embeddings are a machine learning technique used in NLP", the reader has to know what is machine
learning and what is NLP and, most important, how do these two things are related. In Eco's theory,
encyclopedic competence is essential to fulfil the interpretation process. This competence is acquired
in previous textual and verbal exchanges. In a nutshell, the encyclopedia is the shared information that
we must know to communicate and the model reader is the set of instructions on how to combine this
shared knowledge to understand a text.</p>
      <p>Hence, we approached the model reader theory empirically using word embedding arguing that it
could be as an inferential model, precisely a function that takes as input a target text and that produces
interpretation paths as an output. In other words, we can use word embeddings in qualitative analysis,
creating a computational version of the inferential model.</p>
      <p>
        We used this theory to investigate algorithmic personalization [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ] on Facebook. A study on the
Italian elections made in 2018 [
        <xref ref-type="bibr" rid="ref14">14</xref>
        ] highlighted that Facebook algorithm treated politically sources
unevenly, fostering the political ideology of each profile. From a semio-linguistic perspective, it is
interesting to inquire whether also the model readers were different across each political ideology. The
study was made creating six different profiles, all following the same 40 political pages but interacting
only with one political party. We used these six profiles to generate six different word embeddings,
investigating differences within the inferential models like in the example showed in Figure 2.
      </p>
    </sec>
    <sec id="sec-3">
      <title>3. Data and methods</title>
      <p>The dataset of the experiment is the same used for the aforementioned experiment and it is composed
by two different parts: sources and impressions. In the sources dataset we had the entire collection of
each Facebook post made by the whole set of pages followed by the bots, while in the impressions
dataset we had the actual posts that were shown to our profiles.</p>
      <p>We created an embedding model both for the sources dataset and then one embedding for each
alleged model reader, as shown in the example in Fig.2. We noticed that there were some important
issues regarding the explicability and the evaluation of our experiment.</p>
      <p>
        Explicability and evaluation of word embeddings still an issue in NLP. Predictive models are not
fully reproducible, since each time we start a model from scratch, even with the same hyperparameters,
the model would be slightly different. Research on these themes, to best of or knowledge, is very recent
[
        <xref ref-type="bibr" rid="ref15">15</xref>
        ].
      </p>
      <p>
        To sum up, we had three types of problems related to our research.
1. Reproducibility: How can we reproduce an inferential model so that we can perform more
experiments? Recently Hellrich [
        <xref ref-type="bibr" rid="ref15">15</xref>
        ] experimented a Singular Value Decomposition of a PPMI
matrix with weighting-based downsampling to generate reliable word embeddings without
losing performance. In this case, it is possible to have a fully reproducible word embedding
model, meaning that with the same parameters we always get the same vectors. SVD works on
three different matrixes, two orthogonal containing vectors and one diagonal containing values.
These three matrices are then decomposed each time in the same way, so that the same input
would always generate the same matrix. Particularly interesting the solution proposed by
Hellrich that introduced a variant using a PPMI matrix populated via weighting, to enrich its
embeddings.
2. Reliability; intended as the measurable stability of word embeddings, namely how much word
embeddings change each time that they are initialized with the same hyperparameters. SG
model is trained with a stochastic gradient descent that works finding one of the possible
optimum local minima. The fact that the gradient can find slightly different local minima
combined with the fact that the vectors are randomly initialized creates a model which is not
fully reproducible.
3. Accuracy; in probabilistic word embeddings is usually measured using predefined word pairs
and analogies [
        <xref ref-type="bibr" rid="ref16 ref17">16, 17</xref>
        ], testing then the ability of embeddings to produce semantic inferences.
      </p>
      <p>The first two points are related, as a fully reproducible algorithm also generates a reliable model.
Though, in pragmatics, it is hard to find stability because inferences are never determined but only
suggested, the same text might produce different inferences even with the same reader. The model
reader is a set of instructions that guides the empirical reader in its interpretation; the conditions of the
model reader are not rigid and mandatory. We argue that, for our goals, it would be misleading to use
the proposed SVD matrix to build our embeddings, because it would represent a deterministic view of
the inferential model.</p>
      <p>Yet the problem of reproducibility is real and the important work made by Hellrich brought us clear
evidence that we cannot avoid dealing with robust evaluation methods. Thus, we decided to use two
different NLP methods in our experiment.</p>
      <p>The model reader is generated in each text from the combination of author’s intention and
encyclopedic knowledge, namely the shared information among reader and author. This shared
information might be assumed as equal for each model reader and each model author, meaning that we
can use a fully reproducible method to create the semantic model of our encyclopedia.</p>
      <p>For our goals, we were also interested in extracting the main topics that emerged from our corpus.
Therefore, we created a topic modelling using a hierarchical classification [18] on the sources dataset.
This hierarchical classification allows us to extract the most meaningful topics and the words associated
with each one of them. We chose Reinert hierarchical classification (CHD) because of how his
algorithm works; it creates its classification mapping lexical forms with contexts. Although there is not
any stochastic elaboration, this feature makes CHD comparable with word embeddings, since the
representation of words semantics is not created among words but words and contexts, intending
contexts as text chunks. The reason why we chose word embedding to represent the model reader is
that they consider the relations between words and contexts, CHD does the same on a count-based
framework.</p>
      <p>We then selected the most relevant words in the most relevant topics, and we used these words to
create our semantic query to perform the pragmatic move within our model readers. In fact, one of the
characteristics of word2vec is that we can perform algebraic operations with our vectors, adding or
subtracting semantic traits from each word.</p>
      <p>Regarding the last point, accuracy is not easy to evaluate in word embeddings. A review of methods
used to test the quality of embeddings has been made by Wang et al. [19]. These methods could be
divided into two families: intrinsic evaluation and extrinsic evaluation. Extrinsic evaluation is a
downstream method while the former evaluates our model internally. As said, intrinsic evaluation is
probably the most common standard evaluation for word embeddings. Word similarities and analogies
are computed to verify consistency within the vectors. In particular, for our goals analogy was the best
option because we want to investigate inferences. The equation proposed by Mikolov et al. [20]
computes the  of a given linear representation. For instance, if we calculate the analogy
 :  ∷  :  , we compute  =  −  +  and then compute the  to
find the vector with the highest cosine similarity to  . In our case, analogy testing is excellent but at the
same time problematic. Inquiring pragmatics in political ideology implies that we are interested in
discovering inferences that have an ideological value; with the word "discovering", we mean that we
are using word embedding to explore an inferential model that we do not know, hence we do not have
a predefined set of analogies to test the quality of our embeddings.</p>
      <p>Nonetheless, there are for sure some "wrong inferences". We do not perform inferences in a
completely free environment but instead following some textual constraints that are posed by the text
itself and by the encyclopedic context. Suppose I read the word "flat tax". In that case, I expect to infer
words related to this term, namely the political party which is proposing it, words associated with the
economic lexicon and words that are related to the evaluation of the political proposal. It would be
wrong for sure to infer words that are completely unrelated to the semantic field of "flat tax" such as
"dog" or "Travis Scott". We propose to use this method to evaluate the quality of our embeddings,
looking for words that are somehow “intruders” in our semantic field. In this case, we are assuming
Fillmore’s theories on semantic fields [21]. To use the words of Violi [22] words select their contexts,
hence each word would select an appropriate semantic field. We called words that do not belong to the
given semantic field “semantic noise” and we used this concept to test the accuracy of our embeddings.
We took into account the top-50 most similar words, looking for semantic noise. At this stage of the
research, we have not defined how to quantify semantic noise yet. We assumed that up to 10% of
semantic noise in the top-50 would have been fine, however semantic noise within the top-20 or top-10
should be weighted differently. We found significant semantic noise only in the centre-left model
reader, that was also the smallest.</p>
      <p>To sum up, using word embeddings for computational pragmatics we would need two have at least
three corpora: the first corpus representing the encyclopedic knowledge and then at least two to
represent the model readers so that we can compare their inferences. This methodology allows a fully
reproducible experiment as long as we share criteria and methods used to select both corpora. In the
case presented, the experiment is limited to model readers guessed and proposed by Facebook
algorithm, thus only Facebook posts were used to generate the embeddings.</p>
      <p>Our experimented concluded that there were some differences among the model reader, but that
further analysis was necessary to understand the differentiation and their semantic reasons better.</p>
    </sec>
    <sec id="sec-4">
      <title>4. Discussion</title>
      <p>In this paper we are not discussing the findings of the experiment but instead possible flaws and
implications of our evaluation method.</p>
      <p>To have a fully reproducible and reliable model we used two different algorithms to represent the
shared cultural knowledge and the actual model reader. One possible limitation of this approach is that
we are relying on the topic modelling that is built in the first part of the experiment. If this representation
is biased, then also our inferential model would be biased. Although Reinert classification is
welltrusted in literature [23, 24, 25], using different algorithms for topic modelling would be the best
solution so that at least we can compare the most relevant topics and inquiry their consistency. Besides
this, there is also a theoretical question.</p>
      <p>We said that we avoided using an SVD matrix because it was too deterministic in representing
pragmatic inferences. On the other hand, we assumed that we could use a fully reproducible topic
modelling to represent our shared knowledge. This might be questioned. The encyclopedia is the whole
cultural context that each one of us must have and share with other people to which he intends to
communicate. Since each one of us has different cognitive capacities, we might argue that even the
encyclopedic knowledge should be represented with a probabilistic algorithm. However, according to
Eco’s theory, the shared cultural context is something stable and objective. What changes is the capacity
to use and combine this knowledge for each empirical reader and, in the case of the model reader, the
suggestions that might guide the empirical reader in combining and interpreting his encyclopedia.</p>
      <p>We might argue that shared knowledge must be stable and equal, while the ability to combine this
shared knowledge might differ in each interpretation process, meaning that even the same reader might
accomplish different interpretation of the same text, without adding new information to its encyclopedic
competence. Even though it might sound too simplistic, this is the way our communication works. For
instance, the sentence "Boris Johnson has finally made Brexit" requires shared knowledge on Boris
Johnson and Brexit in each model reader. What changes it is the interpretation of these words, that
would reveal pragmatic moves of each model reader. In Umberto Eco semiotics, this is called intentio
operis [26], meaning that the text has a stable value of signification that exists regardless of the author’s
intention and no matter of the reader’s interpretation. The intentio operis could be seen as the objective
semiotic dimension of the textual instance, namely what the text actually means because of its semantic
structures. Thus, we conclude that using a fully reproducible method to represent the encyclopedic
knowledge is necessary both to account for reliability and to correctly represent the semiotic dimension
of intentio operis.</p>
      <p>Nevertheless, we used word2vec to generate our model readers. In this case we still have the
reliability problem and also the accuracy problem. As we said before, accuracy is challenging to
estimate for pragmatic inferences and we used a novel method, defining “semantic noise” words that
do not belong to the inquired semantic field. However, evaluating semantic noise is not always possible,
even relying on databases such as WordNet. In fact, we might have what look like a semantic intruder
that is, instead, a valid inference coming from our corpus. For this reason, we used a quali-quantitative
approach to evaluate accuracy, using corpus linguistic tools to evaluate co-occurrences and
concordances [27]. Besides, we also evaluated the density of our vectors. According to our findings,
similar words usually have a cosine similarity between 0.5 and 0.8 in the top-50 most similar words,
with the most two-three similar words much closer compared to the other. Instead, words that have a
poor representation might either have a sparse cluster of most similar words (&lt;0.50) or a really dense
one (&gt;0.90 for more than three words in the cluster).</p>
      <p>Hellrich also introduced a quantitative evaluation for the reliability of word embedding comparing
cosine similarity and Jaccard coefficient among different word embedding models. However, these
metrics have not yet been explored on large corpora and we decided that it was not suitable for our
experiment since we had relatively small models (&lt; 50k words). Anyhow, should we evaluate
pragmatics embeddings simply calculating a coefficient of variability? Perhaps the answer is yes, since
an extremely high variability would mean that we have a problem in our corpus or our data. On the
other hand, it is difficult to quantify how much variability should we accept while studying
computational pragmatics. This part would probably need dedicated research with a detailed analysis
of the variability of semantic fields and their related pragmatic instructions.</p>
      <p>What about readers embeddings then? We should accept as a compromise a probabilistic model, to
account for variability and complexity of human interpretation.</p>
      <p>Summing up, the encyclopedic model must be computed with methods that allow for complete
reproducibility, so that we have an accurate representation of the intentio operis. On the other hand, we
use probabilistic embeddings to represent the variability of the interpretation proposed by the model
reader. Regarding accuracy evaluation, the first step is to analyze the semantic field that has been
computed for the target word in our model, looking for possible semantic noise. The second step is to
verify the hypothesis of semantic noise using standard corpus linguistics metrics to evaluate the density
of our vectors.</p>
      <p>Concluding, we would like to pinpoint that extrinsic evaluation for computational pragmatics is not
possible. Evaluating word embeddings for tasks such as translation or classification is relatively easy
as we know what we are trying to accomplish with our models. In the case of computing a model reader,
we want to use our computational model to discover something that we do not (perhaps cannot) know
using other methods. What is fascinating of word embeddings models is not merely the fact that we can
compute the model readers but the fact that, for the first time in semiotic analysis, we can study them
data-driven with computational tools. We do not know in advance whether an inference is bad or good,
nor we know if our inferences are deep enough or if they could be improved. This is a new level of
complication in evaluating a process that is already hard to keep transparent and reproducible. The
problem then shifts from computational linguistics to epistemology.</p>
    </sec>
    <sec id="sec-5">
      <title>5. Conclusions</title>
      <p>Computational pragmatics with word embeddings is still unexplored in linguistics and semiotics,
while evaluation methods for word embeddings are vastly understudied also in other applications of
word embedding techniques.</p>
      <p>This work was meant as a first attempt to outline possible methods of evaluation for embeddings
specifically meant to study pragmatics. The evaluation is possible creating a fully reproducible semantic
model of an encyclopedic context using non-probabilistic algorithms; in our case study, we used Reinert
hierarchical classification (CHD). On the other, the variability of the model reader should be computed
with probabilistic embeddings to avoid a deterministic view of its functioning. We should then accept,
as a compromise, to compute our inferences with non-reproducible word embeddings.</p>
      <p>Further research is needed to find reliable quantitative metrics to evaluate word embeddings for
computational pragmatics as, by the time we are writing this paper, for pragmatics goals there are still
no studies on large corpora.</p>
    </sec>
    <sec id="sec-6">
      <title>6. References</title>
      <p>[18] A. Reinert. "Une méthode de classification descendante hiérarchique: application à l'analyse
lexicale par contexte." Cahiers de l'Analyse des Données 8.2 (1983) : 187-198.
[19] B. Wang, A. Wang, F. Chen, Y. Wang, and C. J. Kuo. "Evaluating word embedding models:
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[20] M.A. Bouchard, and S. Kasparian. "La classification hiérarchique descendante pour l’analyse des
représentations sociales dans une pétition antibilinguisme au Nouveau-Brunswick, Canada."
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[21] C. J. Fillmore. “Frame semantics and the nature of language.” Annals of the New York Academy
of Sciences, 280(1), 20-32. (1976)
[22] Violi, P. Significato ed esperienza. Studi Bompiani, 1997
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