# Temporal Analysis of Misinformation on Parler

Eliana Norton
School of Journalism and Communication
The University of Oregon
<EMAIL_ADDRESS>
Thaïs Thomas
College of Arts and Sciences
The University of Oregon
<EMAIL_ADDRESS>
Akaash Kolluri
Computational Media Lab
The University of Texas at Austin
<EMAIL_ADDRESS>
Torie Hyunsik Kim
School of Journalism and Media
The University of Texas at Austin
<EMAIL_ADDRESS>
Dhiraj Murthy
School of Journalism and Media
The University of Texas at Austin
<EMAIL_ADDRESS>

###### Abstract

Social media platforms have facilitated the rapid spread of dis- and mis-
information. Parler, a US-based fringe social media platform that positions
itself as a champion of free-speech, has had substantial information integrity
issues. In this study, we seek to characterize temporal misinformation trends
on Parler. Comparing a dataset of 189 million posts and comments from Parler
against 1591 rated claims (false, barely true, half true, mostly true, pants
on fire, true) from Politifact, we identified 231,881 accuracy-labeled posts
on Parler. We used BERT-Topic to thematically analyze the Politifact claims,
and then compared trends in these categories to real world events to
contextualize their distribution. We identified three distinct categories of
misinformation circulating on Parler: COVID-19, the 2020 presidential
election, and the Black Lives Matter movement. Our results are significant,
with a surprising 69.2% of posts in our dataset found to be ’false’ and 7.6%
’barely true’. We also found that when Parler posts (’parleys’) containing
misinformation were posted increased around major events (e.g., George Floyd’s
murder).

_K_ eywords Misinformation $\cdot$ Parler $\cdot$ Temporal Trends

##  1 Introduction

Social media platforms have been linked to viral misinformation dissemination
[1]. While many social media platforms have taken steps to respond and prevent
harms from misinformation [2, 3], Parler, a US-based alt-right conservative
social media platform, Parler intentionally limits fact-checking on its
platform in the name of free speech [4]. Moreover, Parler posts were found to
be spreaders of harmful misinformation [5]. Furthermore, posts removed from
mainstream social media platforms due to information integrity systems have
remained on Parler [6]. For example, misinformation stating that Donald Trump
won the 2020 US election and that Democrats vote rigged spread widely on
Parler but were labeled as misinformation on other main-stream social media
platforms [7]. COVID-19 misinformation was also widely spread on Parler [8].

Through a case study of Parler which identifies types of misinformation, their
distribution, and their relation to real-world events, this study add to our
understanding of the role of niche, extreme social media platforms and the
roles they might play in the circulation of misinformation online.
Misinformation has been widely studied on mainstream platforms [9, 10]. While
studies have characterized Parler as a platform with a large volume of posts
with misinformation related to the 2020 election [11] and anti-vaccine
misinformation [12], there remains a dearth in the literature of those that
empirically quantify misinformation dissemination across the platform.

##  2 Background

###  2.1 The Emergence of Alt-right Social Media Platforms and Parler

As mainstream social media platforms such as Facebook, Twitter, Instagram, and
even YouTube, started to regulate content, alternative right-wing platforms
such as Parler gained popularity among users in the US who were censored or
banned from mainstream platforms [13]. While many studies examine
misinformation on mainstream social media platforms such as Twitter, there are
far fewer studies about misinformation that focus on alternative, far-right
platforms such as Parler [14]. It is critical to study a variety of non-
mainstream social media platforms, such as Parler in order to gain valuable
insights that studies of Twitter cannot provide. Parler functions very
similarly to Twitter. Posts on Parler are called ‘parleys’ and can be
‘echoed’, which is similar to retweeting on Twitter. Individual users are
called ‘citizens’ and can be ‘verified’ by presenting a valid identification
(e.g., submitting a photograph of themselves and a government-valid photo
identification - [15]. In the same manner as ‘likes’ work on Facebook, Parleys
can only be upvoted; however, comments on parleys can be either upvoted or
downvoted.

Parler is a predominantly US-focused, right-wing social networking service
launched in 2018, which gained popularity by advertising minimal rules and
content guidelines, drawing attention from users censored or banned on other
social media platforms for violating their terms of service [11]. The move to
Parler was led by a group of far-right opinion leaders actively encouraging
migration away from Twitter, such as Mark Levin, a famous talk radio host, and
Maria Bartiromo, Fox News’s news anchor [16]. This exodus was generally
comprised of “conservatives, Trump supporters, religious, and patriot
individuals” [15] who were attracted by the minimal censorship of the
platform. Those included some of the same groups found to be responsible for
instigating the U.S. Capitol Insurrection, which led to hosting services such
as Amazon to de-platform Parler due to its role in giving individuals a space
to organize the event [17]. Before Parler was de-platformed, it had over 10
total million users, with, at its peak on November 9th, 1.4 million users
joining in a single day [15]. This sudden surge of individuals on Parler was
largely due to real-life events such as the American presidential election
[15].

The hashtags mentioned in Parler posts tend to be skewed to the US right wing
(e.g., #stopthesteal, #maga, #trump2020, #votefraud) [11]. Unlike Twitter
where trending hashtags are more evenly distributed, Parler had a skewed
distribution of trending hashtags eg. #stopthesteal was present in 70% of
parley- [11]. This relative homogeneity of political opinions among Parler
users (i.e., right-leaning) contributes to the medium’s role as an echo
chamber. This is similar to Gab, which is also driven by a small number of
elite users, termed “super participants” [18]. [19] comment that this “turns
the platform into an echo chamber for its largest users.” A few right-wing
leaders make up a high percentage of posts on Parler, and the traffic is not
organic, according to [20] calculation of identifying traffic manipulation on
social media [11].

Previous work has found that right-wing social media activity has been found
to engender subsequent, off-line right-wing events. Using geo-temporal data
from Parler alongside ‘right-wing unrest’ data, which is represented by the
Armed Conflict Location and Event Data (ACLED) database, [21] discovered that
prior social media activity and neighboring counties’ right-wing events lead
to subsequent right-wing unrest in the county. They also found that this does
not hold with the inverse, meaning that right wing unrest does not inspire
right wing social media activity. Moreover, others have found that there is a
strong positive correlation between war fatalities in foreign countries and
the number of Parler video uploads from a county [22]. [22] also identified
the correlation between the percentage of the county’s population being white,
the number of people serving in the military before 2003, and Parler activity.

###  2.2 Misinformation on Parler

Misinformation is false or inaccurate information, which is not necessarily
intentionally propagated [23]. Mainstream platforms such as Twitter and Reddit
actively monitor their content and attach warnings to information identified
as potentially containing misinformation. For example, Twitter banned former
US President Donald Trump from the social media platform [24]. As it is
advised by media literacy authorities for users to critically evaluate
information sources [25], users on the prominent platforms often actively flag
potential misinformation themselves [26]. In contrast, Parler does not have
such a system to curb the spread of misinformation and problematic posts
appear and spread on the platform constantly [5]. Parler’s prime coincided
with the start of the COVID-19 pandemic and the 2020 US presidential election,
which enabled it to play a significant role in the propagation of
misinformation related to these events. For example, in the case of the 2020
US presidential election, Parler provided an important space for like-minded
individuals to post about election fraud-related conspiracies and other
election-related misinformation under the hashtags ‘#stopthesteal’ or
‘#trump2020’ [11]. Specifically, misinformation about electoral fraud online
decreased by 73% shortly after Twitter suspended Trump’s account and Parler
was de-platformed [27]. Parler been found to amplify misinformation and
disinformation for right-leaning Americans on issues such as COVID-19 [8]. For
example, posts on Parler were found to have supported anti-vaccination (anti-
vax) campaigns as well as disseminating misinformation and disinformation,
such as vaccines being used as a population control mechanism [12].

###  2.3 Impact of Misinformation

Despite the efforts taken by mainstream platforms to mitigate the spread of
misinformation [9], there remains a plethora of both accurate and inaccurate
information, making it difficult to rapidly gauge the veracity of content on
social media [28]. Unlike research produced by experts, misinformation is
dangerous because it needs no evidence base, knowledge or methods to produce
[28]. Especially during the COVID-19 pandemic, misinformation and conspiracies
in the pandemic have blurred the lines between normally separate groups,
causing further tension in racialized posts as they become intertwined with
scientific disputes [28]. For example, before the pandemic, anti-vaccine and
neonazi groups would have been distinct, but collective sentiments against
“liberal” scientific issues united these groups and has disproportionately
disadvantaged Black Americans [29]. Due to the mass polarization that seems to
be fueled by misinformation, some have termed the coronavirus pandemic as an
infodemic [28].

With the spread of misinformation, scientific claims have become increasingly
politically polarized, and as a result, some people distrust science if it
goes against their beliefs [30]. There has been much misinformation revolving
around cures for COVID-19, from essential oils to cow excreta. However none of
the so-called cures have been backed up by scientifically proven evidence [9].
COVID-19 misinformation is often dangerous, as demonstrated in June 2020, when
15 people in the US consumed disinfectant because they believed it would
prevent them from catching COVID-19, leading to four people dying and three
people becoming permanently visually impaired [9].

Misinformation reinforces cognitive biases, further leading to racism and
polarized political and social beliefs [31]. The chain of misinformation makes
it so that those believing an initial piece of misinformation can continue to
seek out similar information, thus creating entire communities and mindsets
around a false occurrence [32]. Due to the algorithms that platforms are built
on, users are continuously presented with new content, leading to more and
more opportunities for misinformation to become the dominant content [33].
Media has a certain way of reinforcing what the user wants to believe, which,
in many cases, involves the negative stereotyping of groups said user does not
particularly like. Racial stereotyping, in particular, is one of the most
commonly accepted yet detrimental forms of racism and misinformation present
in the media. In the United States, people of color watch film and television
with the underlying notion that the media aims to help maintain white
supremacy [34]. In a hegemonic white society such as ours, these stereotypes
single out minority groups and maintain white power [35].

###  2.4 Detection of Misinformation

Social media platforms flag posts as “rated false” or “disputed,” but these do
not tend to change people’s views [36]. That being said, fact checking remains
critical both to misinformation detection as well as helping to better inform
the public. Politifact, a political fact-checking website, uses a 6-point
scale to show the authenticity of claims made by elected officials [37].
Pennsylvania State University created a fact-checking framework, called SAME,
which uses Politifact and GossipCop, making it more effective than other
state-of-the-art methods [37]. Politifact was found to have an accuracy rate
of 93%, a specificity rate of 90%, a precision rate of 97%, and a recall value
of 90%, with its overall rating being 90% [38]. Fact-checking websites like
Politifact help to improve the quality of information that is reaching society
[37]. Politifact uses fact-based methods to determine the accuracy of news and
has been used to validate and determine the effectiveness of fact-checking
models [39, 40, 41].

Machine learning has also provided automated and scalable systems for
detecting misinformation. Machine learning is a branch of AI that uses data to
predict human interaction. This is the same thing that is used for chatbots
and Netflix algorithms [4]. It also efficiently uses algorithms to predict
misinformation. Aside from Politifact, fuzzy matching is another machine
learning tactic that is used to identify similar elements of text. There have
been other studies using similar methods of fuzzy matching and Politifact data
to better detect misinformation [42, 43] However, while machine learning is
more efficient, users are less likely to trust machine learning labels [44]
than human-derived warnings on posts [45].

##  3 Research Questions

Given the dearth of studies specifically quantifying the amount of
misinformation on niche, extreme social media platforms, this study seeks to
answer the following research questions: RQ1: What types of misinformation
circulate on Parler?, RQ2: How has the distribution of different types of true
and false information changed over time on Parler? and RQ3: Is the frequency
of posts with misinformation associated with real world events?

##  4 Methods

###  4.1 Datasets

We used a publicly available dataset of 183 million comments and posts made by
4.4 million Parler users [15]. The dataset is composed of 98.5 million posts
and 84.5 million comments. [15]. We restricted our study’s scope to posts and
comments made from January to September of 2020.

For our fact checked claims list, we scraped claims made between January 2020
and September 2020 from Politifact111https://www.politifact.com, an
authoritative fact-checking website that classifies a wide range of
information circulated on social media into six categories (pants-on-fire,
false, mostly-false, halt-true, mostly-true, true) depending on
trustworthiness. There were a total of 1591 claims we collected. These
instances serve as benchmarks for which we compare the information in our data
source to verify as true or false.

###  4.2 Fuzzy Matching

We used the package FuzzyWuzzy222https://pypi.org/project/fuzzywuzzy/ to
conduct an approximate string matching between the Parler post and the given
misinformation key from PolitiFact. A partial ratio was calculated rather than
direct string matching because the Parler posts were considerably longer than
the misinformation statements. All data that had below 20% score from
FuzzyWuzzy (indicating a strong match) was kept.

###  4.3 Analytical Methods

To answer RQ1: "What types of misinformation circulate on Parler?", we used
BERTopic, a topic modeling method that uses Bidirectional Encoder
Representations from Transformers (BERT) embeddings and c-TF-IDF, to
thematically break the Politifact statements into categories. Since BERT
produced many different categories, we manually sorted these categories into
posts related to COVID-19, US Politics, and Black Lives Matter (BLM): the
three most prevalent groups.

To answer RQ2: "How has the distribution of different types of true and false
information changed over time on Parler?", we created and studied graphs of
the distribution of the 6 nominal categories from PolitiFact (“true”, “mostly-
true”, “half-true”, “barely-true”, “false”,”pants-on-fire”) and their
distribution over each month from January to September 2020.

To answer RQ3: “Is the frequency of posts with misinformation associated with
real world events?”, we first created comprehensive timelines of key events
related to our 3 categories – COVID-19, the US election, and BLM. For
COVID-19, we used a timeline from the Center for Disease Control that
discusses key milestones in US cases numbers as well as political responses to
COVID-19, the role out of vaccines, and economic milestones [46]. For BLM, we
used an existing timeline of milestone [47, 48, 49, 50, 51]. For US
election/politics, we used a timeline of key events in the 2020 presidential
election [52, 53, 54]. See Appendix A for tables with timelines for all
categories.

After collecting data on the temporal distribution of accurate and inaccurate
information related to our categories (organized monthly), we analyzed the
relationship between temporal misinformation trends by month and our timeline
of key events.

##  5 Results

###  5.1 Categories of Misinformation

To answer RQ1: “What types of misinformation circulate on Parler?", we
successfully categorized content into three main categories: COVID-19, the
2020 US presidential election, and the Black Lives Matter (BLM) Movement.
Table 1 illustrates the distribution of themes by category based on our
BERTopic results. The top 15 categories are included. The majority of topics
are related to politics. In this category, misinformation related to voting
(1), Joe Biden (2), Nancy Pelosi (4), taxes (7), the conflict between Iraq and
Iran (8), Kamala Harris (9), and schools (10) were found. Under COVID-19, we
found misinformation related to face masks (3), Bill Gates and Anthony Fauci
(5), deaths due to COVID-19 (6), COVID-19 (13), the relationship between COVID
and China (14), and water killing the COVID-19 virus (15). Under BLM,
misinformation related to the movement (11) and Jacob Blake (12) were mostly
found.

Category Number | Number in Category |  Top Words
---|---|---
1 | 100 |  ballots, voting, election, mail
2 | 68 |  joe, biden, video, shows
3 | 54 |  masks, mask, wearing, face
4 | 51 |  pelosi, nancy, pelosis, speaker
5 | 31 |  gates, bill, fauci, anthony
6 | 29 |  covid19, death, covid, deaths
7 | 28 |  tax, joe, biden, taxes
8 | 28 |  iraq, iran, beirut, iranian
9 | 26 |  harris, kamala, said, next
10 | 25 |  teachers, schools, education, we
11 | 24 |  black, lives, matter, white
12 | 22 |  kenosha, jacob, police, kyle
13 | 22 |  coronavirus, corona, predicted, virus
14 | 21 |  chinese, china, coronavirus, wuhan
15 | 20 |  kills, coronavirus, it, water

Table 1: BERT-Topic categories of Politifact Statements count

We found high levels of misinformation related to voting in the 2020
presidential election. This includes Trump’s claims of election rigging based
on ballots (1) being “found” and supposedly defective machinery [55].

During the COVID-19 pandemic, we found misinformation circulating that claimed
face masks cause harm to the people wearing them [56]. Initially, the CDC had
attempted to be more reserved with mandating face masks in an attempt to
ensure healthcare workers had adequate supplies of masks. However, they later
changed this to mandate masks after learning more about the virus, sparking
distrust amongst some members of the public [57]. Misinformation relating to
Bill Gates and Anthony Fauci (5) tended to claim that both played a role in
the origin of COVID-19, while other people claim that Bill Gates put
microchips inside of the vaccine [58].

BLM-related misinformation (11) tended to be related to the right-wing
counter–response movements ‘all lives matter’ and ‘white lives matter’ [59].
Jacob Blake-related misinformation (15) tended to be related to Jacob Blake,
who was shot in August 2020 and partially paralyzed by a police officer. As no
charges were brought upon the officer by the US Justice Department, this
sparked widespread protests to the defund the police [60] . Users on Parler
circulated misinformation regarding Blake and the officer that shot him.

###  5.2 Temporal Distribution of Misinformation

To answer RQ2: “How has the distribution of different types of true and false
information changed over time on Parler?”, we studied the monthly distribution
of the varying degrees of truth found in Parler misinformation. As seen in
Figure 1, the majority of claims matching Politifact on Parler were ‘strictly
false’, often spiking after events that Parler users might consider
outrageous. The distributions for information related to COVID-19, the US
election, and BLM (the main categories of misinformation found using the
BERTopic) are shown in figures 2-4 respectively. Misinformation occurs
throughout the year in all three categories. As Figures 1 and 4 indicate, the
peak of misinformation frequency for BLM and misinformation generally for
Parler was in June and July. Meanwhile as Figure 2 illustrates, the peak of
COVID-19 misinformation was seen in July. As Figure 3 indicates, the peak for
US election misinformation was in July and September.

Figure 1: The distribution of accuracy-rated posts from January to September
2020 on Parler.

Figure 2: The distribution of accuracy-rated posts related to US Politics from
January to September 2020 on Parler.

Figure 3: The distribution of accuracy-rated posts related to COVID-19 from
January to September 2020 on Parler.

Figure 4: The distribution of accuracy-rated posts related to the Black Lives
Matter movement from January to September 2020 on Parler.

###  5.3 Misinformation and Real-World Events

To answer “RQ3: Is the frequency of posts with misinformation associated with
real world events?”, we compare the trends found in figures 1-4 with the
timeline of events created in Appendix A. As mentioned above, spikes in the
misinformation trends occurred during more controversial, polarizing real-
world events, which led to increased volumes of posts with misinformation on
Parler in response.

####  5.3.1 2020 US Presidential Election

In January 2020, the US House of Representatives appointed impeachment
managers, and John Delaney dropped out of the Democratic presidential race. A
decrease in information about elections is seen on Parler in February, 2020
when the US Senate ruled that Donald Trump was not guilty. We found a slight
increase in misinformation in March through May, 2020, with May, 2020 showing
the highest levels of true information being shared. In March, 2020, Pete
Buttigieg and Amy Klobuchar dropped out of the presidential race, and in
April, 2020, Bernie Sanders announced that he would be endorsing Joe Biden. In
May, 2020, Trump announced his plans to label Antifa as a terrorist
organization and put the blame on “far-left extremist” groups for starting
riots. There was a significant increase in misinformation between June and
September, 2020, with September reaching a peak. In June, 2020, a poll done by
CNN showed Biden in the lead by 14 points and Trump’s presidential campaign
asked for it to be taken down. Additionally, Biden declined to do another
televised debate with Trump. Biden was officially chosen as the Democratic
presidential nominee and Kamala Harris as his vice presidential running mate
in August, 2020. In September, 2020, when the peak of misinformation is seen,
Trump not only declined a peaceful transfer of power but he also held a rally
despite concerns about COVID-19, which led to canceling a previous rally.

####  5.3.2 COVID-19

The identification of COVID-19 was met with a lot of misinformation posted on
Parler. A minor increase in half-true information was seen on the app in
February, 2020. However, in March and April, 2020, there were two major spikes
of misinformation. In March, 2020, this was due to COVID-19 being officially
declared as a pandemic by the CDC and the placement of the travel ban. In
April, 2020, there was a push by some doctors and civil rights groups to make
the CDC and the government release the race and ethnicity data related to
COVID-19 cases so that people could quantify how the virus impacts people of
color. In June 2020, the number of confirmed COVID-19 cases in the United
States exceeded 2 million. This news led to an increase in fear in some
individuals, which was associated with marked increases in ‘false’ and
‘barely-true’ information since the previous month. The increase in false
information was associated with the announcement that asymptomatic individuals
can spread the virus, the Trump Administration telling hospitals to send their
hospitalization rates and equipment availability to a system used by a private
contractor instead of the CDC, and the announcement CDC made asking people to
wear face masks. There is a significant decrease in information about COVID-19
being shared on the platform in subsequent months.

####  5.3.3 Black Lives Matter

From the New York Times and AP News timelines, posts began emerging after the
murder of George Floyd on May 25, 2020 and spiked in the following months as
the trials proceeded and protests became widespread. This aligns with the
frequency of misinformation on Parler. The murder of George Floyd sparked the
beginning of national news coverage, coinciding with the smattering of posts
beginning to appear in the BLM timeline. In June, 2020, nearly 30,000 posts
related to BLM were made, which occurred synchronously with hundreds of
protests occurring around the country and the Defund the Police movement
becoming popular. By July, 2020, posts created dropped by about 10,000, still
vastly higher than in the months prior, as the legal battle involved with the
case proceeded. By August and September, 2020, the posting rate decreased
significantly, dropping first to around 5,000 and 7,000, which is unsurprising
as protests diminished.

##  6 Limitations

There are limitations involved with our method of misinformation detection.
Politifact is not an exhaustive list of claims that are made online. However,
the findings of this study remain useful because, even operating at a subset
of the misinformation on Parler, we can still discern general, relative
trends. The fuzzy matching algorithm also creates inaccuracy in detection,
since some claims have been misflagged and some may have been missed. Future
work in these areas is needed to address these limitations.

##  7 Discussion

Based on our findings, we were able to successfully group the misinformation
that circulated on Parler in 2020 into three distinct categories: COVID-19, US
Politics, and the Black Lives Matter movement. Between the categories of Black
Lives Matter, COVID-19, and US Politics, the majority of the posts were found
to be false. Based on previous work [61], other social media platforms such as
Twitter and Reddit have shown that misinformation tends to reappear and be
reposted while “true rumors” do not. This coincides with the spikes in the
data signifying increases in misinformation posts on Parler. These spikes
correlate to real-world events that are occurring at the same time of the
posts. As discussed in Section 5, there also tends to be overlaps between
categories leading to a huge spike in multiple graphs during the months of
June and July. These were key months for both the BLM and COVID-19 timelines,
parallel to the mass posting and protests around the death of George Floyd and
the spiking increase of COVID-19 cases from 2 to 3 million cases in the US
[46].

The level and scope of misinformation on Parler is concerning and could have
influenced large numbers of people. Additionally, previous work has found that
once misinformation appears in a user’s social feed, it tends to persist in
their feed [33]. On Parler which purposely avoids the use of fact-checking
mechanisms, misinformation was being newly generated and shared. While it has
been found that many people will actively avoid ideologies that do not reflect
their own [30], most other platforms try to minimize the consequences of this
by flagging posts and removing content or adding warning labels to posts.
While previous studies have found that this is not necessarily an accurate
measure of misinformation [36], it is still more useful in fact-checking than
not having any detection method at all.

##  8 Conclusion

Our findings quantify the prevalence of misinformation on Parler and makes
clear that misinformation on niche, extreme social media platforms needs to be
taken seriously and empirically studied. There can still be a recognition
between the difference of opinion and information that is false regarding
science and political/social movements, but creating clearer guidelines for
social media platforms might contribute to a more transparent environment with
the premise that fact-checking should be employed (perhaps through legal
enforcement). Though we did not seek to draw causal conclusions in the context
of our analysis of Parler misinformation in relation to real-world events, we
noted some of the interactions between major events in Black Lives Matter and
the COVID-19 pandemic and how these related to the frequency of misinformation
we found on Parler. The scope of our study is rather, intentionally
exploratory and does not claim specific causation. However, we hope future
work can build upon our insights and study other polarized, niche social media
platforms as misinformation is not just propagated by alt-right or
conservative social platforms [62].

## Acknowledgments

This work was supported by Good Systems, a research Grand Challenge at the
University of Texas at Austin. This work was supported in part by Oracle Cloud
credits and related resources provided by the Oracle for Research program. We
thank Kami Vinton for her thoughtful feedback on our manuscript.

## References

  * [1] Sadiq Muhammed T and Saji K. Mathew.  The disaster of misinformation: A review of research in social media.  International Journal of Data Science and Analytics, 13(4):271–285, Feb 2022.
  * [2] Addressing misleading info.  Twitter.  https://help.twitter.com/en/resources/addressing-misleading-info.
  * [3] About fact-checking on Facebook and Instagram.  Facebook.  https://www.facebook.com/business/help/2593586717 571940?id=673052479947730/.
  * [4] Abram Brown.  Parler’s founder explains why he built Trump’s new favorite social media app.  Forbes, Jan 2021.  https://www.forbes.com/sites/abrambrown/2020/06/27/parlers-founder-explains-why-he-built-trumps-new-favorite-social-media-app/?sh=1cd384795016.
  * [5] Kaya Yurieff, Brian Fung, and Donie O’Sullivan.  Parler: Everything you need to know about the banned conservative social media platform.  CNN, Jan 2021.  https://www.cnn.com/2021/01/10/tech/what-is-parler/index.html.
  * [6] Aaron Pressman.  Parler is the new Twitter for Conservatives. here’s what you need to know.  Fortune, Jan 2021.  https://fortune.com/2020/06/29/what-is-parler-app-social-media-conservatives-who-owns-free-echo-facebook-twitter-verified-faq/.
  * [7] Alex Newhouse.  Right-wing users flock to parler as social media giants rein in misinformation.  PBS, Dec 2020.  https://www.pbs.org/newshour/nation/right-wing-users-flock-to-parler-as-social-media-giants-rein-in-misinformation.
  * [8] Shayan Sardarizadeh.  Parler ’free speech’ app tops charts in wake of trump defeat.  BBC News, Nov 2020.  https://www.bbc.com/news/technology-54873800.
  * [9] Maria Mercedes Ferreira Caceres, Juan Pablo Sosa, Jannel A Lawrence, Cristina Sestacovschi, Atiyah Tidd-Johnson, Muhammad Haseeb Ul Rasool, Vinay Kumar Gadamidi, Saleha Ozair, Krunal Pandav, Claudia Cuevas-Lou, and et al.  The impact of misinformation on the covid-19 pandemic.  AIMS Public Health, 9(2):262–277, Jan 2022.
  * [10] Nikhil L. Kolluri and Dhiraj Murthy.  CoVerifi: A covid-19 news verification system.  Online Social Networks and Media, 22, Mar 2021.
  * [11] Hitkul, Avinash Prabhu, Dipanwita Guhathakurta, Jivitesh jain, Mallika Subramanian, Manvith Reddy, Shradha Sehgal, Tanvi Karandikar, Amogh Gulati, Udit Arora, and et al.  Capitol (pat)riots: A comparative study of twitter and parler.  arxiv, Jan 2021.
  * [12] Annalise Baines, Muhammad Ittefaq, and Mauryne Abwao.  #scamdemic, #plandemic, or #scaredemic: What parler social media platform tells us about covid-19 vaccine.  Vaccines, 9(5):421, Apr 2021.
  * [13] Jacqueline M Otala, Gillian Kurtic, Isabella Grasso, Yu Liu, Jeanna Matthews, and Golshan Madraki.  Political polarization and platform migration: a study of parler and twitter usage by united states of america congress members.  Companion Proceedings of the Web Conference 2021, page 224–231, Apr 2021.
  * [14] Ariadna Matamoros-Fernández and Johan Farkas.  Racism, hate speech, and social media: A systematic review and critique.  Television & New Media, 22(2):205–224, Jan 2021.
  * [15] Max Aliapoulios, Emmi Bevensee, Jeremy Blackburn, Barry Bradlyn, Emiliano De Cristofaro, Gianluca Stringhini, and Savvas Zannettou.  A large open dataset from the parler social network.  Proceedings of the International AAAI Conference on Web and Social Media, 15(1):943–951, May 2021.
  * [16] Mike Isaac and Kellen Browning.  Fact-checked on facebook and twitter, conservatives switch their apps.  The New York Times, Nov 2020.  https://www.nytimes.com/2020/11/11/technology/parler-rumble-newsmax.html.
  * [17] Saharsh Agarwal, Uttara M Ananthakrishnan, and Catherine E. Tucker.  Deplatforming and the control of misinformation: Evidence from parler.  SSRN Electronic Journal, Mar 2022.
  * [18] Yuchen Zhou, Mark Dredze, David A. Broniatowski, and William D. Adler.  Elites and foreign actors among the alt-right: The gab social media platform.  First Monday, 24(9), Sep 2019.
  * [19] Emma Pieroni, Peter Jachim, Nathaniel Jachim, and Filipo Sharevski.  Parlermonium: A data-driven ux design evaluation of the parler platform.  arXiv, Jun 2021.
  * [20] Ben Nimmo.  Demtech: Measuring traffic manipulation on twitter.  Programme on Democracy & Technology, Jan 2019.
  * [21] Daniel Karell, Andrew Linke, Edward Holland, and Edward Hendrickson.  “Born for a storm”: Hard-right social media and civil unrest.  American Sociological Review, 88(2):000312242311561, May 2021.
  * [22] Richard McAlexander, Michael Rubin, and Rob Williams.  They’re still there, he’s all gone: American fatalities in foreign wars and right-wing radicalization at home.  APSA Preprints, Aug 2021.
  * [23] Misinformation and disinformation.  American Psychological Association, Jan 2023.  https://www.apa.org/topics/journalism-facts/misinformation-disinformation.
  * [24] Kate Conger and Mike Isaac.  Twitter permanently bans trump, capping online revolt.  The New York Times, Jan 2021.  https://www.nytimes.com/2021/01/08/technology/twitter-trump-suspended.html.
  * [25] Miriam J Metzger, Andrew J Flanagin, and Lara Zwarun.  College student web use, perceptions of information credibility, and verification behavior.  Computers & Education, 41(3):271–290, Nov 2003.
  * [26] Vlad Achimescu and Pavel Dimitrov Chachev.  Raising the flag: Monitoring user perceived disinformation on reddit.  Information, 12(1):1–24, Dec 2020.
  * [27] Aaron Rupar.  Trump’s twitter and facebook bans are working.  Vox, Jan 2021.  https://www.vox.com/2021/1/16/22234971/trump-twitter-facebook-social-media-ban-el.
  * [28] Joan Donovan, Claire Wardle, Kate Starbird, and Brandy Zadrozny.  They’re on the misinformation front line. here’s what they predict about the virus.  NBCNews.com, May 2020.  https://www.nbcnews.com/tech/social-media/these-disinformation-researchers-saw-coronavirus-infodemic-coming-n1206911.
  * [29] Tonia Poteat, Gregorio A. Millett, LaRon E. Nelson, and Chris Beyrer.  Understanding covid-19 risks and vulnerabilities among black communities in america: The lethal force of syndemics.  Annals of Epidemiology, 47:1–3, Jul 2020.
  * [30] Naomi Oreskes.  Why you should trust science on vaccines, climate change.  Time, Oct 2019.  https://time.com/5709691/why-trust-science/.
  * [31] Misinformation - Get the Facts.  UCI Libraries, Apr.  https://guides.lib.uci.edu/Misinfo/bias.
  * [32] Michela Del Vicario, Alessandro Bessi, Fabiana Zollo, Fabio Petroni, Antonio Scala, Guido Caldarelli, H. Eugene Stanley, and Walter Quattrociocchi.  The spreading of misinformation online.  Proceedings of the National Academy of Sciences, 113(3):554–559, Jan 2016.
  * [33] Holding ai accountable: Who gets to tell the story?, May 2022.
  * [34] Bell Hooks.  The Oppositional Gaze, page 115–131.  South End Press, 1992.
  * [35] Ellen Seiter.  Stereotypes and the media: A re-evaluation.  Journal of Communication, 36(2):14–26, 1986.
  * [36] Katherine Clayton, Spencer Blair, Jonathan A. Busam, Samuel Forstner, John Glance, Guy Green, Anna Kawata, Akhila Kovvuri, Jonathan Martin, Evan Morgan, and et al.  Real solutions for fake news? Measuring the effectiveness of general warnings and fact-check tags in reducing belief in false stories on social media.  Political Behavior, 42:1073–1095, Feb 2019.
  * [37] Limeng Cui, Suhang Wang, and Dongwon Lee.  Same.  Proceedings of the 2019 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, 2019.
  * [38] Dheeraj Kumar Dixit, Amit Bhagat, and Dharmendra Dangi.  Automating fake news detection using ppca and levy flight-based lstm.  Soft Computing, 26(22):12545–12557, Jun 2022.
  * [39] Rohit Kumar Kaliyar, Anurag Goswami, and Pratik Narang.  Echofaked: Improving fake news detection in social media with an efficient deep neural network.  Neural Computing and Applications, 33(14):8597–8613, Jan 2021\.
  * [40] Michael T. Braun, Lyn M. Van Swol, and Lisa Vang.  His lips are moving: Pinocchio effect and other lexical indicators of political deceptions.  Discourse Processes, 52(1):1–20, Jul 2014.
  * [41] Kai Shu, Deepak Mahudeswaran, Suhang Wang, Dongwon Lee, and Huan Liu.  Fakenewsnet: A data repository with news content, social context, and spatiotemporal information for studying fake news on social media.  arXiv, 8(3), Sep 2018.
  * [42] Shan Jiang, Simon Baumgartner, Abe Ittycheriah, and Cong Yu.  Factoring fact-checks: Structured information extraction from fact-checking articles.  Proceedings of The Web Conference 2020, page 1592–1603, Apr 2020\.
  * [43] Neetu Rani, Prasenjit Das, and Amit Kumar Bhardwaj.  Rumor, misinformation among web: A contemporary review of rumor detection techniques during different web waves.  Concurrency and Computation: Practice and Experience, 34(1):1–21, Jul 2021.
  * [44] Haeseung Seo, Aiping Xiong, and Dongwon Lee.  Trust it or not: effects of machine-learning warnings in helping individuals mitigate misinformation.  Web Science, page 265–274, 2019.
  * [45] Yuehua Zhao, Jingwei Da, and Jiaqi Yan.  Detecting health misinformation in online health communities: Incorporating behavioral features into machine learning based approaches.  ScienceDirect, 58(1), Jan 2021.
  * [46] Cdc museum covid-19 timeline.  Centers for Disease Control and Prevention, Mar 2023.
  * [47] Derrick Bryson Taylor.  George floyd protests: A timeline.  The New York Times, May 2020.  https://www.nytimes.com/article/george-floyd-protests-timeline.html.
  * [48] Timeline of events since george floyd’s arrest and murder.  AP NEWS, Jan 2022.  https://apnews.com/article/george-floyd-death-timeline-2f9abbe6497c2fa4adaebb92ae179dc6.
  * [49] Black lives matter.  Wikipedia, Mar 2023.  https://en.wikipedia.org/wiki/Black_Lives_Matter#2020.
  * [50] 2020–2023 United States racial unrest.  Wikipedia, Mar 2023.  https://en.wikipedia.org/wiki/2020–2023_United_ States_racial_unrest.
  * [51] Ellie Abraham.  A complete timeline of the 2020 black lives matter movement.  indy100, Dec 2020.  https://www.indy100.com/news/a-complete-timeline-of-the-2020-black-lives-matter-movement-b1777733.
  * [52] Timeline of the 2020 United States presidential election (November 2020–January 2021).  Wikipedia, Mar 2023.  https://en.wikipedia.org/wiki/Timeline_of_the_2020_United_States_presidential_election_(November_2020 %E2%80%93January_2021)#: :text=November%203%2C%202020&text=The%20formal%20voting%20by%20the ,inaugurated%20on%20January%2020%2C%202021.
  * [53] Timeline of the 2020 United States presidential election (January–October 2020).  Wikipedia, Jan 2023.  https://en.wikipedia.org/wiki/Timeline_of_the_2020_United_States_presidential_election_(Januar%E%80%93Oct ober_2020).
  * [54] The Electoral College: A 2020 Presidential Election Timeline - Congress.  Congressional Research Service, 2020.  https://crsreports.congress.gov/product/pdf/IF/IF11641.
  * [55] Hope Yen, Ali Swenson, and Amanda Seitz.  Ap fact check: Trump’s claims of vote rigging are all wrong.  AP NEWS, Dec 2020.  https://apnews.com/article/election-2020-ap-fact-check-joe-biden-donald-trump-technology-49a24edd6d10888dbad61689c24b05a5.
  * [56] John W Ayers, Brian Chu, Zechariah Zhu, Eric C Leas, Davey M Smith, Mark Dredze, and David A Broniatowski.  Spread of misinformation about face masks and covid-19 by automated software on facebook.  JAMA internal medicine, Sep 2021.  https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8185625/.
  * [57] Deborah Netburn.  A timeline of the CDC’s advice on face masks.  Los Angeles Times, Jul 2021.  https://www.latimes.com/science/story/2021-07-27/timeline-cdc-mask-guidance-during-covid-19-pandemic.
  * [58] Tom Huddleston.  Bill Gates was ’very surprised’ that ’crazy’ Covid conspiracy theories targeted him and Dr. Fauci.  CNBC, Jan 2021.  https://www.cnbc.com/2021/01/27/bill-gates-was-very-surprised-by-crazy-covid-conspiracy-theories.html.
  * [59] Ryan Kelly.  Explained: Why ’white lives matter’ and ’all lives matter’ misses the point of black lives matter.  Goal, Jun 2020.  https://www.goal.com/en-us/news/explained-why-white-lives-matter-all-lives-matter-misses-point-black-lives-matter/1wud91m963jo318648p0s2rwg8.
  * [60] Joe Barrett.  Jacob Blake shooting: What we know about the shooting in Kenosha.  The Wall Street Journal, Oct 2021.  https://www.wsj.com/articles/jacob-blake-shooting-11598368824.
  * [61] Jieun Shin, Lian Jian, Kevin Driscoll, and François Bar.  The diffusion of misinformation on social media: Temporal pattern, message, and source.  Computers in Human Behavior, 83:278–287, Jun 2018.
  * [62] Scott Barry Kaufman.  Liberals and conservatives are both susceptible to fake news, but for different reasons.  Scientific American Blog Network, Feb 2019.

## Appendix A

### COVID-19 Timeline of Events

Date |  Event
---|---
December 2019 |  First known case
January 2020 |  When COVID was first identified as the cause
February 2020 |  WHO announces the official name of the disease
March 2020 |  COVID declared a pandemic + Trump issues a travel ban
April 2020 |  Shortages in personal protective equipment + CDC announces new mask wearing girdles and recommends wearing masks when outside of home + announces government impersonation fraud (phone scams and phishing attacks that impersonate the CDC and ask for donations) + CDC begins summarizing weekly data on COVID hospitalizations, death and testing + some doctors and civil rights group tell the CDC and the government that they want race and ethnicity data related to COVID to be released so people can see the true impact of the virus on communities of color + Georgia, Alaska, and Oklahoma partially reopen their states despite it being too early
May 2020 |  Unemployment rate in US is 14.7% + death toll surpasses 100,000
June 2020 |  Confirmed cases in US surpasses 2 million
July 2020 |  Confirmed casses in US surpasses 3 million + Who announces that SARS-CoV-2 virus is transmitted through the air and that asymptomatic people can spread it + CDC tells people to wear face masks “a critical tool in the fight against COVID-19” + the Trump Administration tells hospitals across the nation to stop sending critical information about COVID-19 hospitalization rates and equipment availability to the CDC and send it instead to a new system that uses a private contractor
August 2020 |  Becomes 3rd leading cause of death in US (1,000 per day + 5.4 million nationwide) + first documented case of reinfection confirmed in Hong Kong and US
September 2020 |  Death toll in US surpasses 200,000 + 1 million worldwide -
October 2020 |  Donald Trump gets Covid
November 2020 |  Moderna’s vaccine found to be 95.4% effective + Pfizer being 95%
December 2020 |  First COVID vaccine granted regulatory approval + recorded death toll in US surpasses 300,000 + first case of “Alpha” variant in the US

COVID-19 Timeline of Key Events by Month [46]

### US-Politics Timeline of Events

Date |  Event
---|---
January 2020 |  House of Reps appoint impeachment managers + Delaney drops out of the Democratic race
February 2020 |  Senate votes to acquit Trump + Walsh drops out of the Republican primary
March 2020 |  Buttigieg and Klobuchar drop out of the race and endorse Democrats + Super Tuesday
April 2020 |  Sanders endorses Biden
May 2020 |  Trump blames “far-left extremist” groups for organizing violent riots and says he plans to designate Antifa as a terrorist organization
June 2020 |  Police and national guard force protesters to clear out + Trump’s presidential campaign demands that CNN removes their poll that shows Biden leading by 14 points + Biden refuses to do a fourth debate with Trump + Biden announces that he won’t hold anymore campaign rallies due to COVID
July 2020 |  Kanye West announces that he will run for president but doesn’t officially do it + Trump states his intent to withdraw the US from the WHO + Trump struggling according to polls due to his responses to COVID and George Floyd + Biden and Trump campaigns are preparing for if the election is contested
August 2020 |  Biden officially chosen as the presidential nominee by delegates at the Democratic National Convention + Trump files a lawsuit to prevent Nevada from doing primarily mail-in voting + Biden officially chooses Kamala Harris as his vice presidential running mate
September 2020 |  Trump holds a rally after one was canceled due to COVID concerns + Ruth Bader Ginsburg passes away + Trump calls Biden the "dumbest of all candidates … You can’t have this guy as your president … maybe I’ll sign an executive order that you cannot have him as your president" + Trump declines to commit to a peaceful transfer of power after the election
October 2020 |  Melania Trump gets covid + Trump experiencing mild COVID symptoms + Trump says in an interview that Harris is a “monster” and a “communist” because of her stance on open borders + Trump refuses to participate in a virtual debate + National Woman’s March occurs
November 2020 |  “Trump Train” caravans block traffic + Trumps campaigns files a lawsuit in Michigan to stop the vote counting + Trump calls Georgia’s hand ballot recount a waste of time + Trump claims that the election was rigged which is why Biden won
December 2020 |  Electors meet to formally vote for the president and vice president, Biden won + Trump tweets an article stating that people are upset that McConnell congratulated Biden

US-Politics Timeline of Key Events by Month [52, 53, 54]

### Black Lives Matter Timeline of Events

Date |  Event
---|---
February 23, 2020 |  Ahmaud Arbery is murdered. Footage begins circulating May 5
March 13, 2020 |  Breonna Taylor is murdered
May 25, 2020 |  George Floyd is murdered
May 26, 2020 |  Bystander footage of Floyd’s murder is release shortly after police statement claiming his death as a “medical incident.” 4 officers fired + Protests in Minneapolis
May 27, 2020 |  “Mayor Jacob Frey calls for criminal charges against Chauvin. Protests lead to unrest in Minneapolis, with some people looting and starting fires. Protests spread to other cities.”
May 28, 2020 |  Governor Tim Walz activates National Guard
May 29, 2020 |  Chauvin is arrested and charged with third degree murder and manslaughter + Trump Tweets “When the looting starts, the shooting starts.” Protests continue and turn violent
May 30, 2020 |  Trump tries to walk back his Tweet + Minneapolis mayor refers to protests as “domestic terrorism”
May 31, 2020 |  Attorney General Keith Ellison announced to lead prosecutions + Curfews ordered by mayors
June 1, 2020 |  The county ME finds cause of death as Floyd’s heart stopping while police compressed his neck + 2 autopsies reveal Floyd’s death as homicide + Trump threatens to deploy military
June 2, 2020 |  Minnesota Department of Human Rights launches investigation into the Minneapolis PD + Protesters gather at murder site
June 3, 2020 |  Three officers charged for not intervening
June 4, 2020 |  Funeral held for Floyd + Buffalo officers suspended for shoving elderly protester
June 5, 2020 |  Minneapolis bans choke holds for police
June 6, 2020 |  Protests continue + Officers charged with assault
June 7, 2020 |  “A majority of Minneapolis City Council members say they support dismantling the Police Department. The idea later stalls but sparks a national debate over police reform.”
June 8, 2020 |  Thousands pay respects to Floyd in Houston. He is buried the next day
June 10, 2020 |  Floyd’s brother testifies before the House Judiciary Committee for police accountability
June 16, 2020 |  Trump signs executive order for better police practices
July 15, 2020 |  Floyd’s family sues officers and Minneapolis
July 21, 2020 |  “The Minnesota Legislature passes a broad slate of police accountability measures that includes bans on neck restraints, chokeholds and so-called warrior-style training.”
August 23, 2020 |  Jacob Blake shot and killed, sparking protests, many in Kenosha. Two protesters killed by Kyle Rittenhouse (he would later be acquitted of all charges in Nov)
August 26-28, 2020 |  False rumors riot from Eddie Sole Jr.’s suicide
September 23, 2020 |  Protests erupt after jury verdict of Breonna Taylor’s case

Black Lives Matter Timeline of Key Events by Month [47, 48, 49, 50].


set models. For example, in table XIV the MNIST base and overall accuracy
deviations of a naive CDVAE are higher than the respective values for OCDVAE
starting already from the second task increment. Correspondingly, the accuracy
values themselves experience larger decline for CDVAE than for OCDVAE with
progressive increments. This difference is not as pronounced at the end of the
first task increment because the models haven’t been trained on any of their
own generated data yet. Successful literature approaches such as the
variational generative replay proposed by [6] thus avoid repeated learning
based on previous generated examples and simply store and retain a separate
generative model for each task. The strength of our model is that, instead of
storing a trained model for each task increment, we are able to continually
keep training our joint model with data generated for all previously seen
tasks by filtering out ambiguous samples from low density areas of the
posterior. Similar trends can also be observed for the respective pixel
models.

We also see that regularization approaches such as EWC already fail at the
first increment. In contrast to the success that has been reported in prior
literature [16, 56], this is due to the use of a single classification head.
This is intuitive because introduction of new units, as described in the main
body, directly confuses the existing classification. Regularization approaches
by definition are challenged in this scenario because the weights are not
allowed to drift too far away from previous values. For emphasis we repeat
that however this scenario is much more practical and realistic than a multi-
head scenario with a separate classifier per task. While regularization
approaches are largely successful in the latter setting, it is not only
restricted to the closed world, but further requires an oracle at prediction
stage to chose the correct classification head. In contrast, our proposed
approach requires no knowledge of task labels for prediction and is robust in
an open world.

With respect to KL divergences and reconstruction losses we can make two
observations. First, the arguments of the previous section hold and by itself
the small relative improvements between models should be interpreted with
caution as they do not directly translate to maintaining continual learning
accuracy. Second, we can also observe that reconstruction losses at every
increment for all $\gamma_{t,all}$ and respective negative log likelihoods for
only the new task $\gamma_{t,new}$ are harder to interpret than the accuracy
counterpart. While the latter is normalized between zero and unity, the
reconstruction loss of different tasks is expected to fluctuate largely
according to the task’s images’ reconstruction complexity. To give a concrete
example, it is rather straightforward to come to the conclusion that a model
suffers from limited capacity or lack of complexity if a single newly arriving
class cannot be classified well. In the case of reconstruction it is common to
observe either a large decrease in negative log likelihood for the newly
arriving class, or a big increase depending on the specific introduced class.
As such, these values are naturally comparable between models, but are
challenging to interpret across time steps without also analyzing the
underlying nature of the introduced class. The exception is formed by the base
task’s reconstruction loss $\gamma_{t,base}$. In analogy to base
classification accuracy, this quantity still measures the amount of
catastrophic forgetting across time. However, in all tables we can observe
that catastrophic forgetting of the decoder as measured by the base
reconstruction loss is almost imperceivable. As this is not at all reflected
in the respective accuracy over time, it further underlines our previous
arguments that reconstruction loss is not necessarily the best metric to
monitor in the presented continual learning scenario.

TABLE XIV: Results for class incremental continual learning approaches
averaged over 5 runs, baselines and the reference isolated learning scenario
for MNIST at the end of every task increment. Extension of table 3 in the main
body. Here, in addition to the accuracy $\alpha_{t}$, $\gamma_{t}$ and
$KL_{t}$ also indicate the respective NLL reconstruction metrics and
corresponding KL divergences at the end of every task increment $t$.

MNIST | t | CDVAE ISO | CDVAE UB | CDVAE LB | EWC | Dual Model | CDVAE | OCDVAE
---|---|---|---|---|---|---|---|---
$\boldsymbol{\alpha_{base,t}}$ | 1 |  | 100.0 | 100.0 | 99.88 $\pm$ 0.010 | 99.98 $\pm$ 0.023 | 99.97 $\pm$ 0.029 | 99.98 $\pm$ 0.018
2 |  | 99.82 | 00.00 | 00.61 $\pm$ 0.057 | 99.77 $\pm$ 0.032 | 97.28 $\pm$ 3.184 | 99.30 $\pm$ 0.100
3 |  | 99.80 | 00.00 | 00.17 $\pm$ 0.045 | 99.51 $\pm$ 0.094 | 87.66 $\pm$ 8.765 | 96.69 $\pm$ 2.173
(%) | 4 |  | 99.85 | 00.00 | 00.49 $\pm$ 0.017 | 98.90 $\pm$ 0.207 | 54.70 $\pm$ 22.84 | 94.71 $\pm$ 1.792
| 5 |  | 99.57 | 00.00 | 00.45 $\pm$ 0.059 | 97.31 $\pm$ 0.489 | 19.86 $\pm$ 7.396 | 92.53 $\pm$ 4.485
$\boldsymbol{\alpha_{new,t}}$ | 1 |  | 100.0 | 100.0 | 99.88 $\pm$ 0.010 | 99.98 $\pm$ 0.023 | 99.97 $\pm$ 0.029 | 99.98 $\pm$ 0.018
2 |  | 99.80 | 99.85 | 99.70 $\pm$ 0.013 | 99.81 $\pm$ 0.062 | 99.75 $\pm$ 0.127 | 99.80 $\pm$ 0.126
3 |  | 99.67 | 99.94 | 99.94 $\pm$ 0.002 | 99.48 $\pm$ 0.294 | 99.63 $\pm$ 0.172 | 99.61 $\pm$ 0.055
(%) | 4 |  | 99.49 | 100.0 | 99.87 $\pm$ 0.015 | 99.46 $\pm$ 0.315 | 99.05 $\pm$ 0.470 | 99.15 $\pm$ 0.032
| 5 |  | 99.10 | 99.86 | 99.58 $\pm$ 0.052 | 98.59 $\pm$ 0.106 | 99.00 $\pm$ 0.100 | 99.06 $\pm$ 0.171
$\boldsymbol{\alpha_{all,t}}$ | 1 |  | 100.0 | 100.0 | 99.88 $\pm$ 0.010 | 99.98 $\pm$ 0.023 | 99.97 $\pm$ 0.029 | 99.98 $\pm$ 0.018
2 |  | 99.81 | 49.92 | 50.16 $\pm$ 0.029 | 99.79 $\pm$ 0.049 | 98.54 $\pm$ 1.638 | 99.55 $\pm$ 0.036
3 |  | 99.72 | 31.35 | 33.42 $\pm$ 0.027 | 99.32 $\pm$ 0.057 | 95.01 $\pm$ 3.162 | 98.46 $\pm$ 0.903
(%) | 4 |  | 99.50 | 24.82 | 25.36 $\pm$ 0.025 | 98.56 $\pm$ 0.021 | 81.50 $\pm$ 9.369 | 97.06 $\pm$ 1.069
| 5 | 99.45 | 99.29 | 20.16 | 20.26 $\pm$ 0.027 | 96.64 $\pm$ 0.079 | 64.34 $\pm$ 4.903 | 93.24 $\pm$ 3.742
$\boldsymbol{\gamma_{base,t}}$ | 1 |  | 63.18 | 62.08 |  | 62.17 $\pm$ 0.979 | 64.34 $\pm$ 2.054 | 62.53 $\pm$ 1.166
2 |  | 62.85 | 126.8 |  | 63.69 $\pm$ 0.576 | 74.41 $\pm$ 10.89 | 65.68 $\pm$ 1.166
3 |  | 63.36 | 160.4 |  | 67.34 $\pm$ 0.445 | 81.89 $\pm$ 10.09 | 69.29 $\pm$ 1.541
(nats) | 4 |  | 64.25 | 126.9 |  | 70.41 $\pm$ 0.436 | 90.62 $\pm$ 10.08 | 71.69 $\pm$ 1.379
| 5 |  | 64.99 | 123.2 |  | 75.08 $\pm$ 0.623 | 101.6 $\pm$ 8.347 | 77.16 $\pm$ 1.104
$\boldsymbol{\gamma_{new,t}}$ | 1 |  | 63.18 | 62.08 |  | 62.17 $\pm$ 0.979 | 64.34 $\pm$ 2.054 | 62.53 $\pm$ 1.166
2 |  | 88.75 | 87.93 |  | 88.03 $\pm$ 0.664 | 89.91 $\pm$ 0.107 | 89.64 $\pm$ 3.709
3 |  | 82.53 | 87.22 |  | 83.46 $\pm$ 0.992 | 87.65 $\pm$ 0.530 | 85.37 $\pm$ 1.725
(nats) | 4 |  | 72.68 | 74.61 |  | 73.23 $\pm$ 0.280 | 79.49 $\pm$ 0.489 | 74.75 $\pm$ 0.777
| 5 |  | 85.88 | 92.00 |  | 89.32 $\pm$ 0.626 | 93.55 $\pm$ 0.391 | 89.68 $\pm$ 0.618
$\boldsymbol{\gamma_{all,t}}$ | 1 |  | 63.18 | 62.08 |  | 62.17 $\pm$ 0.979 | 64.34 $\pm$ 2.054 | 62.53 $\pm$ 1.166
2 |  | 75.97 | 107.3 |  | 75.64 $\pm$ 0.600 | 82.02 $\pm$ 5.488 | 76.62 $\pm$ 1.695
3 |  | 79.58 | 172.3 |  | 81.24 $\pm$ 0.262 | 89.88 $\pm$ 3.172 | 82.95 $\pm$ 1.878
(nats) | 4 |  | 79.72 | 203.1 |  | 82.92 $\pm$ 0.489 | 95.83 $\pm$ 2.747 | 85.30 $\pm$ 1.524
| 5 | 78.12 | 81.97 | 163.7 |  | 88.29 $\pm$ 0.363 | 107.6 $\pm$ 1.724 | 92.92 $\pm$ 2.283
$\boldsymbol{KL_{all,t}}$ | 1 |  | 12.55 | 13.08 |  | 11.81 $\pm$ 0.123 | 13.00 $\pm$ 0.897 | 13.68 $\pm$ 0.785
2 |  | 18.50 | 25.84 |  | 16.15 $\pm$ 0.149 | 20.20 $\pm$ 1.188 | 18.01 $\pm$ 0.154
3 |  | 20.16 | 24.28 |  | 16.46 $\pm$ 0.122 | 24.24 $\pm$ 1.974 | 20.02 $\pm$ 0.161
(nats) | 4 |  | 20.48 | 26.32 |  | 16.09 $\pm$ 0.177 | 27.01 $\pm$ 1.851 | 20.26 $\pm$ 0.186
| 5 | 22.12 | 21.02 | 24.87 |  | 16.13 $\pm$ 0.225 | 30.61 $\pm$ 1.240 | 21.02 $\pm$ 0.717

TABLE XV: Results for class incremental continual learning approaches averaged
over 5 runs, baselines and the reference isolated learning scenario for
FashionMNIST at the end of every task increment. Extension of table 3 in the
main body. Here, in addition to the accuracy $\alpha_{t}$, $\gamma_{t}$ and
$KL_{t}$ also indicate the respective NLL reconstruction metrics and
corresponding KL divergences at the end of every task increment $t$.

Fashion | t | CDVAE ISO | CDVAE UB | CDVAE LB | EWC | Dual Model | CDVAE | OCDVAE
---|---|---|---|---|---|---|---|---
$\boldsymbol{\alpha_{base,t}}$ | 1 |  | 99.65 | 99.60 | 99.17 $\pm$ 0.037 | 99.58 $\pm$ 0.062 | 99.55 $\pm$ 0.035 | 99.59 $\pm$ 0.082
2 |  | 96.70 | 00.00 | 02.40 $\pm$ 0.122 | 94.50 $\pm$ 0.389 | 92.02 $\pm$ 1.175 | 92.36 $\pm$ 2.092
3 |  | 95.95 | 00.00 | 01.63 $\pm$ 0.032 | 94.88 $\pm$ 0.432 | 79.26 $\pm$ 4.170 | 83.90 $\pm$ 2.310
(%) | 4 |  | 91.35 | 00.00 | 00.33 $\pm$ 0.097 | 82.25 $\pm$ 4.782 | 50.16 $\pm$ 6.658 | 64.70 $\pm$ 2.580
| 5 |  | 92.20 | 00.00 | 00.17 $\pm$ 0.076 | 94.26 $\pm$ 0.192 | 39.51 $\pm$ 7.173 | 60.63 $\pm$ 12.16
$\boldsymbol{\alpha_{new,t}}$ | 1 |  | 99.65 | 99.60 | 99.17 $\pm$ 0.037 | 99.58 $\pm$ 0.062 | 99.55 $\pm$ 0.035 | 99.59 $\pm$ 0.082
2 |  | 95.55 | 97.95 | 96.09 $\pm$ 0.260 | 89.31 $\pm$ 0.311 | 90.98 $\pm$ 0.626 | 92.64 $\pm$ 2.302
3 |  | 93.35 | 99.95 | 99.92 $\pm$ 0.012 | 86.06 $\pm$ 2.801 | 90.26 $\pm$ 1.435 | 83.40 $\pm$ 3.089
(%) | 4 |  | 84.75 | 99.90 | 99.95 $\pm$ 0.060 | 73.63 $\pm$ 3.861 | 85.65 $\pm$ 2.127 | 84.18 $\pm$ 2.715
| 5 |  | 97.50 | 99.80 | 99.60 $\pm$ 0.023 | 93.55 $\pm$ 0.708 | 96.92 $\pm$ 0.774 | 96.51 $\pm$ 0.707
$\boldsymbol{\alpha_{all,t}}$ | 1 |  | 99.65 | 99.60 | 99.17 $\pm$ 0.037 | 99.58 $\pm$ 0.062 | 99.55 $\pm$ 0.035 | 99.59 $\pm$ 0.082
2 |  | 95.75 | 48.97 | 49.28 $\pm$ 0.242 | 91.91 $\pm$ 0.043 | 91.83 $\pm$ 0.730 | 92.31 $\pm$ 1.163
3 |  | 93.02 | 33.33 | 34.34 $\pm$ 0.009 | 79.98 $\pm$ 0.634 | 83.35 $\pm$ 1.597 | 86.93 $\pm$ 0.870
(%) | 4 |  | 87.51 | 25.00 | 25.21 $\pm$ 0.100 | 64.37 $\pm$ 0.707 | 64.66 $\pm$ 3.204 | 76.05 $\pm$ 1.391
| 5 | 89.54 | 89.24 | 19.97 | 20.06 $\pm$ 0.059 | 63.21 $\pm$ 1.957 | 58.82 $\pm$ 2.521 | 69.88 $\pm$ 1.712
$\boldsymbol{\gamma_{base,t}}$ | 1 |  | 209.7 | 209.8 |  | 207.7 $\pm$ 1.558 | 208.9 $\pm$ 1.213 | 209.7 $\pm$ 3.655
2 |  | 207.4 | 240.7 |  | 209.0 $\pm$ 0.731 | 212.7 $\pm$ 0.579 | 212.1 $\pm$ 0.937
3 |  | 207.6 | 258.7 |  | 213.0 $\pm$ 1.854 | 219.5 $\pm$ 1.376 | 216.9 $\pm$ 1.208
(nats) | 4 |  | 207.7 | 243.6 |  | 213.6 $\pm$ 0.509 | 223.8 $\pm$ 0.837 | 217.1 $\pm$ 0.979
| 5 |  | 208.4 | 306.5 |  | 217.7 $\pm$ 1.510 | 232.8 $\pm$ 5.048 | 222.8 $\pm$ 1.632
$\boldsymbol{\gamma_{new,t}}$ | 1 |  | 209.7 | 209.8 |  | 207.7 $\pm$ 1.558 | 208.9 $\pm$ 1.213 | 209.7 $\pm$ 3.655
2 |  | 241.1 | 240.2 |  | 238.7 $\pm$ 0.081 | 241.8 $\pm$ 0.502 | 241.9 $\pm$ 0.960
3 |  | 213.6 | 211.8 |  | 211.6 $\pm$ 0.543 | 215.4 $\pm$ 0.501 | 213.0 $\pm$ 0.635
(nats) | 4 |  | 220.5 | 219.7 |  | 219.5 $\pm$ 0.216 | 223.6 $\pm$ 0.381 | 220.9 $\pm$ 0.522
| 5 |  | 246.2 | 242.0 |  | 242.8 $\pm$ 0.898 | 248.8 $\pm$ 0.398 | 244.0 $\pm$ 0.646
$\boldsymbol{\gamma_{all,t}}$ | 1 |  | 209.7 | 209.8 |  | 207.7 $\pm$ 1.558 | 208.9 $\pm$ 1.213 | 209.7 $\pm$ 3.655
2 |  | 224.2 | 240.4 |  | 223.8 $\pm$ 0.402 | 226.6 $\pm$ 2.31 | 226.9 $\pm$ 0.918
3 |  | 220.7 | 246.1 |  | 221.9 $\pm$ 0.648 | 227.2 $\pm$ 0.606 | 224.9 $\pm$ 0.642
(nats) | 4 |  | 220.4 | 238.7 |  | 225.1 $\pm$ 3.629 | 230.4 $\pm$ 0.524 | 226.1 $\pm$ 0.560
| 5 | 224.8 | 226.2 | 275.1 |  | 230.5 $\pm$ 1.543 | 242.2 $\pm$ 0.754 | 234.6 $\pm$ 0.823
$\boldsymbol{KL_{all,t}}$ | 1 |  | 12.17 | 12.20 |  | 9.710 $\pm$ 0.345 | 13.21 $\pm$ 0.635 | 13.28 $\pm$ 0.644
2 |  | 16.54 | 17.47 |  | 10.65 $\pm$ 0.101 | 17.60 $\pm$ 0.755 | 15.56 $\pm$ 0.696
3 |  | 18.84 | 19.34 |  | 11.34 $\pm$ 0.057 | 21.25 $\pm$ 0.872 | 17.35 $\pm$ 0.307
(nats) | 4 |  | 20.06 | 17.31 |  | 10.96 $\pm$ 0.106 | 25.21 $\pm$ 0.929 | 19.81 $\pm$ 0.462
| 5 | 23.27 | 20.27 | 21.61 |  | 11.45 $\pm$ 0.228 | 26.68 $\pm$ 0.859 | 20.47 $\pm$ 0.742

TABLE XVI: Results for class incremental continual learning approaches
averaged over 5 runs, baselines and the reference isolated learning scenario
for AudioMNIST at the end of every task increment. Extension of table 3 in the
main body. Here, in addition to the accuracy $\alpha_{t}$, $\gamma_{t}$ and
$KL_{t}$ also indicate the respective NLL reconstruction metrics and
corresponding KL divergences at the end of every task increment $t$.

Audio | t | CDVAE ISO | CDVAE UB | CDVAE LB | EWC | Dual Model | CDVAE | OCDVAE
---|---|---|---|---|---|---|---|---
$\boldsymbol{\alpha_{base,t}}$ | 1 |  | 99.99 | 100.0 | 100.0 $\pm$ 0.000 | 100.0 $\pm$ 0.000 | 99.21 $\pm$ 0.568 | 99.95 $\pm$ 0.035
2 |  | 99.92 | 00.00 | 00.16 $\pm$ 0.040 | 93.08 $\pm$ 5.854 | 98.98 $\pm$ 0.766 | 98.61 $\pm$ 0.490
3 |  | 100.0 | 00.00 | 00.29 $\pm$ 0.029 | 83.25 $\pm$ 6.844 | 92.44 $\pm$ 1.306 | 95.12 $\pm$ 2.248
(%) | 4 |  | 99.92 | 00.00 | 00.31 $\pm$ 0.015 | 72.02 $\pm$ 0.677 | 76.43 $\pm$ 4.715 | 86.37 $\pm$ 5.63
| 5 |  | 98.42 | 00.00 | 00.11 $\pm$ 0.007 | 61.57 $\pm$ 0.747 | 59.36 $\pm$ 7.147 | 79.73 $\pm$ 4.070
$\boldsymbol{\alpha_{new,t}}$ | 1 |  | 99.99 | 100.0 | 100.0 $\pm$ 0.000 | 100.0 $\pm$ 0.000 | 99.21 $\pm$ 0.568 | 99.95 $\pm$ 0.035
2 |  | 99.75 | 100.0 | 99.78 $\pm$ 0.019 | 86.25 $\pm$ 8.956 | 91.82 $\pm$ 4.577 | 89.23 $\pm$ 7.384
3 |  | 98.92 | 99.58 | 99.25 $\pm$ 0.054 | 95.16 $\pm$ 1.490 | 95.20 $\pm$ 1.495 | 94.43 $\pm$ 3.030
(%) | 4 |  | 97.33 | 98.67 | 97.03 $\pm$ 0.019 | 62.52 $\pm$ 4.022 | 53.02 $\pm$ 6.132 | 72.22 $\pm$ 8.493
| 5 |  | 98.67 | 100.0 | 99.41 $\pm$ 0.207 | 89.41 $\pm$ 0.691 | 84.93 $\pm$ 6.297 | 89.52 $\pm$ 6.586
$\boldsymbol{\alpha_{all,t}}$ | 1 |  | 99.99 | 100.0 | 100.0 $\pm$ 0.000 | 100.0 $\pm$ 0.000 | 99.21 $\pm$ 0.568 | 99.95 $\pm$ 0.035
2 |  | 99.83 | 50.00 | 50.16 $\pm$ 0.119 | 89.67 $\pm$ 1.763 | 93.84 $\pm$ 2.558 | 93.93 $\pm$ 3.756
3 |  | 99.56 | 33.19 | 33.28 $\pm$ 0.022 | 78.24 $\pm$ 3.315 | 94.26 $\pm$ 1.669 | 95.70 $\pm$ 1.524
(%) | 4 |  | 98.60 | 24.58 | 24.50 $\pm$ 0.017 | 60.43 $\pm$ 4.209 | 77.90 $\pm$ 4.210 | 85.59 $\pm$ 3.930
| 5 | 97.75 | 97.87 | 20.02 | 19.98 $\pm$ 0.032 | 47.42 $\pm$ 1.447 | 81.49 $\pm$ 1.944 | 87.72 $\pm$ 1.594
$\boldsymbol{\gamma_{base,t}}$ | 1 |  | 433.7 | 423.2 |  | 422.3 $\pm$ 0.573 | 435.2 $\pm$ 15.69 | 424.2 $\pm$ 2.511
2 |  | 422.5 | 439.4 |  | 426.6 $\pm$ 2.840 | 423.9 $\pm$ 0.517 | 425.2 $\pm$ 1.402
3 |  | 420.7 | 429.2 |  | 425.0 $\pm$ 0.339 | 422.7 $\pm$ 0.690 | 423.8 $\pm$ 1.148
(nats) | 4 |  | 419.9 | 428.5 |  | 425.4 $\pm$ 0.081 | 422.8 $\pm$ 0.367 | 423.5 $\pm$ 0.937
| 5 |  | 418.4 | 432.9 |  | 425.2 $\pm$ 0.244 | 422.7 $\pm$ 0.182 | 423.5 $\pm$ 0.586
$\boldsymbol{\gamma_{new,t}}$ | 1 |  | 433.7 | 423.2 |  | 422.3 $\pm$ 0.573 | 435.2 $\pm$ 15.69 | 424.2 $\pm$ 2.511
2 |  | 381.2 | 384.1 |  | 381.3 $\pm$ 2.039 | 382.5 $\pm$ 1.355 | 385.3 $\pm$ 12.56
3 |  | 435.9 | 436.7 |  | 436.8 $\pm$ 0.188 | 436.3 $\pm$ 0.639 | 436.9 $\pm$ 0.688
(nats) | 4 |  | 485.9 | 487.1 |  | 486.5 $\pm$ 0.432 | 486.7 $\pm$ 0.385 | 486.5 $\pm$ 0.701
| 5 |  | 421.3 | 425.2 |  | 422.4 $\pm$ 0.784 | 423.9 $\pm$ 0.681 | 422.9 $\pm$ 0.537
$\boldsymbol{\gamma_{all,t}}$ | 1 |  | 433.7 | 423.2 |  | 422.3 $\pm$ 0.573 | 435.2 $\pm$ 15.69 | 424.2 $\pm$ 2.511
2 |  | 401.9 | 411.8 |  | 404.0 $\pm$ 2.407 | 403.2 $\pm$ 0.831 | 403.5 $\pm$ 1.274
3 |  | 412.1 | 418.9 |  | 414.4 $\pm$ 0.385 | 413.6 $\pm$ 0.410 | 413.8 $\pm$ 0.573
(nats) | 4 |  | 430.3 | 438.4 |  | 433.9 $\pm$ 0.374 | 432.4 $\pm$ 0.436 | 432.6 $\pm$ 0.862
| 5 | 429.7 | 427.2 | 440.4 |  | 432.7 $\pm$ 0.385 | 431.4 $\pm$ 0.255 | 430.9 $\pm$ 0.541
$\boldsymbol{KL_{all,t}}$ | 1 |  | 11.65 | 11.20 |  | 4.639 $\pm$ 0.107 | 11.78 $\pm$ 1.478 | 11.16 $\pm$ 0.713
2 |  | 11.78 | 13.61 |  | 5.135 $\pm$ 0.127 | 15.13 $\pm$ 1.128 | 14.06 $\pm$ 1.140
3 |  | 13.40 | 17.09 |  | 5.427 $\pm$ 0.105 | 18.18 $\pm$ 1.140 | 13.61 $\pm$ 0.901
(nats) | 4 |  | 13.61 | 14.41 |  | 5.243 $\pm$ 0.135 | 22.93 $\pm$ 1.134 | 17.58 $\pm$ 1.102
| 5 | 17.89 | 15.15 | 14.52 |  | 5.470 $\pm$ 0.055 | 22.96 $\pm$ 0.912 | 18.52 $\pm$ 1.131

TABLE XVII: Results for PixelVAE based class incremental continual learning
approaches averaged over 5 runs, baselines and the reference isolated learning
scenario for MNIST at the end of every task increment in analogy to table XIV.
Extension of table 4 in the main body. Here, in addition to the accuracy
$\alpha_{t}$, $\gamma_{t}$ and $KL_{t}$ also indicate the respective NLL
reconstruction metrics and corresponding KL divergences at the end of every
task increment $t$.

MNIST | t | Dual Pix Model | PixCDVAE | PixOCDVAE
---|---|---|---|---
$\boldsymbol{\alpha_{base,t}}$ | 1 | 99.97 $\pm$ 0.002 | 99.97 $\pm$ 0.026 | 99.86 $\pm$ 0.084
2 | 99.54 $\pm$ 0.285 | 96.90 $\pm$ 2.907 | 99.64 $\pm$ 0.095
3 | 99.16 $\pm$ 0.611 | 90.12 $\pm$ 5.846 | 98.88 $\pm$ 0.491
(%) | 4 | 98.33 $\pm$ 1.119 | 76.84 $\pm$ 9.095 | 98.11 $\pm$ 0.797
| 5 | 98.04 $\pm$ 1.397 | 56.53 $\pm$ 4.032 | 97.44 $\pm$ 0.785
$\boldsymbol{\alpha_{new,t}}$ | 1 | 99.97 $\pm$ 0.002 | 99.97 $\pm$ 0.026 | 99.86 $\pm$ 0.084
2 | 99.71 $\pm$ 0.122 | 99.74 $\pm$ 0.052 | 99.82 $\pm$ 0.027
3 | 99.41 $\pm$ 0.084 | 99.22 $\pm$ 0.082 | 99.56 $\pm$ 0.092
(%) | 4 | 98.61 $\pm$ 0.312 | 97.84 $\pm$ 0.180 | 98.80 $\pm$ 0.292
| 5 | 97.31 $\pm$ 0.575 | 96.77 $\pm$ 0.337 | 98.63 $\pm$ 0.430
$\boldsymbol{\alpha_{all,t}}$ | 1 | 99.97 $\pm$ 0.002 | 99.97 $\pm$ 0.026 | 99.86 $\pm$ 0.084
2 | 99.60 $\pm$ 0.142 | 98.37 $\pm$ 1.448 | 99.69 $\pm$ 0.051
3 | 98.93 $\pm$ 0.291 | 96.14 $\pm$ 1.836 | 99.20 $\pm$ 0.057
(%) | 4 | 98.22 $\pm$ 0.560 | 91.25 $\pm$ 0.992 | 98.13 $\pm$ 0.281
| 5 | 96.52 $\pm$ 0.658 | 83.61 $\pm$ 0.927 | 96.84 $\pm$ 0.346
$\boldsymbol{\gamma_{base,t}}$ | 1 | 90.52 $\pm$ 0.263 | 100.0 $\pm$ 1.572 | 99.77 $\pm$ 2.768
2 | 91.27 $\pm$ 0.789 | 100.4 $\pm$ 1.964 | 101.2 $\pm$ 3.601
3 | 91.92 $\pm$ 0.991 | 100.3 $\pm$ 4.562 | 101.1 $\pm$ 4.014
(nats) | 4 | 91.75 $\pm$ 1.136 | 102.7 $\pm$ 7.134 | 101.0 $\pm$ 4.573
| 5 | 92.05 $\pm$ 1.212 | 102.4 $\pm$ 6.195 | 100.5 $\pm$ 4.942
$\boldsymbol{\gamma_{new,t}}$ | 1 | 90.52 $\pm$ 0.263 | 100.0 $\pm$ 1.572 | 99.77 $\pm$ 2.768
2 | 115.8 $\pm$ 0.805 | 125.7 $\pm$ 2.413 | 124.6 $\pm$ 3.822
3 | 107.7 $\pm$ 0.600 | 118.3 $\pm$ 3.523 | 116.5 $\pm$ 2.219
(nats) | 4 | 100.9 $\pm$ 0.659 | 107.1 $\pm$ 5.316 | 102.3 $\pm$ 1.844
| 5 | 113.4 $\pm$ 0.820 | 118.2 $\pm$ 1.572 | 113.3 $\pm$ 0.755
$\boldsymbol{\gamma_{all,t}}$ | 1 | 90.52 $\pm$ 0.263 | 100.0 $\pm$ 1.572 | 99.77 $\pm$ 2.768
2 | 102.9 $\pm$ 0.408 | 111.9 $\pm$ 2.627 | 112.7 $\pm$ 3.300
3 | 104.8 $\pm$ 1.114 | 114.9 $\pm$ 4.590 | 114.6 $\pm$ 4.788
(nats) | 4 | 103.9 $\pm$ 0.759 | 114.3 $\pm$ 3.963 | 112.1 $\pm$ 2.150
| 5 | 106.1 $\pm$ 0.868 | 118.7 $\pm$ 5.320 | 111.9 $\pm$ 2.663
$\boldsymbol{KL_{all,t}}$ | 1 | 1.410 $\pm$ 0.181 | 5.629 $\pm$ 3.749 | 5.635 $\pm$ 3.739
2 | 3.177 $\pm$ 0.702 | 9.238 $\pm$ 0.674 | 7.495 $\pm$ 0.738
3 | 4.923 $\pm$ 1.085 | 12.13 $\pm$ 0.977 | 10.17 $\pm$ 1.528
(nats) | 4 | 5.603 $\pm$ 1.250 | 14.32 $\pm$ 1.040 | 11.66 $\pm$ 1.004
| 5 | 9.296 $\pm$ 1.346 | 16.37 $\pm$ 0.970 | 12.49 $\pm$ 0.551

TABLE XVIII: Results for PixelVAE based class incremental continual learning
approaches averaged over 5 runs, baselines and the reference isolated learning
scenario for FashionMNIST at the end of every task increment in analogy to
table XV. Extension of table 4 in the main body. Here, in addition to the
accuracy $\alpha_{t}$, $\gamma_{t}$ and $KL_{t}$ also indicate the respective
NLL reconstruction metrics and corresponding KL divergences at the end of
every task increment $t$.

Fashion | t | Dual Pix Model | PixCDVAE | PixOCDVAE
---|---|---|---|---
$\boldsymbol{\alpha_{base,t}}$ | 1 | 99.57 $\pm$ 0.091 | 99.58 $\pm$ 0.076 | 99.54 $\pm$ 0.079
2 | 82.40 $\pm$ 6.688 | 90.06 $\pm$ 1.782 | 88.60 $\pm$ 1.998
3 | 78.55 $\pm$ 3.964 | 83.70 $\pm$ 3.571 | 87.66 $\pm$ 0.375
(%) | 4 | 54.69 $\pm$ 3.853 | 50.23 $\pm$ 7.004 | 68.31 $\pm$ 3.308
| 5 | 60.04 $\pm$ 5.151 | 47.83 $\pm$ 13.41 | 74.45 $\pm$ 2.889
$\boldsymbol{\alpha_{new,t}}$ | 1 | 99.57 $\pm$ 0.091 | 99.58 $\pm$ 0.076 | 99.54 $\pm$ 0.079
2 | 97.73 $\pm$ 1.113 | 96.47 $\pm$ 0.596 | 97.31 $\pm$ 0.475
3 | 99.09 $\pm$ 0.367 | 97.33 $\pm$ 0.725 | 96.88 $\pm$ 1.156
(%) | 4 | 97.55 $\pm$ 0.588 | 96.12 $\pm$ 0.675 | 95.47 $\pm$ 1.332
| 5 | 98.85 $\pm$ 0.141 | 97.91 $\pm$ 0.596 | 98.63 $\pm$ 0.176
$\boldsymbol{\alpha_{all,t}}$ | 1 | 99.57 $\pm$ 0.091 | 99.58 $\pm$ 0.076 | 99.54 $\pm$ 0.079
2 | 86.22 $\pm$ 3.704 | 92.93 $\pm$ 0.160 | 92.17 $\pm$ 1.425
3 | 76.77 $\pm$ 4.378 | 84.07 $\pm$ 1.069 | 87.30 $\pm$ 0.322
(%) | 4 | 62.93 $\pm$ 3.738 | 64.42 $\pm$ 1.837 | 76.36 $\pm$ 1.267
| 5 | 72.41 $\pm$ 2.941 | 63.05 $\pm$ 1.826 | 80.85 $\pm$ 0.721
$\boldsymbol{\gamma_{base,t}}$ | 1 | 267.8 $\pm$ 1.246 | 230.8 $\pm$ 3.024 | 232.0 $\pm$ 2.159
2 | 273.6 $\pm$ 0.631 | 232.5 $\pm$ 1.582 | 231.8 $\pm$ 0.416
3 | 274.0 $\pm$ 0.552 | 235.6 $\pm$ 2.784 | 231.6 $\pm$ 0.832
(nats) | 4 | 273.7 $\pm$ 0.504 | 236.4 $\pm$ 3.157 | 231.4 $\pm$ 2.550
| 5 | 274.1 $\pm$ 0.349 | 241.1 $\pm$ 1.747 | 234.1 $\pm$ 1.498
$\boldsymbol{\gamma_{new,t}}$ | 1 | 267.8 $\pm$ 1.246 | 230.8 $\pm$ 3.024 | 232.0 $\pm$ 2.159
2 | 313.4 $\pm$ 1.006 | 275.8 $\pm$ 1.888 | 275.3 $\pm$ 1.473
3 | 269.1 $\pm$ 0.616 | 268.3 $\pm$ 3.852 | 262.9 $\pm$ 1.893
(nats) | 4 | 282.4 $\pm$ 0.321 | 259.1 $\pm$ 1.305 | 259.6 $\pm$ 2.050
| 5 | 305.8 $\pm$ 0.286 | 283.2 $\pm$ 2.150 | 283.5 $\pm$ 2.458
$\boldsymbol{\gamma_{all,t}}$ | 1 | 267.8 $\pm$ 1.246 | 230.8 $\pm$ 3.024 | 232.0 $\pm$ 2.159
2 | 293.8 $\pm$ 0.349 | 254.3 $\pm$ 1.513 | 255.8 $\pm$ 0.436
3 | 285.7 $\pm$ 0.510 | 261.5 $\pm$ 2.970 | 259.1 $\pm$ 0.929
(nats) | 4 | 284.9 $\pm$ 0.703 | 263.2 $\pm$ 2.259 | 259.5 $\pm$ 3.218
| 5 | 289.5 $\pm$ 0.396 | 271.7 $\pm$ 2.117 | 267.2 $\pm$ 0.586
$\boldsymbol{KL_{all,t}}$ | 1 | 3.610 $\pm$ 0.856 | 7.164 $\pm$ 0.759 | 7.809 $\pm$ 1.255
2 | 6.247 $\pm$ 0.710 | 13.79 $\pm$ 0.282 | 12.23 $\pm$ 0.287
3 | 7.811 $\pm$ 0.799 | 18.26 $\pm$ 0.818 | 15.36 $\pm$ 0.530
(nats) | 4 | 8.982 $\pm$ 0.812 | 21.75 $\pm$ 0.561 | 18.31 $\pm$ 0.333
| 5 | 9.781 $\pm$ 1.068 | 22.14 $\pm$ 0.377 | 17.93 $\pm$ 0.360

TABLE XIX: Results for PixelVAE based class incremental continual learning
approaches averaged over 5 runs, baselines and the reference isolated learning
scenario for AudioMNIST at the end of every task increment in analogy to table
XVI. Extension of table 4 in the main body. Here, in addition to the accuracy
$\alpha_{t}$, $\gamma_{t}$ and $KL_{t}$ also indicate the respective NLL
reconstruction metrics and corresponding KL divergences at the end of every
task increment $t$.

Audio | t | Dual Pix Model | PixCDVAE | PixOCDVAE
---|---|---|---|---
$\boldsymbol{\alpha_{base,t}}$ | 1 | 100.0 $\pm$ 0.000 | 99.71 $\pm$ 0.218 | 99.27 $\pm$ 0.410
2 | 99.52 $\pm$ 0.273 | 97.86 $\pm$ 0.799 | 97.88 $\pm$ 2.478
3 | 93.15 $\pm$ 3.062 | 81.38 $\pm$ 5.433 | 95.82 $\pm$ 3.602
(%) | 4 | 81.55 $\pm$ 8.468 | 50.58 $\pm$ 14.60 | 91.56 $\pm$ 5.640
| 5 | 64.60 $\pm$ 8.739 | 29.94 $\pm$ 18.47 | 75.25 $\pm$ 10.18
$\boldsymbol{\alpha_{new,t}}$ | 1 | 100.0 $\pm$ 0.000 | 99.71 $\pm$ 0.218 | 99.27 $\pm$ 0.410
2 | 99.71 $\pm$ 0.043 | 99.78 $\pm$ 0.128 | 99.81 $\pm$ 0.189
3 | 98.23 $\pm$ 1.092 | 98.41 $\pm$ 0.507 | 99.30 $\pm$ 0.550
(%) | 4 | 95.31 $\pm$ 0.868 | 94.30 $\pm$ 0.914 | 97.87 $\pm$ 0.293
| 5 | 98.18 $\pm$ 0.885 | 97.00 $\pm$ 0.520 | 99.43 $\pm$ 0.495
$\boldsymbol{\alpha_{all,t}}$ | 1 | 100.0 $\pm$ 0.000 | 99.71 $\pm$ 0.218 | 99.27 $\pm$ 0.410
2 | 99.50 $\pm$ 0.157 | 98.64 $\pm$ 0.875 | 99.67 $\pm$ 0.033
3 | 95.37 $\pm$ 1.750 | 90.10 $\pm$ 1.431 | 97.77 $\pm$ 1.017
(%) | 4 | 86.97 $\pm$ 2.797 | 75.55 $\pm$ 3.891 | 95.41 $\pm$ 1.345
| 5 | 75.50 $\pm$ 3.032 | 63.44 $\pm$ 5.252 | 90.23 $\pm$ 1.139
$\boldsymbol{\gamma_{base,t}}$ | 1 | 434.2 $\pm$ 1.068 | 432.6 $\pm$ 0.321 | 433.8 $\pm$ 0.370
2 | 434.4 $\pm$ 1.082 | 432.5 $\pm$ 0.551 | 433.5 $\pm$ 1.464
3 | 434.6 $\pm$ 0.785 | 432.9 $\pm$ 0.723 | 433.1 $\pm$ 1.269
(nats) | 4 | 434.2 $\pm$ 1.209 | 433.0 $\pm$ 0.781 | 433.0 $\pm$ 1.283
| 5 | 435.1 $\pm$ 1.915 | 431.4 $\pm$ 0.666 | 432.3 $\pm$ 0.189
$\boldsymbol{\gamma_{new,t}}$ | 1 | 434.2 $\pm$ 1.068 | 432.6 $\pm$ 0.321 | 433.8 $\pm$ 0.370
2 | 390.4 $\pm$ 0.694 | 389.4 $\pm$ 0.208 | 389.4 $\pm$ 1.304
3 | 444.7 $\pm$ 0.545 | 442.7 $\pm$ 0.513 | 442.4 $\pm$ 0.275
(nats) | 4 | 497.4 $\pm$ 0.740 | 494.4 $\pm$ 0.700 | 494.8 $\pm$ 0.386
| 5 | 431.9 $\pm$ 1.032 | 428.0 $\pm$ 0.851 | 429.7 $\pm$ 1.223
$\boldsymbol{\gamma_{all,t}}$ | 1 | 435.2 $\pm$ 15.69 | 432.6 $\pm$ 0.321 | 433.8 $\pm$ 0.370
2 | 412.4 $\pm$ 0.871 | 410.9 $\pm$ 0.351 | 411.5 $\pm$ 1.406
3 | 423.3 $\pm$ 0.618 | 421.0 $\pm$ 1.026 | 421.9 $\pm$ 0.661
(nats) | 4 | 441.6 $\pm$ 0.420 | 439.8 $\pm$ 0.833 | 439.8 $\pm$ 0.718
| 5 | 440.3 $\pm$ 1.297 | 436.9 $\pm$ 0.751 | 437.7 $\pm$ 0.432
$\boldsymbol{KL_{all,t}}$ | 1 | 4.361 $\pm$ 0.671 | 9.293 $\pm$ 0.943 | 11.87 $\pm$ 1.504
2 | 5.130 $\pm$ 0.636 | 14.00 $\pm$ 0.748 | 12.40 $\pm$ 0.719
3 | 5.399 $\pm$ 0.724 | 20.28 $\pm$ 0.774 | 14.41 $\pm$ 0.461
(nats) | 4 | 5.817 $\pm$ 1.038 | 24.91 $\pm$ 0.845 | 16.00 $\pm$ 0.505
| 5 | 6.031 $\pm$ 0.832 | 27.14 $\pm$ 1.139 | 17.45 $\pm$ 0.835

(a) CDVAE 2 classes

(b) CDVAE 4 classes

(c) CDVAE 6 classes

(d) CDVAE 8 classes

(e) OCDVAE 2 classes

(f) OCDVAE 4 classes

(g) OCDVAE 6 classes

(h) OCDVAE 8 classes

(i) PixCDVAE 2 classes

(j) PixCDVAE 4 classes

(k) PixCDVAE 6 classes

(l) PixCDVAE 8 classes

(m) PixOCDVAE 2 classes

(n) PixOCDVAE 4 classes

(o) PixOCDVAE 6 classes

(p) PixOCDVAE 8 classes

Figure 13: Generated images for continually learned incremental MNIST at the
end of task increments for CDVAE (a-d), OCDVAE (e-h), PixCDVAE (i-l) and
PixOCDVAE (m-p). Each individual grid is sorted according to the class label
that is predicted by the classifier.

(a) CDVAE 2 classes

(b) CDVAE 4 classes

(c) CDVAE 6 classes

(d) CDVAE 8 classes

(e) OCDVAE 2 classes

(f) OCDVAE 4 classes

(g) OCDVAE 6 classes

(h) OCDVAE 8 classes

(i) PixCDVAE 2 classes

(j) PixCDVAE 4 classes

(k) PixCDVAE 6 classes

(l) PixCDVAE 8 classes

(m) PixOCDVAE 2 classes

(n) PixOCDVAE 4 classes

(o) PixOCDVAE 6 classes

(p) PixOCDVAE 8 classes

Figure 14: Generated images for continually learned incremental FashionMNIST
at the end of task increments for CDVAE (a-d), OCDVAE (e-h), PixCDVAE (i-l)
and PixOCDVAE (m-p). Each individual grid is sorted according to the class
label that is predicted by the classifier.

(a) CDVAE 2 classes

(b) CDVAE 4 classes

(c) CDVAE 6 classes

(d) CDVAE 8 classes

(e) OCDVAE 2 classes

(f) OCDVAE 4 classes

(g) OCDVAE 6 classes

(h) OCDVAE 8 classes

(i) PixCDVAE 2 classes

(j) PixCDVAE 4 classes

(k) PixCDVAE 6 classes

(l) PixCDVAE 8 classes

(m) PixOCDVAE 2 classes

(n) PixOCDVAE 4 classes

(o) PixOCDVAE 6 classes

(p) PixOCDVAE 8 classes

Figure 15: Generated images for continually learned incremental AudioMNIST at
the end of task increments for CDVAE (a-d), OCDVAE (e-h), PixCDVAE (i-l) and
PixOCDVAE (m-p). Each individual grid is sorted according to the class label
that is predicted by the classifier.

## G. Generative replay examples with CDVAE and OCDVAE

In this section we provide visualization of data instances that are produced
during generative replay at the end of each task increment. In particular, we
qualitative illustrate the effect of constraining sampling to the aggregate
posterior in contrast to naively sampling from the prior without statistical
outlier rejection for low density regions. Figures 13, 14 and 15 illustrate
generated images for MNIST, FashionMNIST and AudioMNIST respectively. For both
a naive CDVAE as well as the autoregressive PixCDVAE we observe significant
confusion with respect to classes. As the generative model needs to learn how
to replay old tasks’ data based on its own former generations, ambiguity and
blurry interpolations accumulate and are rapidly amplified. This is not the
case for OCDVAE and PixOCDVAE, where the generative model is capable of
maintaining higher visual fidelity throughout continual training and
misclassification is scarce.