Effective response to a health crisis requires society to forge a consensus on many levels: scientists and doctors have to learn about the disease and quickly and accurately communicate their research findings to others; public health professionals and policy experts have to translate the research into policies and regulations for the public to follow; and people have to follow guidelines to reduce infection threat. However, the fast-moving COVID-19 pandemic has brought into sharp relief our critical vulnerabilities at all these levels. Instead of orderly consensus-building, we have seen disagreement and controversy that exacerbated the disease. Research papers are rushed through the review, with results sometimes disputed or retracted 1 ; policy makers give conflicting advice; scientists and many in the public disagree on Copyright © 2020, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. 1 https://retractionwatch.com/retracted-coronavirus-covid-19papers/ many issues-from the benefits of therapeutics to the need for lockdowns and face covering. The conflicting viewpoints create conditions for polarization to color perceptions of the pandemic.
Polarization is characterized by division of a group by sharply contrasting opinions. While diverse opinions are necessary in a healthy society, political scientists have observed a phenomenon called pernicious polarization, where one social or cultural ideology precludes the possibility of a rational public discussion on the topic (McCoy and Rahman 2016). Surveys have identified a partisan gulf in the attitudes about COVID-19 and the costs and benefits of mitigation strategies. According to a Pew Report (Pew 2020), partisanship significantly affects perceptions of public health measures. Polarization has colored the messages of US political leaders about the pandemic (Green et al. 2020) , as well as discussions of ordinary social media users (Jiang et al. 2020) . Coupled with a distrust of science and institutions, polarization can have a real human cost if it leads the public to minimize the benefits face coverings or reject a vaccine when it becomes available.
Current research measures polarization as divergence of opinions along the political dimension and its effect on other opinions, for example, discussion of scientific topics (Bessi et al. 2016 ). However, opinions on controversial issues are often correlated (Baumann et al. 2020b ): for example, those who support transgender rights also believe in marriage equality, and those who oppose lockdowns also resist universal face covering. Inspired by this idea, we capture some of the complexity of polarization by projecting opinions in a multi-dimensional space, with different axes corresponding to different semantic dimensions. Once we identify the dimensions of polarization and define how to measure them, we can study dynamics of polarization and interactions between opinions.
Our work analyzes tweets related to the COVID-19 pandemic collected between January 21, 2020 and May 01, 2020 (Chen, Lerman, and Ferrara 2020). We study polarization along three dimensions-political (liberal vs conservative) and science (pro-science vs anti-science), and moderacy (hardline vs moderate). User alignments along the science axis identifies the polarization over scientific discus-sions related to the pandemic. A user's political identity is defined in a two dimensional space. Working in tandem with the political axis, the moderacy dimension recognizes the intensity of political standing from hardline to moderate. For the hardliners identified along moderacy dimension we leverage the political axis to identify their partisanship as Liberal or Conservative.
Leveraging a set of media sources that have been classified by nonpartisan sites along these dimensions, we identify a seed-set that define the poles of each dimension. These media sources include mainstream news and a large variety of other sources, such as government agencies, nongovernmental organizations, crowdsourced content, and alternative medicine news and health sites. We then describe network and content based inference methods to classify users along these multiple dimensions of polarization. Inferring the polarization of users discussing COVID-19 allows us to study the relationships between polarized ideologies and their temporal and geographic distributions. We show that political and science dimensions are highly correlated and that politically hardline users are more likely to be antiscience, while politically moderate users are more often proscience. We also identify regions of the US and timepoints where the different ideological subgroups are comparably more active and their topics of conversation.
The contributions of this work are as follows:
• We describe a framework for quantifying multidimensional polarization.
• We describe two novel methods to infer multidimensional polarization from the text of online conversations and compare their performance to state-of-the-art methods.
• We provide empirical evidence for multi-dimensional polarization in Twitter conversations about COVID-19.
• We study the relationships between these dimensions, showing that political and science dimensions are highly correlated.
• We study the geographical distribution of users with polarized opinions and identify US states with larger proportion of Twitter users along each polarized axis.
As the amount of COVID-19 information explodes, we need the ability to proactively identify emerging areas of polarization and controversy. Early identification will lead to more effective interventions to reduce polarization and also improve the efficacy of disease mitigation strategies.
Polarization is a well-recognized issue spanning the fields of psychology (Myers and Lamm 1976; Isenberg 1986) , political science (McCoy and Rahman 2016), and even physics (Sasahara et al. 2020) , as well as the present context of computer science (Conover et al. 2011) . The foundation of polarization starts with initial studies in psychology on group polarization (Myers and Lamm 1976; Isenberg 1986) , in which opinions of a group become more extreme than initial opinions of each individual. In the present context, this could help explain why initially moderate individuals become more entrenched in the left, right, or antiscience domains. Polarization is also explored in political science in order to explain its potential effects on government efficiency and democracy (McCoy and Rahman 2016; Somer and McCoy 2019). These results show commonly negative effects of polarization on governments, thus motivating many explorations into this field. Moreover, they distinguish political polarization-the effect of polarization on elections-from societal polarization-its effect on social connections, with extreme polarization affecting both.
While polarization has traditionally been measured using surveys (Pew 2020), in recent years researchers have instead begun to measure polarization with social media discussions (Conover et al. 2011; Bessi et al. 2016; Schmidt et al. 2017; Bail et al. 2018) . Three consistent effects in social media have been observed. First, there is strong polarization in what people consume, measured directly from content or indirectly from retweets (Conover et al. 2011; Smith et al. 2013; Schmidt et al. 2017) . In other words, people seem to selectively confine what they watch due to, e.g., confirmation bias (Nickerson 1998) , thus exacerbating polarization. Moreover, viewing information from the other ideological side does not necessarily affect ones opinion (Bail et al. 2018) . Second, polarization is seen in different fields not directly related to left-right political polarization. This includes climate science (Tyagi, Uyheng, and Carley 2020) and even opinions about the COVID-19 epidemic (Pew 2020). Our goal in this paper is to combine these separate findings to better understand how some of these polarizations, such as pro-or anti-science and left and right polarization, relate to one another.
Finally, polarization has had real-world consequences outside of elections, by shaping people's perceptions of the pandemic (Chen, Lerman, and Ferrara 2020; Green et al. 2020; Jiang et al. 2020) . Recent research finds, for example, that polarization has affected the language policy makers use (Green et al. 2020) , which can drive policies in different directions due to a disunited front. Moreover, sentiment towards government measures (Jiang et al. 2020) or towards medical professionals (Pew 2020), has become more polarized, further reducing the efficacy of public health measures. Our work extends on these results by exploring how polarization is more generally impacting beliefs in science, and to what degree is this correlates with partisan polarization.
Sadly polarization is not altogether unexpected. Simple models of human behavior that were inspired by psychology have been created over several years. Under the simple assumptions of social influence and selectively cutting ties with ideological opposites, echo chambers form with large disparate groups of people (Durrett et al. 2012; Baumann et al. 2020b; Sasahara et al. 2020; Baumann et al. 2020a) . This is also alike to homophily, in which users might form ties with people who are similar (McPherson, Smith-Lovin, and Cook 2001) . Echo chambers could then drive group polarization, and therefore drive the current social media landscape.
Our model work uniquely applies both network and text analysis to infer the degree of polarization in the network.
For text analysis, we apply a number of candidate methods inspired by previous research, such as Latent Dirichlet Allocation (LDA) (Blei, Ng, and Jordan 2003) , and hashtag bag-of-words (BOW) (Conover et al. 2011) . We, however, find the best results using text embedding. Text embedding was discovered in 2013 (Mikolov et al. 2013) , and was rapidly extended due to its uniquely useful features associated with both words and text (Pennington, Socher, and Manning 2014; Joulin et al. 2016) . The basic nature of these methods are to embed text into a vector space such that nearby vectors represent semantically similar text. Finally, to analyze networks, we apply a Label Propagation Algorithm (LPA) proposed by Raghavan et al., 2007 . This algorithm, while first applied to community detection in networks, effectively assumes homophily drives how opinions form, and therefore its performance would test to some degree how homophily drives polarization.
Our work differs from these previous methods via systematic analysis of multiple polarized dimensions in social media. We also contrast with previous work via multidimensional polarization of COVID-19. This provides a test of some results predicted in polarization models (Baumann et al. 2020b; Baumann et al. 2020a ).
We describe the data and methods for measuring polarization and also inferring it from text and online interactions.
In this study, we use a public dataset of COVID-19 tweets (Chen, Lerman, and Ferrara 2020). This dataset comprises of 115M tweets from users across the globe, collected over a period of 101 days from January 21, 2020 to May 01, 2020. These tweets contain at least one of a predetermined set of COVID-19-related keywords (e.g., coronavirus, pandemic, Wuhan, etc.). We specifically focus on tweets from users located in the US (at state-level granularity) based on information contained in their profile and tweets. This georeferenced dataset consists of 27M tweets posted by 2.4M users over the 101 day period.
We characterize individual opinions along three polarization dimensions. The political dimension, standard dimension for characterizing partisan polarization, captures the difference between Left/ liberal and Right/conservative political stances for users with Hardline opinions. The science dimension captures an individual's acceptance of evidence-based Pro-Science views or the propensity to hold Anti-Science views. People believing and promoting conspiracies, especially health-related and pseudo-scientific conspiracies, are often grouped in the anti-science camp. Finally, the moderacy dimension describes the intensity of partisanship-from Moderate or neutral opinions to politically Hardline opinions.
We begin with a set of web domains of curated information sources that were labeled along these dimensions by non-partisan organizations, such as Media Bias-Fact Check (https://mediabiasfactcheck.com/), Allsides (https:// https://www.allsides.com/) and Newsguard, which tracks coronavirus misinformation. We quantify a user's position along the dimensions of polarization by tracking the number of links to curated domains the user shares. Specifically, we extract domains shared by users in the 101 day period and filter for relevant domains present in our curated list of domains (Table 1) . This gives us a set of 136K users who shared Science domains, 169K users who shared Political domains and 234K users who shared domains along the Moderacy dimension. After filtering out users who shared fewer than three relevant domains, this leaves us with 18.7K users who have shared domains across all three dimensions. For each user, we compute a domain score δ along each of the three dimensions, as the average of mapped domain values of a dimension:
where, δ i is the domain score of user i and D i,d represents the set of domains shared by user i relevant to dimension d. Figure 1 shows the distribution of domain scores across the three dimensions for users who post domains across all three dimensions of interest. The distribution are peaked at their extreme values, showing more users sharing information from Anti-Science than Pro-Science domains and more Conservative than Liberal domains.
For network level analysis, we then built a web scraper that maps domains to their respective Twitter handles. The scraper initiates a simple Google query of the form "Domain N ame Twitter Handle". This tool relies on the search engine to rank results based on relevance and picks out the title of the first result containing the sub-string "|T witter". This substring is of the form "Account N ame (@handle)| Twitter" which is parsed to retrieve the domain's corresponding handle. We manually verified the mapped domains.
The mapped Twitter handles form our seed sets for semisupervised learning at the network level. Each dimension's seed-set comprises key-value pairs of Twitter handles and their corresponding orientation along the dimension. Table 2 illustrates the number of seeds along each polarization axis.
Using domain scores, we can quantify the polarization of just a small fraction (0.7%) of users in the dataset. In this section we describe how we leverage this data to infer the polarization of the remaining users in our dataset along multiple dimensions. In the results, we compare the performance of these inference methods.
We classify binned domain scores along each dimension because we find classifiers work better than regression in this dataset. In light of this fact, we bin the extreme ends of domain score distribution into two classes along each dimension as shown in Figure 1 .
Label Propagation Label propagation was used in the past to label user ideology based on the ideology of accounts the user retweets (see, for example (Badawy, Ferrara, and Lerman 2018) ). The idea behind label propagation is that people prefer to connect to-and retweet content posted by-others who share their opinions (Boyd, Golder, and Lotan 2010; Metaxas et al. 2015) . This gives us an opportunity to leverage topological information from the retweet network to infer users propensity to orient themselves along ideological dimensions.
To this end, we build a network from 9.8M retweet interactions between 1.9M users from the geocoded Twitter dataset. In the retweet network, an edge runs from A to B if, user A retweets user B. Descriptive statistics of the retweet network are shown in Table 2 . We then use a semisupervised greedy learning algorithm to identify clustsers in the retweet network. LPA proposed by (Raghavan, Albert, and Kumara 2007) is a widely-used near-linear time network community detection algorithm. This greedy learning approach starts off with an initial random label assignment and, iteratively re-assigns labels to nodes along a dimension. This reassignment eventually converges to a state of equilibrium where all nodes in the network are assigned labels which are shared by the majority of their corresponding neighbors. However, owing to arbitrary tie-breaking, a certain amount of randomness creeps into the results produced by this algorithm. Courtesy of this stochasticity, LPA tends to generate different cluster assignments (user polarization) for the same network.
We extend the method used by (Conover et al. 2011) to measure user's political ideology to additional dimensions of interest. First, we identify seed hashtags defining the extremes of each dimension of polarization and generate vectors of 100 hashtags that co-occur with these seeds. For the Science dimension, the two seed hashtags we picked are #stayhome and #plandemic. For the Political dimension, we identify hashtags that co-occur with the seeds #trumpvirus and #chinavirus; and for the Moderacy dimension, we find hashtags co-occurring with two moderate seeds -#pandemic, #lockdown and two hardline seeds -#trumpvirus, #chinavirus . We then, compute the dimension-wise TF-IDF transformations of corresponding vectors to generate feature vectors for each user, representative of each user's content along a dimension over time.
However, this method suffers from a critical shortcoming: a significant number of users don't use any of the hashtags in our seed sets. This results in empty feature vectors. Considering only users with non-zero feature vectors and domain scores along each dimension gives us 1.96K users along the Science dimension, 1.6K users along the Political dimension and 4.6K users along the Moderacy dimension.
To infer user polarization, we train a simple Logistic Regression model on the feature vector matrix with the domain scores as ground truth.
To reduce the dimensionality of hashtag feature vectors, we use LDA (Blei, Ng, and Jordan 2003) to identify topics, or groups of hashtags, and represent users as vectors in this topic space. In contrast to the hashtag BOW method, we consider all hashtags generated by a user as a document representing that user (after ignoring hashtags used by fewer than 10 users or more than 75% of the users)-leaving us with 25.2K hashtags. We use 20 topics, as that gives the higher coherence score. We use the document-topic affinity matrix generated by LDA to represent users. An affinity vector is comprised of 20 likelihood scores, adding up to 1, with each score indicating the probability of corresponding topic being a suitable representation for the set of hashtags generated by the user. Using these affinity vectors, we generate feature vector matrices for each of the three dimensions of interest. In doing so, we can represent over 900K users who use some hashtag in their tweets with a dense vector of length 20.
Text Embedding Previous methods (see (Conover et al. 2011) ) classified user's political polarization based on the text of their tweets by generating TF-IDF weighted unigram vectors for each user. However, the advent of more powerful text-embedding techniques (Mikolov et al. 2013; Pennington, Socher, and Manning 2014; Joulin et al. 2016) allows us to generate sentence embedding vectors to better represent content.
We group the tweets generated by each of the 2.4M users over a 101-day period from January to May 2020. More specifically, we collect all tweets generated by a user in this time period and concatenate them to form a text document for each user. After preprocessing the 2.4M documents to remove hashtags, URLs, mentions, handles and stopwords, we use fastText sentence embedding model pretrained on Twitter data, to generate tweet embeddings for each user. The Sent2vec Python package (Gupta, Pagliardini, and Jaggi 2019) provides us with a Python interface to quickly leverage the pretrained model and generate 700-dimension feature vectors representing each user's discourse.
First, we visualize the domain scores of the 18.7K user, showing the relationship between the Science, Moderacy and Political dimensions. Then we compare the performance of algorithms for classifying users along the three dimensions of polarization, using domain scores as ground truth data. We used the inferred scores to study the dynamics and spatial distribution of polarized opinions of users engaged in online discussions about COVID-19. Figure 2 shows the relationship between dimensions of polarization, leveraging domain scores of 18.7K users who shared information from curated domains. The heatmap shows the density of users with specific domain scores. Large numbers of users are aligned with Pro-Science-Left (top-left corner) or Anti-Science-Right (bottom-right corner) extremes, with lower densities along the diagonal between these extremes ( Fig. 2(a) ). This illustrates the strong correlation between political partisanship and scientific polarization, thereby highlighting the influence of pernicious political divisions on evidence-based discourse during the pandemic, with Conservatives being more likely to share Anti-Science information than Pro-Science sources. Figure  2(b) , highlights the interplay between the Science and Moderacy axes. The white region in the bottom right corner shows there are few Anti-Science users who are politically moderate. The shading also highlights a higher density of Pro-Science users identifying as politically moderate.
To run the LPA, we start from a set of labeled seeds-Twitter handles corresponding to domains categorized along the dimensions of interest (Tables 1 & 2) . We reserve some of the seeds along each dimension for testing LPA predictions and report accuracy of 5-fold cross validation.
For content-based approaches, we used binned domain scores of 18.7K users as ground truth data to train Logistic Regression models to classify user polarization along the three dimensions. We represented each user as a vector of features generated by different content-based approaches: hashtag frequencies for the BOW approach, topic vectors for LDA and sentence embeddings for the fastText approach. We reserved a subset of users for testing performance. Table 3 compares the performance of polarization classification methods. LPA works best when it tries to identify user alignment along the Political and Science dimensions. However, it fails to capture the subtler distinctions along the Moderacy axis. Training is further hampered by the low number of retweet interactions with Moderate domains in comparison to Hardline ones. Of the 1.8M retweet interactions, only 250K involve some Moderate seed nodes, whereas over 1M interactions involve some Hardline seed nodes. Moreover, poor classification performance with LPA reveals an important pattern: that moderates surround themselves with diverse opinion and thus a clear distinction cannot be made by observing who they retweet.
Hashtag BOW describes users as vectors of weighted frequencies of hashtags they use. This method critically suffers from the curse of dimensionality and the lack of uniformity of usage among users. Since the dimensionality of hashtag vectors is the entire vocabulary, each vector describing a user is sparse, resulting in non-competitive performance.
LDA modeling on hashtags allows us to generate reduceddimension, dense feature vectors for over 900K users who use hashtags in their tweets. This representation allows us to design better learning models that significantly outperform the Hashtag BOW and LPA models.
A Logistic Regression model trained on user-text embeddings and domain scores (fastText) outperforms all other models described in this study. Coupled with fastText's ability to better handle out-of-vocabulary terms, the model's access to finer levels of detail at tweet text, culminates in it better predicting dimensions of polarization. Given the model's superior performance across all three dimensions, we lever- age its predictions in subsequent analyses. We classify users along the three polarization dimensions. However, since the definition of the Hardline extreme of the Moderacy dimension overlaps with the Political dimension, we need to report only six ideological groups, rather than all eight combinations. 
Research shows that opinions of Twitter users about controversial topics do not change over time (Smith et al. 2013) . To investigate whether user alignments along the three polarization dimensions change over time, we group tweets by time into seven biweekly intervals: January 21-31,2020; February 1-15,2020; February 16-29, 2020; March 1-16, 2020; March 17-31, 2020; April 1-15, 2020 ; April 16-May 1, 2020. There are 3.0K users who tweet consistently in all the 7 biweekly intervals. For each of the N users, we compute cumulative domain scores along Science, Political and Moderacy dimensions for all time intervals t and compute the average absolute change∆ t,t−1 in domain score from biweekly period t − 1 along each dimension given by,
t represents the domain score for a user i in biweekly period t. The small values of∆ t,t−1 in Table 4 confirm that user alignments do not change significantly over time.
Although individual's alignments do not change, the number of users within each ideological group does change over time. User alignments do not change, therefore we leverage polarization classification results to show biweekly fractions of active users per ideological category. Figure 3 shows the composition of active users in all categories. As time progresses, we can clearly see the growth in the Pro-Science-Moderate category accompanied by a corresponding decline in Anti-Science-Right users.
To better understand what each of the six groups tweets about, we collect the 50 most frequent hashtags used by each group, after removing hashtags common to all six groups. Figure 4 shows the wordclouds of the most common hashtags within each group, sized by the frequency of their occurrence. Most striking is the use of topics related to conspiracy theories, such as #qanon, #wwg1wga, by the Anti-Science-Right group, along with politically charged references to the #ccpvirus and #chinavirus. This group also uses hashtags related to President Trump's re-election campaign, showing the hyper-partisan nature of COVID-19 discussions. Another partisan issue appears to be #hydroxychloroquine, a drug promoted by President Trump. It shows up in both Pro-Science-Right and Anti-Science-Right groups, but is not discussed by other groups.
The polarized nature of the discussions can be seen in the user of the hashtags #trumppandemic and #trumpvirus by the Left and Pro-Science groups. However, in contrast to Anti-Science groups, Pro-Science groups talk about COVID-19 mitigation strategies, using hashtags such as #stayhomesavelives, #staysafe and #flattenthecurve.
Responses to the coronavirus pandemic in the US have varied greatly by state. While governors of New York, California, Ohio and Washington reacted early by ordering lockdowns, governors of Florida and Mississippi have downplayed the gravity of the situation for a longer time. To explore the geographical variation in ideological alignments, we group users by the state from which they tweet and compute the fraction of their respective state's Twitter users belonging to an ideological group. We then generate geo-plots, shown in Figure 5 , to highlight the ideological composition of each state.
We see a higher composition of Pro-Science-Moderates ( Figure 5(b) ) in Washington, Oregon, DC, Vermont. As expected, these states have a lower fraction of Anti-Science users as can be seen from Figures 5 (d) ,(e) and (f). Governors of these states were quick to enforce lockdowns and spread pandemic awareness amongst the general public.
Over the course of the pandemic, we have seen the strong opposition to masking mandates and closing down of businesses in California, Nevada, Hawaii, Georgia and Texas. These anti-science sentiments are reflective in Figure 5 (e), which shows that these states have a comparatively higher proportion of their Twitter users in the Anti-Science-Moderate ideology group.
States such as South Carolina, Mississippi, Louisiana, Wyoming, Texas and Arizona have had chequered responses to the pandemic with political and religious leaders consistently downplaying the pandemic. The geo-plot is reflective of the same with these states have a higher fraction of Anti-Science hardline-right users.
Our analysis of a large corpus of online discussions about COVID-19 confirm the findings of opinion polls and surveys (Pew 2020): opinions about COVID-19 are strongly polarized along partisan lines. Political polarization strongly interacts with attitudes toward science: conservatives are more likely to share conspiracy and anti-science information, while liberals and moderates are more likely to share information from pro-science sources. On the positive side, we find that the number of pro-science, politically moderate users dwarfs other ideological groups, especially antiscience groups. This is reassuring from the public health point of view, suggesting that a plurality of people are ready to accept scientific evidence and trust scientists to lead the way out of the pandemic. The geographical analysis of polarization identifies regions of the country, particularly in the South and the West where anti-science attitudes are more common. Messaging strategies should be tailored in these regions to communicate with science skeptics. A larger issue of polarization is that it creates societalscale vulnerabilities by amplifying distrust of authorities and making it easier for malicious actors to influence public opinion through concentrated digital misinformation campaigns (Thorp 2020; Ferrara 2020). Amplifying the negative opinions about face coverings or vaccines within even a fraction of the population could create a cascade of adverse effects. Once polarization gets a life of its own it can lead to political instability, paralysis, and at worst democratic erosion (Conover et al. 2011; McCoy and Rahman 2016) . If societal trust is weakened, cynicism towards politics intensifies and confidence in public institutions wanes (McCoy and Rahman 2016). Because we find a slow-but-steady increase in moderate users, we believe that ongoing efforts to inform the public could be benefiting user behavior online.
Although we show good performance on classifying polarized opinions, additional work is required to infer finergrained opinions. Namely, by predicting fine-grain polarization among users, we could better infer, for example, network effects such as whether users prefer to interact with more polarized neighbors. Moreover, longer-term trends need to be explored in order to better understand how opinions change dynamically. This will better test whether whether social influence or selective formations of ties are the drivers of echo chambers and polarization. Finally, we want to explore polarization across countries to understand how different societies and governments are able to address polarization and how these polarized dimensions relate to one another across the world.