# Detection of Abuse in Financial Transaction Descriptions Using Machine
Learning

Anna Leontjeva, Genevieve Richards, Kaavya Sriskandaraja, Jessica Perchman,
Luiz Pizzato All authors are with Artificial Intelligence Labs, Commonwealth
Bank of Australia, Sydney, Australia

###### Abstract

Since introducing changes to the New Payments Platform (NPP) to include longer
messages as payment descriptions, it has been identified that people are now
using it for communication, and in some cases, the system was being used as a
targeted form of domestic and family violence. This type of tech-assisted
abuse poses new challenges in terms of identification, actions and approaches
to rectify this behaviour. Commonwealth Bank of Australia’s Artificial
Intelligence Labs team (CBA AI Labs) has developed a new system using advances
in deep learning models for natural language processing (NLP) to create a
powerful abuse detector that periodically scores all the transactions, and
identifies cases of high-risk abuse in millions of records. In this paper, we
describe the problem of tech-assisted abuse in the context of banking
services, outline the developed model and its performance, and the operating
framework more broadly.

###### Index Terms:

Abuse, NLP, Machine Learning, Offensive Language

##  I Introduction

###  I-A Technology Assisted Abuse

Digital communication plays an increasingly important role in everyday life.
As of 2021, 4.55 billion people are active social media users, equating to
57.6% of the world population [1]. The prevalence and variety of digital
communication have given us the ability to contact someone 24 hours a day
through many different ways such as social media, text-messaging, and email.
Although this has increased convenience for a lot of people, it has also
presented significant challenges for personal security and privacy, and in
particular for domestic violence victims/survivors [2].

Technology-facilitated abuse is commonly defined as the use of technology such
as mobile, online or other digital technologies, as a tool for people to
engage in behaviours such as coercive control, intimidation, stalking,
monitoring, psychological and emotional abuse, consistent harassment and
unwanted contact, sexual harassment, to cause harm and distress to the
recipient [3]. This term can be extended to include broader forms of online
harassment and cyber bullying; however, it is typically focused on gendered
violence (domestic violence) [4]. The impacts of technology-facilitated abuse
on the recipient can include depression, worthlessness, fatigue, self-harm,
traumatisation, fear, isolation, emotional distress and more. There are also
reported economic impacts, functional harms and an intrusion on the
recipient’s personal freedom [4].

###  I-B Technology assisted abuse in Banking

Modern payment systems have increased the speed of financial transactions and
also enabled richer descriptions of those transactions [5]. The introduction
of the New Payment Platform (NPP) in Australia in 2018111See:
https://nppa.com.au/the-platform/ allows a person or a business to conduct a
transfer to others in real-time and include up to 280 UTF-8 characters for
payment description and an additional 35 printable ASCI characters for payment
reference. NPP has also provided customers with the ability to set up a simple
identifier (PayID®) for their accounts, such as a mobile number or an email
address, so that they no longer need to remember their Bank State Number
(BSB)222BSB is a number that indicates the bank and branch that holds ones
account in Australia, facilitating a transaction between banks.

and account number. It resulted in a simple and fast way for people to
transfer funds to each other in Australia. As of June 2022, 107 Australian
financial institutions use these services, and more than 10 million PayIDs
have been registered by customers and businesses [6]. New technologies such as
PayID simplified banking increasing the ease and volume of transactions,
however, it also provided perpetrators another tool to use for abuse.

In early 2020, we as the Commonwealth Bank of Australia (CBA) identified the
use of real-time transactions as a means of communication between individuals,
typically through the use of low value transactions. We found that more than
8,000 customers in a three-month period had received multiple low-value
deposits with messages in the transaction description that were potentially
abusive. We identified that the intent of the messages ranged from “jokes”
using profanity to serious threats or references to domestic abuse and family
violence [5]. Utilizing transaction descriptions as a mode of either criminal
communication or abuse rather than as means to transfer funds is being
detected in financial institutions across the world. Australian Transaction
Reports and Analysis Centre (AUSTRAC) Fintel Alliance report [5] notes that it
is not unique to the Australian banking industry. For example, several
Brazillian news groups report the arrest of a man harassing a young woman
through bank transfers after having his number blocked [7]. We can see that
any payment that contains a free text field to be completed by the sender and
viewed by the recipient can be a vehicle for criminal communication.

###  I-C Role of the Bank

Although online banking was never intended to be used as a digital
communication technology, its occurrence has meant that financial institutions
had to take action in order to protect those being abused. Initial responses
by financial institutions have involved actions such updating their terms and
conditions to include references to abusive transactions and introducing real-
time word blocks from reference lists [8]. These measures have shown to
significantly reduce the use of profanity and some abuse in transaction
description, however, they have not completely stop serious abuse from
happening.

Although these solutions have seen a reduction in profanity used in online
banking transactions, they are not stopping abusers with the intention to
cause harm or distress to the recipients as they have simply learnt how to
circumvent these initial solutions. For example, the word _unblock_ , which is
associated with these abusive payments, was observed to be modified to _un-
block_ , _u.n.b.l.o.c.k_ and other versions to bypass it. Because of this, we
decided to protect our customers by building a monitoring system that can work
in the background identifying cases of serious abuse that may need to be
further investigated.

Building a system that identifies abuse involves, among many things, the
definition of abuse, and the design of a system and processes that can help
the victims and dissuade the perpetrator. To proactively stop abusers or to
reach out and provide support to the affected customers, we first need to
identify these cases. There is a lot of complexity in this task alone
including the volume of transactions sent each day, understanding the context
of the transaction sent and the nuances of the language and behaviour used. We
have addressed the issue by using a multi-step approach. First, the model is
applied to score all the transactions. The cases with the highest score are
then sent to a dedicated team of customer vulnerability specialists that
manually review and contact the victims of abuse identified by the model. The
team will then take the most appropriate action, for example, it may involve
contacting the victim, as well as sending warning letters to the perpetrator
and let them know their behaviour is not tolerated. In some cases it might
involve welfare checks to ensure their safety and to gain their consent to
take further action. Due to the capacity and complexity of cases and
interventions offered, the team is only able to manually review and process a
limited number of cases a month. Therefore, it is crucial that we control the
number of false positive cases ensuring we detect all the true positive cases.

Due to the novelty of the problem, the current approach doesn’t contain
comparison with the other models, and we believe can be improved by efforts of
the wider research community. However, the current work establishes a solid
baseline to compare it to. We also hope that it helps to adopt these
techniques in the other financial institutions that are currently utilising
simple filters and keyword detection that can be easily overcome and bypassed.

##  II Problem Statement

In this paper we propose an approach to the problem of high-risk abuse case
detection in the banking payment systems using a combination of features from
different deep learning models. Despite the fact that technology assisted
abuse is not a new problem and some research has been conducted to investigate
it (see Section III for more details), this type of abuse using banking
transactions was only recently identified and poses a new set of challenges.
One of the biggest challenges is the sensitivity of the matter. It should be
handled with uttermost care considering that both action and no-action can be
potentially dangerous. Bank transactions are different to social media
messages that can be easily deleted or blocked. The transactions have much
longer “life-span”. They might be visible to someone beyond the victim. They
might be delivered in printed form. They might be used as evidence for
people’s applications to loans and other services, which can cause re-
traumatisation by revisiting them. Similarly, the victim might have much lower
tolerance towards the abuser’s behaviour and all these situations can be
difficult to deal with.

In terms of actions taken, the bank often contacts abusers asking them to
stop. If the behaviour continues, it is possible to _unbank_ a customer.
However, differently to social media bans, unbanking is a decision of a
financial institution to ends its relationship with a particular individual
and could lead to serious consequences affecting peoples’ lives. To complicate
things further, transaction descriptions are often limiting in context and
often open to the interpretations. Therefore, a dedicated team has to
investigate and approach to each case individually, which is a labour-intense
process that leads to the prioritisation of the cases. This is known as a
human-in-the-loop system, defined by needing both human and machine
performance to contribute to improving the overall system results [9].
Therefore, in this paper we focus on the framework of detecting high-risk
cases that need to be prioritised, allowing us to adhere to Australia’s AI
Ethics Principles of reliability and safety [10].

###### Definition II.1

High-risk cases of abuse are defined by the severity and volume of the
following:

  * •

the presence of repetitive, abusive, degrading or hateful comments about a
person or persons

  * •

threats of physical or sexual violence to a person

  * •

threats of self-harm

  * •

endangering or causing distress to a minor

  * •

repeated or unwanted sexual requests to a person.

##  III Literature review

A report by [11] provides an in-depth investigation of different technology
utilized by abusers to commit technology facilitated abuse related to Domestic
Violence. The report explores types of abuse associated with coercive control,
financial abuse, smart homes and stalking, and how these are misused by
abusers. The report also provides a framework for inclusive safety when
designing technology systems however does not suggest any solutions around how
to identify when a system is being misused. Although the report touches on how
financial abuse can happen in banking systems it does not explore a problem of
transactions descriptions being utilized by abusers to send abusive messages
and exhibit control and stalking behaviours.

The problem of detecting abusive messages in bank transaction descriptions is
novel. While similar problems of detecting offensive language, toxicity levels
in text, bullying and hate speech has been a subject of research over the past
20 years, it has mostly been in the context of social network moderation, for
example, employing machine learning techniques to identify this type of
content from Twitter [12] and Facebook [13].

In a similar fashion to the issue of abusive messages, data within social
networks is highly unstructured, informal, and often misspelled, therefore,
papers such as [14] have utilised natural language processing techniques to
detect both lexical and syntactic features of sentences. Branching out from
solely using features from the text, [14] used style, structure and posting
pattern features to improve detection of offensive messages. [15] used joy,
emoticons, uppercase, number of followers, amongst other features.

[13] outlines a new approach called Entailment as Few Shot Learner (EFL). With
the aim to improve language models as few-shot learners, the approach involves
converting class labels into a natural language sentence which is used to
describe the label, and determine whether the label entails the description.
The EFL approach can also leverage techniques such as unsupervised contrastive
data augmentation and can be extended to multilingual few-shot learning. [16]
proposes a novel shallow neural network using GloVe embeddings on Wikipedia
public datasets to classify whether the comments are toxic or are instances of
attack in cyber bullying context.

[12] leveraged machine learning to detect targeted vs untargeted offensive
language. This was done by creating a three-level annotation schema,
corresponding to three subtasks. The first Subtask A focussed on purely the
language in a dataset, classifying it as either offensive or non offensive.
Subtask B further classified the data as targeted or untargeted, i.e. general
offensive language or hate speech, and Subtask C classifies whether the hate
speech was targeted at an individual or a group.

Other techniques to detect abuse have leveraged systems based on pre-trained
language models such as RoBERTa and BERT [17], which have reached new state-
of-the-art performances on numerous tasks [18]. In [19], a BERT model fine-
tuned with binary cross-entropy loss was used to identify abusive language in
Twitter Hatespeech and Wikipedia datasets. BERT embedded models outperformed
other embeddings such as fastText, TextCNN and TextCNN + Character n-grams.
One issue that was found with pre-trained models is that they are trained on
general datasets, so they have limitations on domain-specific language tasks.
Re-training pre-trained models on domain-specific datasets is a popular method
to address this as seen in [20]. This is especially useful contexts such as
abusive language detection where there is not enough data to train a BERT-like
model from scratch. Their model, ‘TweetBERT’, was re-trained on a Twitter-
based corpus and outperformed other BERT based models when analysing Twitter
content.

Paper [21] outlined another method to improve BERT based models in order to
detect instances of cyberbullying and harmful speech on Australian-based
Twitter data. This was done through appending additional features onto BERT as
special tokens. The features included emoji paths, metadata such as user
information (e.g. age, gender, number of posts), data on their network (e.g.
number of follower and friends) and their power (followers/friends ratio).
Results showed that BERT with the extra tokens (BERT + emoji + network +
power) yielded the most accuracy.

We observed that prior work focuses on identifying instances of abusive
messaging instead of the abusive relationship. As mentioned in Definition II.1
of High-Risk abuse these transactions descriptions need to be relatively
consistent and occur in a higher frequency. In a similar fashion, some papers
have implemented techniques on user-centric data to identify potentially
abusive users, rather than lone instances of abusive language. For example,
[22] used graph machine learning to identify hateful users. Hateful accounts
were characterised using attributes such as creation date, user activity,
network centrality, sentiment and lexical analysis, amongst other attributes.
The methodology involved using a process based on DeGroot’s learning model
[22] to sample users in a neighbourhood, and label them as hateful or non-
hateful. There were significant patterns found to be associated with ‘hateful
users’, including increased activity and increased frequency in using
particular language.

While there is a lot of work that focus on online social networks, there has
been no research into detecting abuse in transaction descriptions in a context
of financial services. In this work, we leverage several machine learning
techniques to not only identify abusive language in transaction descriptions,
but identify the transaction relationships of the customers who are using it.

##  IV Data

In this section, we introduce the specifics of the dataset we use as well as
the data preprocessing methods. This paper relies on Commonwealth Bank
transaction data. We extracted details from the bank’s database, including
transaction descriptions, the corresponding dollar amounts, date of the
transaction, sender and recipient account numbers. We gathered transaction
data from both the new payment platform (NPP) and the non-NPP processes. This
data was used to generate features for the model training, which were
aggregated by _relationships_ , as described in Section V. Note, a
relationship in this context means a sender and a recipient pair of a
transaction; that is, if sender $a$ sends a transaction to recipient $b$, we
have the $\langle{a,b}\rangle$ relationship, if $b$ sends a transaction to $a$
this creates a different and new $\langle{b,a}\rangle$ relationship. The
number of transactions we used by relationship is defined by the historical
time-window we used. In this study we fixed time-window to be one month.

Our dataset contains 1,039 relationships that were labelled as either (1)
highly abusive or (0) non-abusive. Among those unique relationships, 283 were
branded as ’highly-abusive’ by several domestic violence experts who used the
definition of high-risk abuse as a guide (see Definition II.1). They had an
agreement score of 87%. Negative sampling was created by randomly choosing
non-abusive relationships as well as a sample of cases where transactions had
“conversational” descriptions that do not meet the abuse requirements but were
significantly different to normal transactions. Some cases, for example,
included customers sending song lyrics to one another or a perfectly natural
chat. This was done to avoid using a machine learning model to detect only
long messages rather than high-risk abuse. This training set contains data
from July 2021 to January 2022. We used this dataset for our experiments and
validated our proposed system using k-fold cross validation. It is important
to note that there are no overlapping relationship pairs between folds.

In addition, for an out-of-sample dataset, we extracted one month of
transaction data. We used data from the month of February 2022 for this. This
demonstrates a model scoring use-case as part of the current business process.
In any given month, less than 0.0005% of cases are abusive, resulting in a
highly imbalanced situation. As manually scoring all of these monthly
transactions is impractical, the out-of-sample test set was created by
labelling the top 50 highest scored relationships of the corresponding month
for each of the candidate models, 35 of which turned out to be highly abusive.

##  V Methodology

In this section we described our approach in more details. The first task was
to decide whether it was better to detect abuse at the transaction, customer,
or relationship level. The transaction level lacks sufficient textual
information to capture the context. Consider a transaction text that says “I
love you”. Without more transactions to observe the dynamics, it’s unclear
whether this is a case of harassment or a regular message between a couple.
However, if this type of description is sent every 5 minutes and the other
party requests to stop, the case becomes much clearer. However, if we consider
collecting all transactions at the customer level, the abusive information may
be diluted. For example, abusive customers frequently harass only one person
among their recipients despite having a large network of regular recipients.
As a result, we detect abuse at the relationship level, using descriptions
gleaned from transactions between each sender-recipient pair. Figure 1 shows
an example of an abuser having multiple victims, which in this case we would
flag as two distinct relationships of high risk.

Figure 1: Some abusers intimidate several people. In this case, Abuser’s
communication with ex-wife and Abuser’s communication with his child are
considered as separate relationship in our dataset. Note: the transaction
descriptions in this image are not real and were made up as illustrations of
how abusive these messages are.

Following that, we describe the overall approach developed to detect abuse in
transaction descriptions (AITD). It should be noted here that our target is to
detect the highly abusive cases. Figure 2 diagram depicts an overview of our
system involving the following steps:

  1. 1.

Transaction-level feature generation: creating appropriate features from each
single transaction description (Section V-A)

  2. 2.

Relationship-level feature generation: aggregating these features on each
relationship (sender-recipient pair) in order to detect abusive customers, not
just individual abusive transactions (Section V-B)

  3. 3.

Incorporating reciprocity information: generating features related to the
replies a potential victim might have sent (Section V-C)

  4. 4.

Training a machine learning model to predict the labels: Random Forest model
was used to classify relationships as either highly abusive or non-abusive

Figure 2: An overview of the system architecture. Three sets of the features
are created from the raw data and combined on the level of relationships. The
final model takes both original features and reciprocity features.

###  V-A Transaction-level feature generation

As described previously, the first step is to generate features on a
transaction level. This transaction-level feature vector is then aggregated to
create features on a relationship level. There are three types of features
involved in our model, as follows:

  * •

Transaction details features (TRX) are solely related to the specifics of the
transaction between sender and receiver, such as: dollar amount transacted,
date of the transaction, number of transactions a day, maximum number of
transactions per day and the time between maximum and minimum number of
transactions.

  * •

Simple text features (ST) are related to the basic information we can extract
from the transaction description, such as length of the transaction
description, upper/lower/mixed case flags, number of words, length of the
longest word in the transaction description, does the message contains special
characters/numbers, empty description flag, various punctuation and number-
related flags.

  * •

Emotion, Toxicity and Sentiment features (ETS) are features based on three
pre-trained language models that are able to provide valuable information for
the abuse detection based on the text in the message descriptions. Seven
_toxicity_ features were generated per transaction using the unbiased version
of the BERT-based, pre-trained language model Detoxify [23]. The unbiased
version of Detoxify recognises toxicity and minimises unintended bias of
identities. It scores the text on seven categories of toxicity, such as
toxicity, severe toxicity, obscene, threat, insult, identity attack and sexual
explicit. These scores were then used as the seven toxicity features for the
proposed AITD model. For _emotion_ features we used DistilBERT models trained
on four data sources, including dailydialog, emotion-stimulus, isear and
huggingface emotion datasets [24]. This pre-trained model determines whether
the given text is neutral, joyful, sad, angry, contains love, fear, or
surprise emotions. We predicted the scores for each emotion class for each
transaction description. We used VADER (Valence Aware Dictionary for Sentiment
Reasoning) for finding the _sentiment_ of a transaction description. It
indicates both the polarity (positive/negative) and the intensity (strength)
of emotion. The sentimental analysis of VADER is based on a dictionary that
maps lexical features to emotion intensities known as sentiment scores. A
text’s sentiment score can be calculated by adding the intensity of each word
in the text. VADER’s Sentiment intensity analyser accepts a string and returns
a dictionary of scores in four categories, including positive, negative,
compound, and neutral [25].

###  V-B Relationship level feature generation

The above-mentioned features were calculated for every transaction. Because
our prediction task focus is on relationships, we need to aggregate the
information from all the transactions between a sender and a receiver. This
aggregation is done in a slightly different way depending on the features used
as shown in Table I.

TABLE I: Aggregation type for features. Feature aggregation is performed for all transactions within a relationship. Aggregation |  Features
---|---
Maximum |  All the sentiment features
Minimum, Maximum, Median |  Length of transactions, number of words, the longest word length, proportion of word breaks to the message description length333This feature helps to identify when spaces were removed
Sum |  All the toxicity features
Mean |  All the emotion features, transaction amount, number of lower case words, number of upper case words, number of mixed case words, number of punctuation found

We also used additional features derived from all transactions in a
relationship. These are the number of transactions sent in a relationship, the
maximum number of transactions sent in a single day and the number of unique
days in that a transactions has occured.

###  V-C Reciprocity

We also include the same features that are calculated on the replies of a
relationship. That is, we calculate features on relationship
$\langle{a,b}\rangle$ as well as features on the reciprocal relationship
$\langle{b,a}\rangle$. This is to confirm our hypothesis that reciprocity
might be useful as a recipient often avoids replying to an abusive sender.

##  VI Results and Discussion

First, we performed an experiment to investigate what sets of features are
able to discriminate the best between highly abusive and non-abusive cases. We
evaluated the models with the following combinations of the feature sets:
transaction details (TRX), simple text (ST), and toxicity and sentiment
features (ETS). We show the results of repeated 5-fold cross-validation in
Table II and use precision, recall, F1, AUC and AUC-PR metrics for evaluation.
Overall, the best performing model was the random forest model using simple
text, transaction details, emotion, toxicity and sentiment features and
recipricity combined (ETS + ST + TRX). After selecting the best sets of
features, we experimented with adding reciprocal features and observed further
improvements (see Table III)

TABLE II: Experimental results for combinations of emotion, toxicity and sentiment (ETS), simple text (ST) and transaction (TRX) features. Features | Performance
---|---
ETS |  ST |  TRX |  Prec |  Rec |  F1 |  AUC-PR |  ROC AUC
✓ |  |  |  0.618 |  0.740 |  0.670 |  0.526 |  0.766
|  ✓ |  |  0.615 |  0.686 |  0.645 |  0.505 |  0.748
|  |  ✓ |  0.575 |  0.666 |  0.614 |  0.474 |  0.731
✓ |  ✓ |  |  0.633 |  0.728 |  0.671 |  0.531 |  0.775
|  ✓ |  ✓ |  0.657 |  0.721 |  0.683 |  0.547 |  0.790
✓ |  |  ✓ |  0.638 |  0.709 |  0.669 |  0.532 |  0.780
✓ |  ✓ |  ✓ |  0.659 |  0.730 |  0.690 |  0.554 |  0.795

Next, we evaluated our results on an out-of-sample test set as outlined in
Section IV. The best system (ETS + ST + TRX + reciprocity) of the previous
experiment was used to demonstrate the capability of our model. The aim of
this validation was to make sure that the model had consistency and had no
false positives for the highest scored results, thus, allowing us to
confidently select top cases for a manual review. Table 3 displays the ROC
curve of the models on the out-of-sample test set of the transaction
descriptions collected over one month, whith no overlap of this month of data
with our training dataset.

TABLE III: Experimental results with the addition of reciprocity to the best model that contains emotion, toxicity and sentiment (ETS), simple text (ST) and transaction (TRX) features. Prec | Rec | F1 | AUC-PR | ROC AUC
---|---|---|---|---
0.678 | 0.738 | 0.703 | 0.570 | 0.800

Next, the top 50 cases of sender-recipient pairs are manually labelled and
used to produce the ROC curve, however, we did not manually verify the rest of
the cases as it contains hundreds of transaction descriptions and requires a
lot of manual effort. The ROC curve shows the trade-off between sensitivity
(true positive rate or recall), and specificity (1 - false positive rate). A
black dotted line in Figure 3 corresponds to a random guess. Note that
classifiers that produce curves closer to the top-left corner indicate a
better performance for the highest-scored cases. From Fig. 3 we can clearly
see that the best system predicts the highly abusive cases successfully with
the first true negative in the 26th case.

Figure 3: ROC curve (blue line) for the top 50 cases with the highest assigned
probability of out-of-sample test set, which is predicted against our best
model (ETS+ST+TRX) + reciprocity. Here the black dotted line is the ROC for a
model with an AUC equal to 0.5 which is the perfectly diagonal line and it
represents a model that makes random classifications.

##  VII Conclusion

In this paper we outlined a new problem related to the harassment and abuse
happening in the financial services’ domain. While resembling similarities
with the other online social platforms, this problem poses new challenges and
requires careful consideration. We outlined a particular case of abuse in
transaction descriptions in the largest bank of Australia, and suggested ways
to resolve it. We explored models with different feature sets and measured
their performance in a real-life scenario. We showed that the best performing
model is a supervised model trained on a variety of features that range in
complexity from simple transaction and text features to the toxicity and
emotions features that are calculated using state-of-the art advances in the
field of NLP. The final model is already fully operational in the bank. To
increase the model’s robustness, we regularly retrain it when the sent cases
are verified from the customer vulnarability specialists.

We are continue improving our system in order to provide better protection to
our customers. There are a range of potential improvements we are currently
working on and aim to published in future work. Some examples of potential
improvements are: better foreign language coverage, use of several months
conversation history to detect a long-term abuse, use of BERT embeddings
instead of high-level features when labelled training set is large enough.

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dynamics. Alternatively, we may choose a very small $\delta P_{m}\neq 0$, and
thus initiate the wrinkling instability (provided that the system is actually
unstable to wrinkling, as discussed in the main text). We solved the equations
in both configurations to generate the axisymmetric and non-axisymmetric
numerical results.

Because we are treating a system of DAEs, it is not possible to integrate the
equations directly (either explicitly or implicitly). We solved the equations
using the method of lines via Mathematica’s DAE solver implemented in the
NDSolve function. As a general rule, the equations were stable as long as
$\sqrt{\epsilon}/T\lesssim 1$, as can be expected from the
$\epsilon^{2}\partial_{t}$ structure in Eqs. (88)-(89), and as long as the
wrinkling fields did not grow too large, since our equations does not include
stabilizing terms for saturating the instability. We did not systematically
investigate the stability of the equations.

### Boundary conditions

As discussed in the main text, the development of the front-disclination pair
and the following dynamics of the bubble collapse require non-homogeneous
boundary conditions for the Airy stress function. In what follows we detail
the numerical boundary conditions we used in our simulations.

Boundary | $\Phi_{0}$ | $z_{0}$
---|---|---
$r_{0}=0$ |  | $D_{f}(\Phi_{0})_{0}=n_{0}(t)$
---
$r_{3/2}^{-1}D_{f}(\Phi_{0})_{1}=1$
| $D_{f}(z_{0})_{0}=-\frac{1}{2}h$
---
$r_{3/2}^{-1}D_{f}(z_{0})_{1}=1$
$r_{N-1}=1$ |  | $D_{b}^{3}(\Phi_{0})_{N-1}=0$
---
$(\Phi_{0})_{N-1}=0$
| $D_{b}^{2}(z_{0})_{N-1}=-1$
---
$(z_{0})_{N-1}=0$

The Neumann boundary condition for $\Phi_{0}$ at $r=0$ is denoted as
$n_{0}(t)$, given by

$n_{0}(t)=\frac{a_{0}}{2}e^{-t/T}.$ (95)

The reason for this choice is to interpolate smoothly from the initial
conditions, which do not obey Neumann boundary conditions on the discrete
lattice, to the final one which does. Leaving the original $O(a_{0})$
condition does not change the numerics qualitatively but did affect the
stability of the numerics and the behavior near $r=0$. This is true for other
boundary conditions as well: changing the boundary conditions did not
qualitatively change our results, with the exception that, as discussed in the
main text, changing the $r=0$ boundary conditions for $\Phi_{0}$ to fully
homogeneous ones leads to formation of a phantom bubble, rather than a
propagating front. As a general rule, changing the conditions by e.g.
modifying the constants $1,-1$ to other numbers, or by changing the second
derivative constraint on $z_{0}(r=1)$ to a first order one, just resulted in
the formation of a boundary layer of order $\ell_{BL}$.

For the undulating fields we used fully homogeneous boundary conditions, i.e.
$\varphi_{0}=\varphi_{1}=\varphi_{N-1}=\varphi_{N-1}=0$, and similarly for
$\zeta$.

Finally, in order to initialize the non-axisymmetric dynamics, we introduced a
very small fictitious undulating force (see Eq. (89)), of the form

$\delta P_{m}(t)=p_{0}m^{2}\frac{t^{2}}{T^{2}+t^{2}}e^{-5t/T},$ (96)

where $p_{0}$ was typically in the range $10^{-10}-10^{-30}$. The form above
was picked for convenience, and the final results do not depend strongly on
the form, except as regards the linear instability time, as discussed in Secs.
III.2 and IV.

### Detailed description of the figures and the analysis used to generate them

We now provide details of our figure production. For each figure, we first
give a sketch of the technique used (if relevant), and then provide the
relevant parameters.

#### Figure 1

In this figure, only panel (b) is a quantitative solution of our equations.
The parameters used to generate it are:

$\epsilon=3\times 10^{-3},m=36,T=0.05,N=2^{9},p_{0}=10^{-12}.$ (97)

#### Figure 4

The parameters used to generate this figure are:

$\epsilon=1\times 10^{-5},m=1\times 10^{3},T=0.05,N=2^{9},p_{0}=10^{-30}.$
(98)

We chose a quite large $m$ in this figure and also in the following ones, in
order to increase stability and suppress deviations from our large $m$
predictions.

#### Figure 5

In order to generate this figure, we solved the equations numerically for the
set of parameters given below. Then, we extracted the positions of
$r_{f}(t),\mathcal{S}(t)$ by fitting the numerical $g^{2}(r,t)$ to the
relevant Sievert surface expression in Eqs. (19) and (20) (we regularized the
Heaviside functions by a boundary layer of width
$\sqrt{\epsilon}\sim\ell_{BL}$). Fig. 17 depicts some typical results of the
fitting process, showing excellent agreement with the analytic expressions and
the resulting high accuracy of the fit.

The analytic expressions are just those appearing in the main text. They do
not depend on any fitting parameter except for $\ell_{core}$. In our fitting
we took

$\ell_{core}=3h,$ (99)

which is exactly the size of the numerical core defined by the boundary
conditions above. This choice also appeared, in a qualitative analysis, to
give a best fit to the data.

Figure 17: Fitting the numerics of the axisymmetric evolution to the
analytical expressions. The dots are the numerical solution, and the thin
lines are the analytic expressions of Eqs. (19) and (20).

The parameters used to generate this figure are:

$\epsilon=1\times 10^{-5},T=0.01,N=2^{9}.$ (100)

#### Figure 6

The parameters used to generate this figure are the same as those of Fig. 4,
see Eq. (98). The three traces are taken at $t=0.55,0.59,0.9$.

#### Figure 7

(a)

(b)

Figure 18: Fitting the numerics of the non-axisymmetric evolution to the
analytical expressions. The dots are the numerical solution, and the thin
lines are the analytic expressions of Eqs. (19) and (20). (a) The evolution of
$g^{2}(r,t)$, the Sievert surface, which yields $r_{o}(t),\mathcal{S}(t)$. (b)
The evolution of $\Phi_{0}(r,t)$, the disclination potential, yielding
$r_{i}(t)$. Note how $r_{o}(t)$ also appears in the data but is not captured
by the fitting process.

In order to generate this figure, we solved the equations numerically for the
set of parameters given below. Then, we extracted the positions of
$r_{i}(t),r_{o}(t),\mathcal{S}(t)$ by fitting the numerical $g^{2}(r,t)$ to
the relevant Sievert surface expressions, and simultaneously fitting
$\Phi_{0}(r,t)$ to the disclination expressions, as given in Eqs. (19) and
(20). (As above, we regularized the Heaviside functions by a boundary layer of
width $\sqrt{\epsilon}\sim\ell_{BL}$). The fit for $g^{2}$ gave us
$r_{o},\mathcal{S}$ and the fit for $\Phi_{0}$ gave us $r_{i}$ Fig. 18 depicts
some typical results of the fitting process, showing excellent agreement with
the analytic expressions and the resulting high accuracy of the fit.

As discussed in the main text, the analytic expressions for the non-
axisymmetric dynamics take as input the time $T_{ins}$, which is the time in
which the bulk stress is fully relieved in the wrinkled region. We identified
$t=T_{ins}$ as the time when the predictions for $r_{o}(t)$ given by the
Sievert surface, and for $r_{i}(t)$ given by the disclination, begin to
diverge (see also discussion of Fig. 8). As for the axisymmetric case, we took
$\ell_{core}=3a_{0}$, see Eq. (99) and the discussion regarding Fig. 5.

The parameters used to generate this figure are:

$\epsilon=1\times 10^{-5},m=1\times 10^{3},T=0.01,N=2^{9},p_{0}=10^{-30}.$
(101)

#### Figure 8

We generated this figure by solving the non-axisymmetric equations, varying
$p_{0}$, see Eq. (89), and keeping all other parameters constant. We then
identified the resulting $T_{ins}$ as the moment (to an accuracy of $\pm
0.01$), where the single propagating front $r_{f}(t)$ split into two fronts
$r_{i}(t),r_{o}(t)$, see e.g. Fig. 7, the discussion regarding that figure
above, and Fig. 18 which demonstrates how such splitting is identified.

The parameters used to generate this figure are:

$\epsilon=1\times 10^{-5},m=1\times
10^{3},T=0.01,N=2^{9},p_{0}=10^{-6}-10^{-14}.$ (102)

#### Figure 9

We generated this figure by solving the axisymmetric equations, varying the
number of lattice points $N$ and holding other parameters constant. Then, we
fit the slope of $z_{0}(0,0)-z_{0}(0,t)$ to a linear fit using Mathematica’s
FindFit procedure. The analytic expression was obtained by plotting the time
derivative of Eq. (65), with $\mathcal{S}(t)$ evaluated to logarithmic
accuracy as in Eq. (28), using the usual Eq. (99) for $\ell_{core}$.

The parameters used to generate this figure are:

$\epsilon=1\times 10^{-5},T=0.01,N=2^{7}-2^{11}.$ (103)

#### Figure 10

The data in this figure was received directly from the authors of Ref. 1. The
values of $R,a_{0},\gamma,\eta,\rho$ necessary for the scaling analysis were
all taken from the experimental data and can be obtained either from the work
itself or from the authors. The four colors blue, yellow, green and red
represent different viscosities $\eta=10,100,800,300$ Pa$\cdot$s,
respectively. We obtained each panel in the figure by rescaling the horizontal
axis differently; the scaling is given in the label of each panel. We then fit
the data to a linear equation using Mathematica’s FindFit procedure.

#### Figure 13

The parameters used to generate this figure are:

$\epsilon=1\times 10^{-5},m=1\times 10^{3},T=100,N=2^{9},p_{0}=10^{-30}.$
(104)

#### Figures 12 \- 15

The parameters used to generate these figures are:

$\epsilon=1\times 10^{-5},T=0.01,N=2^{9}.$ (105)

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