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+The AAAI 2023 Workshop on Representation Learning for Responsible Human-Centric AI (R2HCAI)
+A system for Human-AI collaboration for Online Customer Support
+Debayan Banerjee*
+Mathis Poser*
+Christina Wiethof*
+Varun Shankar Subramanian
+Richard Paucar
+Eva A. C. Bittner
+Chris Biemann
+Universit¨at Hamburg, Hamburg, Germany
+{debayan.banerjee,mathis.poser,christina.wiethof,eva.bittner,chris.biemann}@uni-
+hamburg.de,{varunshankar55,rfpaucar}@gmail.com
+Abstract
+AI enabled chat bots have recently been put to use to answer
+customer service queries, however it is a common feedback
+of users that bots lack a personal touch and are often unable to
+understand the real intent of the user’s question. To this end,
+it is desirable to have human involvement in the customer
+servicing process. In this work, we present a system where
+a human support agent collaborates in real-time with an AI
+agent to satisfactorily answer customer queries. We describe
+the user interaction elements of the solution, along with the
+machine learning techniques involved in the AI agent.
+Introduction
+In the pursuit of operational efficiency, companies across
+the globe have been deploying automation technology aided
+by Artificial Intelligence (AI) for Online Customer Support
+(OCS) use cases 1. With the explosive growth of social me-
+dia usage, incoming customer queries have grown exponen-
+tially and to handle this growth, the use of proper technology
+is critical. Some estimates say that by the year 2025, 95%
+of all customer interactions will be processed in some form
+by AI 2. However, AI in its present state is not advanced
+enough to completely replace human agents for most cus-
+tomer support scenarios. Additionally, the complete replace-
+ment of human workforce by AI is a topic of active ethical
+and political debate. For these reasons the development of a
+hybrid working environment is required, where both human
+agents and AI agents can co-operate to satisfy OCS require-
+ments.
+In this work we briefly describe a web based user inter-
+face that allows a customer to interact with a human sup-
+port agent, where the human agent receives helpful sugges-
+tions in parallel from an AI agent. In subsequent sections, we
+elaborate further on the machine learning techniques used
+for the AI agent.
+Our present work is a part of a project which aims to find
+ways of integrating AI agents into customer support based
+workflows, with an aim of reducing workload of human
+*These authors contributed equally.
+1https://www.gartner.com/smarterwithgartner/4-key-tech-
+trends-in-customer-service-to-watch
+2https://servion.com/blog/what-emerging-technologies-future-
+customer-experience/
+agents. It is one of the primary goals of the project not to
+entirely replace the human agent with AI, and instead find
+productive means of co-existence of the two. As a part of
+this project, an international volunteer-driven organisation,
+which organises internships and projects for students across
+the globe was involved. In this organisation, prospective stu-
+dents participate in text based chat with human agents, and
+typically enquire about available opportunities and how to
+participate in them. The human agents in turn use their do-
+main expertise to provide the necessary information to the
+students.
+All the students and human agents involved were resi-
+dents of Germany and hence the conversations were car-
+ried out in the German language. After collecting the con-
+versations, an annotation phase was undertaken, where rele-
+vant utterances of the conversation were annotated with the
+corresponding FAQ IDs. When the conversations originally
+took place, there was no singular FAQ database in existence.
+For the purpose of this project, such a database was created.
+This made it possible to annotate the utterances with relevant
+FAQ IDs.
+The goal of the dataset is to train an AI agent that can pas-
+sively listen to the ongoing conversation and make relevant
+suggestions visible only to the human agent, not to the stu-
+dent. The human agent may then forward the suggested FAQ
+answer to the student, or decide not to do so if the quality of
+suggestion is poor. The eventual goal is for the human agent
+to spend less time looking for the right answer in a Knowl-
+edge Base, and instead offload this task to the AI agent.
+Later, a web UI was constructed, as described in the Web
+Interface section, that the human agent uses to interact with
+the student. The student is not aware of the UI’s existence
+and is operating on a separate chat platform. The AI agent
+provides timely suggestions in this UI which is visible to the
+human agent.
+Our scenario differs from conventional Conversational
+Question Answering (CQA) or Interactive Information Re-
+trieval (IIR) where the user interacts directly with the AI
+agent, and the AI agent is responsible for a response at each
+turn. In our case, the AI agent is in a passive listening role.
+It observes the ongoing conversation between two humans,
+and makes suggestions that are only visible to the human
+agent. Since the task of the AI agent is not just to suggest
+relevant FAQs but also to remain silent when no relevant
+1
+arXiv:2301.12158v1  [cs.AI]  28 Jan 2023
+
+Figure 1: Screenshot of web based prototype
+FAQ is to be suggested, we evaluate both of these aspects in
+the evaluation section.
+The user interface presented in this work has been pub-
+lished before (Poser et al. 2022). The machine learning tech-
+niques used to train the AI agent are yet to be published, and
+hence a larger focus in this work is on the AI training aspect.
+Web Interface
+The web-based frontend in Figure 1 is labelled with cer-
+tain design features (DF) to be explained shortly. The in-
+terface was implemented with Bootstrap and ReactJS while
+the backend API is hosted as a Python Flask app. The inter-
+face greets humans agents with an avatar named Charlie that
+presents a brief usage explanation (DF1). In addition, setting
+options for AI support and learning behavior are provided
+(DF2). The integrated chat window is based on the open-
+source chat framework Rocket Chat. The backend generates
+a ranked list of FAQ suggestions based on ML techniques to
+be described later. In the frontend, two FAQ items - includ-
+ing theme and accuracy in percent - with the highest agree-
+ment are displayed (DF3). The discard buttons can be used
+to sequentially display four additional FAQ suggestions with
+decreasing accuracy. The copy-to-chat buttons insert FAQ
+text into the input field of the chat window. Detailed infor-
+mation about a respective FAQ can be viewed via the get-
+more-info button (DF4). With a counter, points are added
+(copy-to-chat) or subtracted (discard), if buttons are clicked
+(DF5). A feedback field allows entering search terms to se-
+lect and submit a FAQ that matches the interaction (DF6).
+Based on customers’ chat messages, exact keyword-based
+text matching is performed to automatically record interests
+and suggest suitable projects from a database (DF7).
+Related Work
+The earliest dialogue systems, or chat-bots, were rule based
+(Weizenbaum 1966; Colby et al. 1972) and subsequently
+corpus based chat-bots were developed (Serban et al. 2015)
+. In recent times neural chat-bots are frequently encountered
+in day to day customer support scenarios (Ni et al. 2021).
+Recently, an interplay of human and AI collaboration in
+the process has been explored (Liu et al. 2021). However
+current research in this area is focused on the AI bot be-
+ing the first line of service, and only in the case of failures
+of the bot, a handover is initiated to a human agent, who
+plays a secondary role in the process. In contrast, our sce-
+nario makes the human agent the first line of support with
+the AI agent assisting in parallel.
+To train chat-bots, conversational QA datasets such as the
+Ubuntu corpus (Lowe et al. 2015), CoQA (Reddy, Chen,
+and Manning 2019), DoQA (Campos et al. 2020) and QuAC
+(Choi et al. 2018) have made progress in providing the
+community with rich grounds for conversational research.
+While CoQA relies on passages from broad domains
+such as children’s stories and science to retrieve answers,
+QuAC relies on Wikipedia articles to create conversations
+and answers. DoQA on the other hand, focuses on three
+specific domains of cooking, travel and movies from stack-
+exchange.com. In scope of how our dataset is modelled,
+it is most similar to DoQA, which is a domain specific
+conversational dataset which also requires retrieval of the
+correct FAQ from a database. CoQA, DoQA and QuAC
+datasets are crowd-sourced and collected by the Wizard of
+2
+
+IntelligentSupportAgent
+三
+E
+Hi there, I'am Charlie your personal assistant!
+Your Personal Settings?
+information and knowledge. You can control my settings anytime, To elevate
+Do you want my assistance?
+on
+to learn more about my features.
+May I learn from your conversations and interaction with me?
+DF2
+On
+Happy to work with you!
+DF1
+Knowledge
+DF3
+Charlie's Suggestions?
+Feedback?
+FAQ Theme:
+Find here the right question, and then press send button.
+Copy to chat
+Dscardo
+DF6
+Get mareinfo 
+FAQ Theme:
+DF4
+Copy ochat
+DiacardO
+Get moreinfoO
+Charlie's Explanations (Get more info)
+Ccopyfo chat
+Points for Charlie
+DF5
+EP's Interest
+Projects
+Where
+DF7
++ Charlie's Suggestions
+Indicate Location (country)
+Small text
+Copy to chat 
+When
+Discarda
+Indicate month
+Small teat
+Message
+What
+Copy to chat 
+Small text
+DiscardQ
+Indicate what type of projectFigure 2: A sample conversation from the dataset with relevant corresponding FAQ annotation. The text in red is English
+translation of the conversation for the purpose of this paper, and not a part of the dataset.
+Oz method. On the contrary, our dataset consists of genuine
+conversations between two humans whose sole purpose is
+to find the best internship possible for the student. During
+the conversations, neither of the parties were aware of the
+need to form an annotated dataset. Hence, our dataset has
+no artificial aspects in the flow of conversation.
+The Dortmunder Chat Korpus (Beißwenger et al. 2013) and
+The Verbmobil (Wahlster 1993) project provide German
+conversational corpus but they do not address the Question
+Answering or Information Retrieval domains.
+Recently, the GermanQuAD and GermanDPR (M¨oller,
+Risch, and Pietsch 2021) projects from DeepSet have
+enabled access to Transformer based models trained on
+the German text, which we make use of in our evaluation
+section, however the dataset they are based on is in the form
+of Questions and Answers, and not conversational in nature.
+Dataset Creation
+To train the AI agent, a conversational dataset had to be con-
+structed. For this purpose, the conversations were carried out
+on the popular mobile application WhatsApp 3, where both
+the human agent and the student were on Whatsapp. The
+Web Interface described in the previous section was not in-
+cluded in this process. The conversations centered around
+topics such as how to register for a project, which projects
+are available in a given location, and whether there will be
+certifications available at the end etc. The chats were ex-
+tracted using the export functionality of WhatsApp. The
+3https://play.google.com/store/apps/details?id=com.whatsapp
+conversations have been collected over a period of two years,
+between 2018 and 2020. In some cases, an individual con-
+versation may also span over a duration of several months,
+where the student and the human agent re-established con-
+tact after a gap of more than a few days. Such information
+is visible through the inclusion of the timestamp field in the
+dataset for each message that is exchanged.
+Relevant consent for releasing their conversations was col-
+lected from the participating students and agents. More-
+over, the identities of the participants and the organisation
+are pseudo-anonymised. Instead of the names of the partici-
+pants, they are given a numerical name such as KundeSech-
+sundzwanzig, which stands for Customer 26 in German. The
+human agent is represented by the term Mitarbeiter which
+stands for employee.
+A single human agent handled all the 26 conversations
+on WhatsApp over a period of time. When the conversa-
+tions were carried out between 2018-2020, no single FAQ
+database existed at the organisation. The human agent in-
+stead used relevant domain expertise and experience within
+the organisation, and referred to a set of disjoint sources of
+information when the chats took place. Later in 2021, the hu-
+man agent and a fellow domain expert colleague compiled a
+single FAQ database that covers most of the issues discussed
+in the conversations. Specific turns of the conversations were
+manually annotated with relevant FAQs by the human agent
+and then verified by the domain expert colleague.
+Dataset Analysis
+Chats and FAQs. As depicted in Figure 4 the 26 collected
+conversations vary in length ranging from 22 utterances
+3
+
+Mitarbeiter : Hey! ich bin Mitarbeiter. Du hast dich bei
+FAQ 1
+uns angemeldet und ich wurde gerne mit dir daruber
+sprechen / telefonieren :). Wann hattest du denn dafur
+"Question":"wann kann ich ein projekt machen?"
+Zeit?
+Employee : Hey!I am an employee here.You have
+"When can Idoaproject?"
+registered with us and I would like to talk to you about it
+"Answer":"projekte sind jederzeitmoglich",
+KundeVierzehn : Guten Morgen, Ich interessiere mich
+"Projects can be done atany time”
+sehr fur Projekte in der Turkei. Wenn der Start im Januar
+moglich ist.
+Customer Fourteen: Good Morning,Iam very interested
+in projects in Turkey. If the start is possible in January.
+FAQ55
+Mitarbeiter/Employee : https://<Organisation>.org/opportunity/984743
+"Question": "was mache ich nun nachdem ich mich
+https://<Organisation>.org/opportunity/1002581
+beworbenhabe?"
+KundeVierzehn : Hallo Mitarbeiter, ich habe mich gerade
+'what do I doafter I haveapplied?"
+beworben.
+Customer Fourteen: Hello Employee, I just applied.
+"Answer":"prozess:bewerben-kontaktmit
+auslandspartner-akzeptiert-vertrag und gebuhr
+Mitarbeiter : Ah super! Ich kummere mich darum dass du
+approved",
+schnell kontaktiert wirst :)
+"process:apply-contactwithforeign
+Employee: Ah great! I will make sure that you will be
+contacted quickly :)
+partner -accepted-contract and fee -approved'to 607 utterances, with an average of 239 utterances per
+conversation. The entire set of conversations consists of
+6,219 utterances. 20.9 % of the utterances are annotated
+with the relevant FAQ ID. A significant portion of the
+dataset consists of chit-chat or other non-specific topics
+where no suggestion is supposed to be made by the AI agent
+to the human agent.
+Since certain topics in the chat are discussed more often
+than others, as seen in Figure 3, the distribution of relevant
+annotated FAQ IDs also is imbalanced with FAQ ID 71
+being the most frequent. FAQ 71 pertains to the procedure
+of registering online for projects.
+We have split the dataset into train, dev and test splits in
+roughly 70:10:20 ratios. The train, dev and test splits have
+17, 3 and 6 conversations, respectively, consisting of 3,693 ,
+891 and 1,635 utterances.
+Experimental Setting
+Task Definition
+We define the task with the following inputs: current utter-
+ance uk, the set of FAQs F, and the history of utterances so
+far {u1, u2, ...., uk−1}. The task for the model is to rank the
+correct FAQ item from F to the top. If for a given utterance
+no FAQ is appropriate, the model must produce as the top-
+ranked output a special class that denotes absence of FAQ
+suggestion. We hereby call this class no-suggestion.
+Models
+As baselines we use the following settings:
+dumb In this setting, the system produces 10 suggestions,
+with class no-suggestion at the top and FAQ IDs 1 to 9
+as the subsequently ranked suggestions as output.
+random In this setting, the system produces at random 10
+classes as output without repetition. The output may contain
+one of the FAQ IDs or the no-suggestion class.
+Additionally.
+we
+employed
+BM25
+(Robertson
+and
+Zaragoza 2009) based text search ranking as a baseline
+method. In this method we searched the input query string
+against the FAQ database and used the ranked list of results.
+To produce strong performance, we employ Dense Pas-
+sage Retrieval (Karpukhin et al. 2020) techniques . As a
+baseline, we use fb-multiset-english, which is a set of en-
+coders 4 that were pre-trained on English Natural Questions
+(Kwiatkowski et al. 2019), TriviaQA (Joshi et al. 2017), We-
+bQuestions (Berant et al. 2013), and CuratedTREC (Baudiˇs
+and ˇSediv´y 2015).
+Finally, we use pre-trained context and query encoders
+for the German language provided by DeepSet
+5 and
+fine-tune them on our dataset for 100 epochs with a learning
+rate of 1e-05 with the Adam optimizer. We use random
+sampling for choosing negative examples during training.
+We choose the best performing model based on mrr@10
+on the dev split. We used deepset-german encoders, which
+come comes from DeepSet and is trained on GermanQuAD
+4facebook/dpr-ctx encoder-multiset-base
+5https://www.deepset.ai/germanquad
+Figure 3: Distribution of conversation topics in the dataset.
+Figure 4: The length of each conversation
+(M¨oller, Risch, and Pietsch 2021) dataset.
+For query, we concatenate 4 consecutive utterances of
+conversation and consider it the input to the model. For con-
+text, we concatenate the question and answer for each FAQ
+and make the DPR model consider these as the passages
+database from which it has to rank the best possible FAQ.
+Evaluation Metrics
+As our metric, we choose the Mean Reciprocal Rank
+(MRR). For each query candidate, the model produces an
+MRR, which is the reciprocal of the position of the correct
+FAQ in the ranked list. We consider only the top 10 candi-
+dates, and hence, if the correct candidate is not in the top 10,
+we consider the MRR as 0. We compute the eventual MRR
+by taking a mean of the MRR of each query sample in the
+test set.
+4
+
+payment
+project planning
+organisation
+insurance
+conditions
+browser
+benefits
+location
+project
+certificate
+breach of contract
+price
+postprocessing
+time
+supervisor
+scholarship
+preparation
+application
+0
+100
+200
+300
+400Conversation ID
+0
+100
+200
+300
+400
+500
+600
+TurnsWe evaluate separate MRRs for those utterances which have
+empty FAQ suggestions as gold annotation, and the ones
+which have non-empty FAQ gold suggestions. As explained
+before, the task of the AI agent is not just to recommend the
+right FAQ when needed, but it must also remain silent when
+no FAQ is suitable. We measure the ability of AI agent on
+both these tasks in Table 1.
+Experimental Setup
+Since a large percentage of the utterances (79.1%) belongs
+to the no-suggestion class we experiment with differ-
+ent mixture of faq classes and the no-suggestion class.
+During preparation of train and dev sets to be fed to the
+model, we calibrate the ratio of no-suggestion utter-
+ances differently as follows:
+mean In this setting, we compute the mean of the frequency
+of the faq classes and include these many samples of ran-
+domly chosen no-suggestion utterances as input.
+highest-freq In this setting, we find the most frequent faq
+class and include the same number of no-suggestion
+class samples.
+sum In this setting, the number of samples of the utterances
+in no-suggestion class is equal to the sum of the num-
+ber of utterances in all the faq classes combined.
+original In this setting we consider all utterances as in-
+put which leads to roughly 80:20 class imbalance of
+no-suggestion class and the faq classes.
+It must be noted that in all the above settings, we
+always include every faq class utterance. For input
+to the model we concatenate 4 consecutive utterances
+{uk−3, uk−2, uk−1, uk} for each utterance uk. When con-
+catenating the utterances, we also append the sender name
+to the beginning of each utterance.
+Model/Setting
+no-suggestion
+faq
+dumb
+1.0
+0.02
+random
+0.04
+0.06
+BM25
+0
+0.27
+fb-multiset-english
+mean
+0.12
+0.40
+highest-freq
+0.35
+0.48
+sum
+0.81
+0.44
+original
+0.96
+0.33
+deepset-german
+mean
+0.12
+0.58
+highest-freq
+0.42
+0.57
+sum
+0.84
+0.50
+original
+0.95
+0.38
+Table 1: MRR@10 values for different models and settings
+on test split of dataset
+Results
+We first analyse the baseline results from Table 1
+:
+The
+dumb
+setting
+achieves
+perfect
+MRR
+in
+the
+no-suggestion category since in this setting the AI
+agent chooses ’silence’ as the top ranked candidate for all
+turns. However it produces extremely poor results for turns
+that do require suggestions, since there is no intelligence or
+logic built in to his setting when fetching FAQ items. This
+also highlights why we need to evaluate our system on two
+different classes. If we had computed a singular MRR score
+for all turns, a model which remains silent all the time would
+score high accuracy. The random setting achieves poor per-
+formance in both categories. The BM25 setting produces 0
+MRR in no-suggestion class because there is no way
+to ask a text search method to not return any results. It al-
+ways fetches some set of results, and in effect, is unable to
+produce silence as output.
+The Deep Passage Retrieval approaches using the
+deepset-germandpr set of models perform the best,
+which comes as no surprise since these encoders were pre-
+trained on German QA datasets, and further fine-tuned on
+our dataset. In comparison fb-multiset-english per-
+forms worse since the encoders are not aware of the German
+language. We find that among the different settings of vary-
+ing proportions of the inclusion of no-suggestion class
+in the input, the sum setting produces a balanced perfor-
+mance in the two categories of no-suggestion and faq.
+Another notable point in the table is the performance of the
+dumb model which always produces no-suggestion as
+output hence achieving perfect MRR@10 of 1.0 in the rel-
+evant samples, but it produces the worst results in the faq
+classes, hence rendering it of little use to human agent. We
+observe that as no-suggestion class performance im-
+proves, faq class performance drops. This brings forth in-
+teresting questions on how to calibrate the performance of
+the model to reach a sweet spot for the human agent. An
+MRR of 0.5 or greater for the faq classes means that the
+right FAQ is generally either in the first or in the second
+position, which is a positive contribution to lessen the hu-
+man agent’s workload, since most user interface implemen-
+tations for our scenario would display the top 3 FAQs to hu-
+man agent together. It is, however, more important for the
+no-suggestion MRR to be closer to 1.0, since the si-
+lence class being ranked second still produces suggestions
+that the human agent has to process, increasing noise for the
+human agent.
+Human Evaluation
+To evaluate the usability aspects of the prototype and its in-
+fluence on the task, we conducted interviews with 18 human
+agents after usage. Additionally, we inspected their usage
+behavior via screen recordings to supplement the qualita-
+tive results. Overall, human agents indicated that they would
+continue to use the prototype and highlighted that it is partic-
+ularly helpful for agents who do not have much experience
+in handling customers. During customer interactions, agents
+sent on average 16 (SD: 5; Median: 14) messages during the
+customer interaction. 17 agents used the FAQ answer sug-
+gestions via the copy-to-chat-button at least three times. On
+average, agents edited two (SD: 2; Median: 2) of the sug-
+gested responses in the input field before sending them.
+Overall, an average of six (SD: 2.5; Median: 7) sugges-
+tions were used, whereby the detailed version via get-more-
+info button (Mean: 3.7; SD: 2.6; Median: 4.5) was used more
+5
+
+frequently than the short version (Mean: 2.6; SD: 2.4; Me-
+dian: 2). To receive alternative FAQ answer suggestions, the
+discard-button was clicked on average 15 times (SD: 10.8;
+Median: 15). The display of two suggestions and the op-
+tion for additional explanatory information via the get-more-
+info-button were perceived as helpful “so that you can think
+in which direction you might go” (agent1). Agents experi-
+enced relief through displayed suggestions and the majority
+saved time making decisions, especially by using the copy-
+to-chat-button: “ I just had to copy them, which affected the
+speed” (agent14). 16 agents utilized the feedback function
+on average four times, while nine people successfully pro-
+vided feedback. However, agents expressed the need for an
+adaptation of the feedback function, as it was unclear. Con-
+cerning the recommendation of projects, the pressure to re-
+call knowledge or search in parallel to the customer inter-
+action was reduced as relevant information was presented.
+Thereby, it “took out the uncomfortable part of working with
+such a consultation, which is looking up stuff ” (agent16)
+Limitations
+The current solution suffers from the following limitations:
+1) The web interface was developed for internal evaluation
+purposes and is not available for general public use. 2) The
+collection of the dataset suffers from class imbalance and
+bias issues, since only a single person was involved in col-
+lecting the conversations. 3) The feedback function of the UI
+did not work as expected by the human agents. The human
+agents expected the feedback regarding wrong suggestions
+to be immediately learnt by the system, however during the
+evaluation phase we did not re-train our models, or perform
+on-line learning from the provided feedback.
+Conclusion and Future Work
+In this work we present a web interface for demonstrating
+hybrid human-AI collaborative system that can handle cus-
+tomer support queries. We show through machine based and
+human based evaluations, that with the limited and imbal-
+anced data we collected, we found appropriate methods to
+train an AI agent that is able to provide appropriate assis-
+tance to its human counterpart, which is the goal of our re-
+search.
+For future work, we wish to implement active on-line
+learning from the human agent’s usage of the feedback fea-
+ture in the UI. We would also like to collect a larger and
+more balanced dataset for future iterations of the AI agent.
+Acknolwedgements
+The research was financed with funding provided by the
+German Federal Ministry of Education and Research and the
+European Social Fund under the ”Future of work” program
+(INSTANT, 02L18A111).
+References
+Baudiˇs, P.; and ˇSediv´y, J. 2015. Modeling of the Question
+Answering Task in the YodaQA System. 222–228. ISBN
+978-3-319-24026-8.
+Beißwenger, M.; Herold, A.; L¨ungen, H.; and St¨orrer, A.
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+Tracing the Origin of Adversarial Attack for Forensic Investigation and
+Deterrence
+Han Fang1, Jiyi Zhang 1, Yupeng Qiu 1, Ke Xu 2, Chengfang Fang 2, Ee-Chien Chang 1*
+1 National University of Singapore
+2 Huawei International
+[email protected], [email protected], qiu [email protected], [email protected]
+Abstract
+Deep neural networks are vulnerable to adversarial attacks.
+In this paper, we take the role of investigators who want to
+trace the attack and identify the source, that is, the particular
+model which the adversarial examples are generated from.
+Techniques derived would aid forensic investigation of at-
+tack incidents and serve as deterrence to potential attacks. We
+consider the buyers-seller setting where a machine learning
+model is to be distributed to various buyers and each buyer
+receives a slightly different copy with same functionality. A
+malicious buyer generates adversarial examples from a par-
+ticular copy Mi and uses them to attack other copies. From
+these adversarial examples, the investigator wants to iden-
+tify the source Mi. To address this problem, we propose a
+two-stage separate-and-trace framework. The model separa-
+tion stage generates multiple copies of a model for a same
+classification task. This process injects unique characteristics
+into each copy so that adversarial examples generated have
+distinct and traceable features. We give a parallel structure
+which embeds a “tracer” in each copy, and a noise-sensitive
+training loss to achieve this goal. The tracing stage takes in
+adversarial examples and a few candidate models, and iden-
+tifies the likely source. Based on the unique features induced
+by the noise-sensitive loss function, we could effectively trace
+the potential adversarial copy by considering the output logits
+from each tracer. Empirical results show that it is possible to
+trace the origin of the adversarial example and the mechanism
+can be applied to a wide range of architectures and datasets.
+1
+Introduction
+Deep learning models are vulnerable to adversarial attacks.
+By introducing specific perturbations on input samples, the
+network model could be misled to give wrong predictions
+even when the perturbed sample looks visually close to
+the clean image (Szegedy et al. 2014; Goodfellow, Shlens,
+and Szegedy 2014; Moosavi-Dezfooli, Fawzi, and Frossard
+2016; Carlini and Wagner 2017). There are many existing
+works on defending against such attacks (Kurakin, Good-
+fellow, and Bengio 2016; Meng and Chen 2017; Gu and
+Rigazio 2014; Hinton, Vinyals, and Dean 2015). Unfortu-
+nately, although current defenses could mitigate the attack
+to some extent, the threat is still far from being completely
+eliminated. In this paper, we look into the forensic aspect:
+from the adversarial examples, can we determine which
+*Corresponding Authors.
+Figure 1: Buyers-seller setting. The seller has multiple mod-
+els Mi, i ∈ [1, m] that are to be distributed to different
+buyers. A malicious buyer batt attempts to attack the vic-
+tim buyer bvic by generating the adversarial examples with
+his own model Matt.
+model the adversarial examples were derived from? Tech-
+niques derived could aid forensic investigation of attack in-
+cidents and provide deterrence to future attacks.
+We consider a buyers-seller setting (Zhang, Tann, and
+Chang 2021), which is similar to the buyers-seller setting
+in digital rights protection (Memon and Wong 2001).
+Buyers-seller Setting.
+Under this setting, the seller S dis-
+tributes m classification models Mi, i ∈ [1, m] to different
+buyers bi’s as shown in Fig. 1. These models are trained for
+a same classification task using a same training dataset. The
+models are made accessible to the buyer as black boxes, for
+instance, the models could be embedded in hardware such as
+FPGA and ASIC, or are provided in a Machine Learning as a
+Service (MLaaS) platform. Hence, the buyer only has black-
+box access, which means that he can only query the model
+for the hard label. In addition, we assume that the buyers do
+not know the training datasets. The seller has full knowledge
+and thus has white-box access to all the distributed models.
+Attack and Traceability.
+A malicious buyer wants to at-
+tack other victim buyers. The malicious buyer does not have
+direct access to other models and thus generates the exam-
+ples from its own model and then deploys the found exam-
+ples. For example, the malicious buyer might generate an ad-
+versarial example of a road sign using its self-driving vehi-
+cle, and then physically defaces the road sign to trick passing
+vehicles. Now, as forensic investigators who have obtained
+the defaced road sign, we want to understand how the ad-
+versarial example is generated and trace the models used in
+generating the example.
+arXiv:2301.01218v1  [cs.CR]  31 Dec 2022
+
+M1
+M2
+M1
+M3
+Matt
+Attacking
+20
+Generating
+Adversarial
+ExamplesProposed Framework.
+There are two stages in our solu-
+tion: model separation and origin tracing. During the model
+separation stage, given a classification task, we want to gen-
+erate multiple models that have high accuracy on the clas-
+sification task and yet are sufficiently different for tracing.
+In other words, we want to proactively enhance differences
+among the models in order to facilitate tracing. To achieve
+that, we propose a parallel network structure that pairs a
+unique tracer with the original classification model. The role
+of the tracer is to modify the output, so as to induce the at-
+tacker to adversarial examples with unique features. We give
+a noise-sensitive training loss for the tracer.
+During the tracing stage, given m different classification
+models Mi, i ∈ [1, m] and the found adversarial example,
+we want to determine which model is most likely used in
+generating the adversarial examples. This is achieved by ex-
+ploiting the different tracers that are earlier embedded into
+the parallel models. Our proposed method compares the out-
+put logits (the output of the network before softmax) of those
+tracers to identify the source.
+In a certain sense, traceability is similar to neural network
+watermarking and can be viewed as a stronger form of water-
+marking. Neural network watermarking schemes (Boenisch
+2020) attempt to generate multiple models so that an investi-
+gator can trace the source of a modified copy. In traceability,
+the investigator can trace the source based on the generated
+adversarial examples.
+Contributions.
+1. We point out a new aspect in defending against adver-
+sarial attacks, that is, tracing the origin of adversarial
+samples among multiple classifiers. Techniques derived
+would aid forensic investigation of attack incidents and
+provide deterrence to future attacks.
+2. We propose a framework to achieve traceability in the
+buyers-seller setting. The framework consists of two
+stages: a model separation stage, and a tracing stage.
+The model separation stage generates multiple “well-
+separated” models and this is achieved by a parallel
+network structure that pairs a tracer with the classifier.
+The tracing mechanism exploits the characteristics of the
+paired tracers to decide the origin of the given adversarial
+examples.
+3. We investigate the effectiveness of the separation and the
+subsequent tracing. Experimental studies show that the
+proposed mechanism can effectively trace to the source.
+For example, the tracing accuracy achieves more than
+97% when applying to “ResNet18-CIFAR10” task. We
+also observe a clear separation of the source tracer’s log-
+its distribution, from the non-source’s logits distribution
+(e.g. Fig. 5a-5c).
+2
+Related Work
+In this paper, we adopt black-box settings where the adver-
+sary can only query the model and get the hard label (final
+decision) of the output. Many existing attacks assume white-
+box settings. Attack such as FGSM (Goodfellow, Shlens,
+and Szegedy 2014), PGD (Kurakin, Goodfellow, and Bengio
+2016), JSMA (Papernot et al. 2016), DeepFool (Moosavi-
+Dezfooli, Fawzi, and Frossard 2016), CW (Carlini and Wag-
+ner 2017) and EAD (Chen et al. 2018) usually directly rely
+on the gradient information provided by the victim model.
+As the detailed information of the model is hidden in black-
+box settings, black-box attacks are often considered more
+difficult and there are fewer works. Chen et. al. introduced
+a black-box attack called Zeroth Order Optimization (ZOO)
+(Chen et al. 2017). ZOO can approximate the gradients of
+the objective function with finite-difference numerical esti-
+mates by only querying the network model. Thus the ap-
+proximated gradient is utilized to generate the adversarial
+examples. Guo et. al. proposed a simple black-box adver-
+sarial attack called “SimBA” (Guo et al. 2019) to generate
+adversarial examples with a set of orthogonal vectors. By
+testing the output logits with the added chosen vector, the
+optimization direction can be effectively found. Brendel et.
+al. developed a decision-based adversarial attack which is
+known as “Boundary attack” (Brendel, Rauber, and Bethge
+2018), it worked by iteratively perturbing another initial im-
+age that belongs to a different label toward the decision
+boundaries between the original label and the adjacent la-
+bel. By querying the model with enough perturbed images,
+the boundary as well as the perturbation can be found thus
+generating the adversarial examples. Chen et. al. proposed
+another decision based attack named hop-skip-jump attack
+(HSJA) (Chen, Jordan, and Wainwright 2020) recently. By
+only utilizing the binary information at the decision bound-
+ary and the Monte-Carlo estimation, the gradient direction of
+the network can be found so as to realize the adversarial ex-
+amples generation. Based on (Chen, Jordan, and Wainwright
+2020), Li et. al. (Li et al. 2020) proposed a query-efficient
+boundary-based black-box attack named QEBA which es-
+timate the gradient of the boundary in several transformed
+space and effectively reduce the query numbers in gener-
+ating the adversarial examples. Maho et. al. (Maho, Furon,
+and Le Merrer 2021) proposed a surrogate-free black-box
+attack which do not estimate the gradient but searching the
+boundary based on polar coordinates, compared with (Chen,
+Jordan, and Wainwright 2020) and (Li et al. 2020), (Maho,
+Furon, and Le Merrer 2021) achieves less distortion with
+less query numbers.
+3
+Proposed Framework
+3.1
+Main Idea
+We design a framework that contains two stages: model sep-
+aration and origin tracing.
+During the model separation stage, we want to generate
+multiple models which are sufficiently different under ad-
+versarial attack while remaining highly accurate on the clas-
+sification task. Our main idea is a parallel network structure
+which pairs a unique tracer with the original classifier. The
+specific structure will be illustrated in Section 3.2.
+As for origin tracing, we exploit unique characteristics of
+different tracers in the parallel structure, which can be ob-
+served in the tracers’ logits. Hence, our tracing process is
+conducted by feeding the adversarial examples into the trac-
+ers and analyzing their output.
+
+Figure 2: The framework of the proposed method. The left part of the framework indicates the separation process of the seller’s
+distributed models Mi, i ∈ [1, m]. The right part of the framework illustrates the origin tracing process.
+The whole framework of the proposed scheme is shown
+in Fig. 2. As illustrated in Fig.2, each distributed model Mi
+consists of a tracer Ti and the original classification model
+C, and the tracer is trained with a proposed noise-sensitive
+loss LNS. During the tracing stage, the adversarial examples
+are fed into each Ti and the outputs are analyzed to identify
+the origin.
+3.2
+Model Separation
+We design a parallel network structure to generate the dis-
+tributed models Mi, i ∈ [1, m], which contains a tracer
+model Ti and a main model C, as shown in Fig. 3a. Ti is
+used for injecting unique features and setting traps for the
+attacker. C is the network trained for the original task. The
+final results are determined by both C and Ti with a weight
+parameter α. In each distributed model, C is fixed and only
+Ti is different.
+The specific structure of Ti is shown in Fig. 3b, it is
+linearly cascaded with one “SingleConv” block (Conv-BN-
+ReLU), two “Res-block” (He et al. 2016), one “Conv” block,
+one full connection block and one “Tanh” activation layer.
+The training process of Ti can be described as:
+1) Given the training dataset1 and tracer Ti, we first ini-
+tialize Ti with random parameters.
+2) For each training epoch, we add random noise No 2 on
+the input image x to generate the noised image xNo.
+3) Then we feed both x and xNo into Ti and get the out-
+puts Ox and OxNo. We attempt to make Ti sensitive to noise,
+so Ox and OxNo should be as different as possible. The loss
+function of Ti can be written as:
+LNS =
+|Ox ◦ OxNo|
+∥Ox∥2∥OxNo∥2
+=
+|Ti(θTi, x) ◦ Ti(θTi, xNo)|
+∥Ti(θTi, x)∥2∥Ti(θTi, xNo)∥2
+(1)
+1The training dataset for Ti only contains 1000 random sampled
+images from the dataset of the original classification task
+2No follows a uniform distribution over [0, 0.03)
+where ◦ represents the Hadamard product. θTi indicates the
+parameters of Ti.
+Each distributed Ti for different buyers is generated by
+randomly initializing and then training. We believed the ran-
+domness in initialization is enough to guarantee the differ-
+ence from different Ti. It should be noted that when pro-
+ducing a new distributed copy, we only have to train one
+new tracer without setting more constraints on former trac-
+ers. So such a separation method can be applied to multiple
+distributed models independently.
+As for C, it is trained in a normal way which utilizes the
+whole training dataset and cross-entropy loss. For the main
+classification task, C only has to be trained once. Besides, the
+training of C is independent of the training of Ti. After train-
+ing C, we could get a high accuracy classification model.
+The final distributed model Mi is parallel combined with C
+and Ti. The specific workflow of Mi can be described as:
+For input image x, Ti and C both receive the same x and
+output two different vectors OTi and OC respectively. OTi
+and OC have the same size and will be further added in a
+weighted way to generate the final outputs OF , as shown in
+Eq. 2.
+OF = OC + α × OTi
+(2)
+where α is the weight parameter. It is worth noting that for
+the output of C, we use the normalization form of it, which
+can be formulated as:
+OC =
+C(x) − min(C(x))
+max(C(x)) − min(C(x))
+(3)
+where x indicates the input image, max and min indicate
+the maximum value and minimum value respectively.
+By
+utilizing
+the
+aforementioned
+model
+separation
+method, two properties are well satisfied: (I) The attack
+could be tricked to focus more on Ti than C. Since after the
+training, Ti will be sensitive to random noise. Therefore, the
+output of Ti is easy to be changed by adding noise. Com-
+pared with C, the boundary of Ti is more likely to be esti-
+mated and Ti is more likely to be attacked. Thus, the attacker
+
+Model Separation Stage
+Origin Tracing Stage
+ Attacker's Model !
+Main Model
+Initialized Tracer Model
+Distributed Tracer
+(source model)
+Ms
+c
+T1
+T2
+Tini
+Tini
+Tini
+2
+m
+Adversarial
+Trace's Outputs Obtaining
+Model Combination
+Tracer Model Training
+Examples
+Outputs OTi(x)
+Outputs
+Outputs
+Outputs
+Adversarial
+Tracer
+Image
+Example
+OT1
+OT2
+OTs
+OTm
+Ti
+X
+Tracer
+Noise-sensitive
+Loss L'is.
+Image
+Main
+Ti
+ Noised
+x
+ Image
+c
+Attacked Model Tracing
+Identified Tracer :
+xNo
+Outputs OTi(xNo)
+Mi
+Ts
+Outputs
+Tracing mechanism
+OTm
+no
+Generated Models
+OTs
+arg max 0
+ho
+true
+Identified Model :
+att: attacked label
+M1
+M2
+M3
+M4
+Ms
+Mm
+true: true label
+Ms(a) Parallel network structure.
+(b) The architecture of tracer.
+(c) Differences in logits.
+Figure 3: The specific network design in model separation.
+will fall into the trap of Ti and the generated adversarial per-
+turbations will bring the feature of the source Ti. (II) Based
+on random initialization, each distributed Ti will correspond
+to different adversarial perturbations. This property helps us
+in tracing, since the source Ts which generates adversarial
+examples will output unique responses compared with other
+Ti, i ̸= s when feeding the generated adversarial examples,
+as shown in Fig. 3c.
+3.3
+Tracing the Origin
+The tracing process is conducted by two related compo-
+nents:
+• The first component keeps white-box copies for each of
+the m distributed copies 3. This component allows us to
+obtain the output logits of each tracer on an input x.
+• The second component is an output logits-based mech-
+anism. It gives a decision on which copy i is the most
+likely one to generate the adversarial example.
+The specific tracing process can be described as follows:
+1) Given an appeared adversarial examples denoted as
+xatt, we feed the adversarial example into all Ti, i ∈ [1, m]
+and obtain the output logits of them, noted as OTi, i ∈
+[1, m].
+2) Then we extract two values that are corresponding to
+the attacked label and true label in each OTi, denoted as OTi
+att
+and OTi
+true respectively. 4
+3) The source model can be determined by:
+s = arg max
+i,i∈[1,m]
+(OTi
+att − OTi
+true)
+(4)
+To simplify the description, we denote the difference of out-
+put logits (OTi
+att−OTi
+true) as DOL. The tracer corresponded to
+the largest DOL is regarded as the source model. The reason
+is as follows:
+Since the perturbation are highly related to Ti, when feed-
+ing the same adversarial example, the outputs of Ti and Tj
+3This setting is reasonable because when an adversarial attack
+appeared, the model seller who has all the details of the distributed
+network takes responsible to trace the attacker.
+4Attacked label can be easily determined by the output logits
+and the true label can be tagged by the model owner. If this sample
+cannot be accurately tagged by the owner, then this sample is not
+regarded as an adversarial example.
+(i ̸= j) will be certainly different. For source model Ts
+where the adversarial examples are generated from, OTs is
+likely to render a large value on the adversarial label and a
+small value on the ground-truth label. Since the weight of
+OTs in the final OFs is small, so in order to achieve ad-
+versarial attack, OTs will be modified as much as possible.
+Thus DOL of Ts should be large. But for victim model Tv,
+the DOL will be small. Therefore, according to the value of
+DOL, we can trace the origin of the adversarial example.
+4
+Experimental Results
+4.1
+Implementation Details
+In order to show the effectiveness of the proposed frame-
+work, we perform the experiments on two network architec-
+ture (ResNet18 (He et al. 2016) and VGG16 (Simonyan and
+Zisserman 2014)) with two small image datasets (CIFAR10
+(Krizhevsky, Hinton et al. 2009) of 10 classes and GTSRB
+(Houben et al. 2013) of 43 classes) and two deeper network
+architecture (ResNet50 and VGG19) with one big image
+dataset (mini-ImageNet (Ravi and Larochelle 2016) of 100
+classes). The main classifier C in experiments is trained for
+200 epochs. All the model training is implemented by Py-
+Torch and executed on NVIDIA RTX 2080ti. For gradient
+descent, Adam (Kingma and Ba 2015) with learning rate of
+1e-4 is applied as the optimization method.
+4.2
+The Classification Accuracy of The Proposed
+Architecture
+The most influenced parameter for the classification accu-
+racy is the weight parameter α. α determines the partici-
+pation ratio of Ti in final outputs. To investigate the influ-
+ence of α, we change the value of α from 0 (baseline) to 0.2
+and record the corresponding classification accuracy of each
+task, the results are shown in Table 1.
+It can be seen from Table 1 that for CIFAR10 and GTSRB,
+the growth of α will seldom decrease the accuracy of the
+classification task. Compared with the baseline (α = 0), the
+small value of α will keep the accuracy at the same level as
+the baseline. But for mini-ImageNet, the accuracy decreases
+more as α increases, we believe it is due to the complexity
+of the classification task. But even though, the decrease rate
+is still within 3% when α is not larger than 0.15.
+
+Tracer Model
+Ti
+Image
+Main Model
+x
+cTracer Model T;Tv
+Ti
+Ti
+c
+c
+c
+cα
+CIFAR10
+GTSRB
+Mini-ImageNet
+ResNet18
+VGG16
+ResNet18
+VGG16
+ResNet50
+VGG19
+0
+94.30%
+93.68%
+96.19%
+97.59%
+73.12%
+75.79%
+0.05
+94.24%
+93.64%
+96.14%
+97.52%
+72.32%
+75.04%
+0.1
+94.24%
+93.63%
+96.07%
+97.36%
+71.88%
+74.96%
+0.15
+94.07%
+93.63%
+95.72%
+96.84%
+70.50%
+73.75%
+0.2
+93.95%
+93.57%
+95.09%
+95.52%
+68.14%
+71.75%
+Table 1: The classification accuracy with different α.
+4.3
+Traceability of different black-box attack
+It should be noted that the change of α will not only influ-
+ence the accuracy but also affect the process of black-box
+adversarial attack. Therefore, in order to explore the influ-
+ence of α, the following experiments will be conducted with
+α = 0.05, 0.1 and 0.15.
+Setup and Code. To verify the traceability of the pro-
+posed mechanism, we conduct experiments on two dis-
+tributed models. We set one model as the source model Ms
+to perform the adversarial attack and set the other model
+as the victim model Mv. The goal is to test whether the
+proposed scheme can effectively trace the source model
+from the generated adversarial examples. The black-box at-
+tack we choose is Boundary (Brendel, Rauber, and Bethge
+2018), HSJA (Chen, Jordan, and Wainwright 2020), QEBA
+(Li et al. 2020) and SurFree (Maho, Furon, and Le Merrer
+2021). For Boundary (Brendel, Rauber, and Bethge 2018)
+and HSJA (Chen, Jordan, and Wainwright 2020), we use Ad-
+versarial Robustness Toolbox (ART) (Nicolae et al. 2018)
+platform to conduct the experiments. For QEBA (Li et al.
+2020) and SurFree (Maho, Furon, and Le Merrer 2021), we
+pull implementations from their respective GitHub reposito-
+ries 5 6 with default parameters. For each α, each network
+architecture, each dataset and each attack, we generate 1000
+successful attacked adversarial examples of Ms and con-
+duct the tracing experiment.
+Evaluation Metrics. Traceability is evaluated by tracing
+accuracy, which is calculated by:
+Acc = Ncorrect
+NAll
+(5)
+where Ncorrect indicates the number of correct-tracing sam-
+ples and NAll indicates the total number of samples, which
+is set as 1000 in the experiments.
+The tracing performance of different attacks with different
+settings is shown in Table 2. It can be seen that when apply-
+ing ResNet-based architecture as the backbone of C, the trac-
+ing accuracy is higher than 90%. Especially for α = 0.15,
+most of the tracing accuracy is higher than 96%, which indi-
+cates the effectiveness of the proposed mechanism. Besides,
+for a different level of classification task and different attack-
+ing methods, the tracing accuracy can stay at a high level,
+which shows the great adaptability of the proposed scheme.
+The influence of α. We can see from Table 2 that the trac-
+ing accuracy increases with the increase of α. We conclude
+5QEBA:https://github.com/AI-secure/QEBA
+6SurFree:https://github.com/t-maho/SurFree
+the reason as: α determines the participation rate of tracer
+Ti in final output logits, the larger α will make the final de-
+cision boundary rely more on T . Therefore, when α gets
+larger, making DOL of T larger would be a better choice to
+realize the adversarial attack. The bigger DOL of T will cer-
+tainly lead to better tracing performance. To verify the cor-
+rectness of the explanation, we show the distribution of DOL
+for task “ResNet18-CIFAR10” with different attacks in Fig.
+4. We first generate 1000 adversarial examples of model Mi
+for each α (0.05,0.1,0.15) with Boundary, HSJA, QEBA and
+SurFree attack, then we record the DOLs of Ti. The distri-
+bution of DOLs are shown in Fig. 4.
+(a) The results of Boundary.
+(b) The results of HSJA.
+(c) The results of QEBA.
+(d) The results of SurFree.
+Figure 4: The distributions of output differences with differ-
+ent black-box attacks.
+It can be seen that compared with α = 0.05 and α = 0.1,
+the DOL of α = 0.15 concentrate more on larger values,
+which indicates that the larger α will result to larger DOL.
+The influence of network architecture. The tracing re-
+sults vary with different networks and different datasets.
+With the same dataset, the tracing accuracy of ResNet18 will
+be higher than that of VGG16. We attribute the reason to
+the complexity of the model architecture. According to (Su
+et al. 2018), compared with ResNet, the structure of VGG is
+less robust, so VGG-based C might be easier to be adversar-
+ial attacked. Therefore, once C is attacked, there is a certain
+probability that Ti is not attacked as we expected, so DOL of
+Ti will not produce the expected features for tracing. Fortu-
+nately, the network architecture can be designed by us, so in
+practice, choosing a robust architecture would be better for
+tracing.
+The influence of classification task. In our experiments,
+we test the classification task with different classes. It can
+be seen that with the increase of classification task complex-
+ity, traceability performance decreases slightly. But in most
+cases, when α = 0.15, the traceability ability can still reach
+more than 90%.
+The influence of black-box attack. The mechanism of
+the black-box attack greatly influences the tracing perfor-
+mance. For Boundary attack(Brendel, Rauber, and Bethge
+
+600
+α = 0.05
+500
+α = 0.1
+umbers of sampl
+α = 0.15
+400
+300
+200
+100
+0.7
+1.6
+1.9
+Outout crferences800
+α = 0.05
+α = 0.1
+0
+ sam
+600
+α = 0.15
+of
+400
+mbers
+200
+0.5
+0.8
+Outout dirference800
+α = 0.05
+α = 0.1
+Jumbers of samp
+600
+α= 0.15
+400
+200
+3
+1.9
+Outout dirferences800
+α = 0.05
+α = 0.1
+Q
+Jumbers of samr
+600
+α = 0.15
+400
+200
+0.5
+0.8
+2
+Output differencesAttack
+Boundary
+HSJA
+QEBA
+SurFree
+alpha
+0.05
+0.1
+0.15
+0.05
+0.1
+0.15
+0.05
+0.1
+0.15
+0.05
+0.1
+0.15
+CIFAR10
+ResNet18
+98.1%
+98.9 %
+99.2 %
+98.2%
+99.1%
+99.3%
+99.6%
+99.7%
+99.7%
+94.5%
+95.7%
+97.9%
+VGG16
+92.1%
+95.6 %
+98.2%
+92.3 %
+96.4 %
+97.9 %
+92.6 %
+96.6%
+99.2%
+64.2 %
+82.1 %
+87.8 %
+GTSRB
+ResNet18
+97.6%
+97.6 %
+98.9 %
+97.6 %
+97.7 %
+98.7 %
+97.6%
+97.7%
+99.6 %
+89.8 %
+95.7 %
+96.8%
+VGG16
+94.1 %
+96.8 %
+97.6 %
+95.5 %
+97.3 %
+98.3%
+86.3%
+92.6%
+95.0 %
+89.7%
+95.7%
+96.8%
+mini ImageNet
+ResNet50
+96.2%
+96.4 %
+98.7 %
+94.5%
+95.5 %
+97.5 %
+91.7%
+93.8%
+95.4 %
+82.1 %
+87.3 %
+90.5%
+VGG19
+89.4 %
+94.7 %
+98.2%
+93.4 %
+95.1 %
+95.4%
+89.5%
+90.4%
+90.8 %
+75.7 %
+88.7 %
+88.8%
+Table 2: The trace accuracy of different attacks.
+2018), HSJA(Chen, Jordan, and Wainwright 2020) and
+QEBA(Li et al. 2020), the tracing accuracy shows similar
+results, but for SurFree (Maho, Furon, and Le Merrer 2021),
+the tracing accuracy will be worse than that of the other
+attacks. The reason is that Boundary attack, HSJA(Chen,
+Jordan, and Wainwright 2020), QEBA(Li et al. 2020) are
+gradient-estimation-based attacks, which tries to use random
+noise to estimate the gradient of the network and further
+attack along the gradient. Since the gradient is highly re-
+lated to Ti, such attacks are more likely to be trapped by
+Ti. But SurFree(Maho, Furon, and Le Merrer 2021) is at-
+tacking based on geometric characteristics of the boundary,
+which may ignore the trap of Ti especially when α is small.
+So compared with Boundary attack(Brendel, Rauber, and
+Bethge 2018), HSJA(Chen, Jordan, and Wainwright 2020)
+and QEBA(Li et al. 2020), the proposed mechanism may
+get worse performance when facing SurFree(Maho, Furon,
+and Le Merrer 2021) attack.
+4.4
+The influence of distributed copy numbers
+In this section, we will discuss the traceability of the algo-
+rithm in multiple distributed copies. When training tracer Ti,
+the parameter is randomly initialized and each Ti is trained
+independently. So the distribution of DOL corresponding to
+any two branches should follow independent and identically
+distribution. Therefore, the traceability results of multiple
+copies could be calculated from the results of two copies.
+In order to verify the correctness, we perform the following
+experiments.
+For experiment verification, we trained 10 different Ti
+first, then we randomly choose one Ms as the source model
+to generate the adversarial examples. We record the tracing
+performance on the n, n ∈ [2, 10] models.
+To estimate the tracing results for n, n ∈ [2, 10] models,
+we utilize the Monte-Carlo sampling method in the distri-
+bution of two models’ DOL. The specific procedure is de-
+scribed as:
+1). We randomly choose one source model Ms and one
+other victim model Mv as the fundamental models, then we
+perform the black-box attack on Ms with 1000 different im-
+ages and record the DOL of Ts and Tv.
+2). We draw the distribution of DOL corresponding to Ts
+and Tv as the basic distribution, denoted as Ds and Dv, as
+shown in Fig. 5a- 5c.
+3). For the tracing results of n, n ∈ [2, 10] models, we
+conduct the sampling process (take one sample Ss from Ds
+and n − 1 sample Sn−1
+v
+from Dv) 10000 times.
+4) For each sampling, if Ss > max(Sn−1
+v
+), we consider
+it as a correct tracing sample. We record the total number
+of correct tracing N n
+C in 10000 samplings. The final tracing
+accuracy of n models can be calculated with N n
+C/10000.
+The results are shown in Fig. 5d-5f. The attack we choose
+is HSJA(Chen, Jordan, and Wainwright 2020), and α is fixed
+as 0.15. It can be seen that with the increasing number of
+distributed copies, the tracing accuracy gradually decreases.
+But with 10 branches, it can still maintain more than 90%
+accuracy for CIFAR10 and GTSRB. Besides, the estimated
+tracing performance is almost the same as the actual experi-
+ment results, which indicates the correctness of our analysis.
+5
+Discussion
+5.1
+The importance of noise-sensitive loss
+In the proposed mechanism, making Ti easier to be attacked
+is the key for tracing. We design the noise-sensitive loss to
+meet the requirement. In this section, experiments will be
+conducted to show the importance of noise-sensitive loss.
+We use two randomly initialized tracers as the comparison
+to conduct the tracing experiment on 1000 adversarial im-
+ages. The adversarial attack is set as HSJA(Chen, Jordan,
+and Wainwright 2020), α is fixed as 0.15. The experimental
+results are shown in Table 3.
+Attack
+CIFAR10
+GTSRB
+mini-ImageNet
+ResNet18
+VGG16
+ResNet18
+VGG16
+ResNet50
+VGG19
+Random
+57.9%
+62.4%
+53.9%
+57.0%
+56.2%
+59.8%
+Proposed
+99.3%
+97.9%
+98.7%
+98.3%
+97.5%
+95.4%
+Table 3: The trace accuracy of HSJA attack with different T .
+It can be seen that without noise-sensitive loss, the trac-
+ing accuracy of the random initialized tracer only achieves
+60%, which is much lower than the proposed noise-sensitive
+tracer. This indicates that noise-sensitive loss is very impor-
+tant in realizing accurate tracing, only setting different pa-
+rameters of tracer is not enough to trap the attack to result in
+specific features.
+5.2
+Non-transferability and traceability
+The concept of traceability is related but not equivalent
+to non-transferability. A non-transferable adversarial exam-
+ple works only on the victim model it is generated from.
+Therefore, tracing such non-transferable example may be
+a straightforward task. On the other hand, a transferable
+sample may be generic enough to work on many copies/-
+models. The task of tracing becomes more meaningful in
+
+(a) The distribution of CIFAR10.
+(b) The distribution of GTSRB.
+(c) The distribution of mini-ImageNet.
+(d) The tracing results of CIFAR10.
+(e) The tracing results of GTSRB.
+(f) The tracing results of mini-ImageNet.
+Figure 5: The distribution of DOL with HSJA and ResNet backbone and tracing performance of multiple branches.
+this scenario. Our ability to trace a non-transferable exam-
+ple demonstrates that the process of adversarial attack intro-
+duces distinct traceable features which are unique to each
+victim model. In this sense, traceability can serve as a fail-
+safe property in defending adversarial attacks. There are
+many defense methods can satisfy non-transferrability, but
+once the defense fails, the model will not be effectively pro-
+tected. But our experimental results show that for the pro-
+posed method, even if the defense fails, we still have a cer-
+tain probability to trace the attacked model, as shown in
+Table 4. We use the data of “ResNet-CIFAR10” task with
+HSJA (Chen, Jordan, and Wainwright 2020) and QEBA (Li
+et al. 2020) as examples to show the specific tracing results.
+Attack
+α
+NTr
+NTr(+)
+Tr
+Tr(+)
+Tr Rate
+Total Rate
+HSJA
+0.05
+672
+672
+328
+313
+95.43%
+98.50%
+0.1
+973
+973
+27
+19
+70.37%
+99.20%
+0.15
+993
+993
+7
+0
+0%
+99.30%
+QEBA
+0.05
+840
+840
+160
+156
+97.50%
+99.60%
+0.1
+879
+879
+121
+118
+97.52%
+99.70%
+0.15
+859
+859
+141
+138
+97.87%
+99.7%
+Table 4: The trace accuracy of different attacks.
+In Table 4, NTr and Tr indicate the number of non-
+transferrable samples and transferrable samples respectively.
+NTr(+) and Tr(+) indicate the number of successful tracing
+samples. We can see that for QEBA with α = 0.05, 0.1, and
+0.15, the traceability to transferrable samples is all keep at
+a high level which is greater than 97%. As for HSJA, when
+α = 0.05, 328 samples can be transferred, and the trace-
+ability of transferrable examples achieves 95.43%. When
+α = 0.15, although the traceability of transferrable exam-
+ples decreases to 0%, only 7 samples are transferrable. So
+the total tracing rate is still at a high level. In general, the pro-
+posed method either guarantees the high non-transferability
+or the high tracing accuracy for transferred samples.
+5.3
+Limitations and adaptive attacks
+Although the proposed system maintains certain traceability
+in the buyers-seller setting, there are still some limitations
+that need to be addressed. For example, once the attacker
+finds a way to attack C and bypass Ti, the tracing perfor-
+mance may degrade. But we found that attacking such sys-
+tem could be a challenging topic itself (in our setting) as
+the attackers do not have access to all other copies and thus
+are unable to avoid the differences that our tracer exploits.
+Besides, it seems a more adaptive attack also comes with
+“cost”. For instance, the approach of attacking C and by-
+passing Ti would degrade the visual quality of the attack.
+So future work may be paid on how to evade the attack by
+utilizing such “cost”.
+6
+Conclusion
+This paper researches a new aspect of defending against ad-
+versarial attacks that is traceability of adversarial attacks.
+The techniques derived could aid forensic investigation of
+known attacks, and provide deterrence to future attacks in
+the buyers-seller setting. As for the mechanism, we de-
+sign a framework which contains two related components
+(model separation and origin tracing) to realize traceabil-
+ity. For model separation, we propose a parallel network
+structure which pairs a unique tracer with the original classi-
+fier and a noise-sensitive training loss. Tracer model injects
+the unique features and ensures the differences between dis-
+tributed models. As for origin tracing, we design an output-
+logits-based tracing mechanism. Based on this, the traceabil-
+ity of the attacked models can be realized when obtaining
+
+400
+Source
+350
+INon-Source
+300
+250
+200
+150
+100
+50
+1.5450
+400
+Source
+INon-Source
+350
+300
+250
+200
+150
+100
+50500
+450
+Source
+INon-Source
+400
+350
+300
+250
+200
+150
+100
+50110
+105
+Tracing Accuracy (
+100
+95
+90
+ResNet18-R
++--ResNet18-S
+85
+-VGG16-R
++-- VGG16-S
+80
+Number of Distributed Models100
+Tracing Accuracy (%)
+66
+98
+96
+95
+94
+ResNet18-R
+--ResNet18-S
+93
+VGG16-R
++--VGG16-S
+92
+10
+Number of Distributed Models110.00
+100.00
+Tracing Accuracy
+90.00
+80.00
+70.0
+ResNet50-R
+ResNet50-S
+60.0
+—VGG19-R
++-- VGG19-S
+50.00
+2
+3
+4
+5
+D
+10
+Number of Distributed Modelsthe adversarial examples. The experiment of multi-dataset
+and multi-network model shows that it is possible to achieve
+traceability through the adversarial examples.
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+

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+Springer Nature 2021 LATEX template
+A massive quiescent galaxy at redshift 4.658
+Adam C. Carnall1*, Ross J. McLure1, James S. Dunlop1, Derek J.
+McLeod1, Vivienne Wild2, Fergus Cullen1, Dan Magee3, Ryan
+Begley1, Andrea Cimatti4,5, Callum T. Donnan1, Massissilia L.
+Hamadouche1, Sophie M. Jewell1 and Sam Walker1
+1Institute for Astronomy, School of Physics & Astronomy, University of
+Edinburgh, Royal Observatory, Edinburgh, EH9 3HJ, UK.
+2School of Physics & Astronomy, University of St Andrews, North
+Haugh, St Andrews, KY16 9SS, UK.
+3Department of Astronomy and Astrophysics, UCO/Lick Observatory,
+University of California, Santa Cruz, CA 95064, USA.
+4Department of Physics and Astronomy (DIFA), University of Bologna,
+Via Gobetti 93/2, I-40129, Bologna, Italy.
+5INAF, Osservatorio di Astrofisica e Scienza dello Spazio, Via Piero
+Gobetti 93/3, I-40129, Bologna, Italy.
+*Corresponding author email: [email protected]
+Abstract
+We report the spectroscopic confirmation of a massive quiescent galaxy,
+GS-9209 at a new redshift record of z = 4.658, just 1.25 Gyr after
+the Big Bang, using new deep continuum observations from JWST NIR-
+Spec. From our full-spectral-fitting analysis, we find that this galaxy
+formed its stellar population over a ≃ 200 Myr period, approximately
+600 − 800 Myr after the Big Bang (zform = 7.3 ± 0.2), before quench-
+ing at zquench = 6.7 ± 0.3. GS-9209 demonstrates unambiguously that
+massive galaxy formation was already well underway within the first bil-
+lion years of cosmic history, with this object having reached a stellar
+mass of log10(M∗/M⊙)
+>
+10.3 by z = 7. This galaxy also clearly
+demonstrates that the earliest onset of galaxy quenching was no later
+than ≃ 800 Myr after the Big Bang. We estimate the iron abundance
+and α-enhancement of GS-9209, finding [Fe/H] = −0.97+0.06
+−0.07 and
+[α/Fe] = 0.67+0.25
+−0.15, suggesting the stellar mass vs iron abundance rela-
+tion at z ≃ 7, when this object formed most of its stars, was ≃ 0.4 dex
+lower than at z ≃ 3.5. Whilst its spectrum is dominated by stellar emis-
+sion, GS-9209 also exhibits broad Hα emission, indicating that it hosts
+an active galactic nucleus (AGN), for which we measure a black-hole
+1
+arXiv:2301.11413v1  [astro-ph.GA]  26 Jan 2023
+
+Springer Nature 2021 LATEX template
+2
+A massive quiescent galaxy at redshift 4.658
+mass of log10(M•/M⊙) = 8.7 ± 0.1. Although large-scale star forma-
+tion in GS-9209 has been quenched for almost half a billion years, the
+significant integrated quantity of accretion implied by this large black-
+hole mass suggests AGN feedback plausibly played a significant role
+in quenching star formation in this galaxy. GS-9209 is also extremely
+compact, with an effective radius of just 215 ± 20 parsecs. This intrigu-
+ing object offers perhaps our deepest insight yet into massive galaxy
+formation and quenching during the first billion years of cosmic history.
+1 Summary
+The discovery of massive galaxies with old stellar populations at early cosmic
+epochs has historically acted as a key constraint on models for both galaxy for-
+mation physics and cosmology [1–4]. Today, the extremely rapid assembly of
+the earliest galaxies during the first billion years of cosmic history continues to
+challenge our understanding of galaxy formation physics [5, 6]. The advent of
+the James Webb Space Telescope (JWST) has exacerbated this issue by con-
+firming the existence of galaxies in significant numbers as early as the first few
+hundred million years [7–9]. Perhaps even more surprisingly, in some galaxies,
+this initial highly efficient star formation rapidly shuts down, or quenches, giv-
+ing rise to massive quiescent galaxies as little as ∼ 1.5 billion years after the
+Big Bang, at redshifts up to z ≃ 4 [4, 10]. Due to their faintness and red colour,
+it has proven extremely challenging to learn about these extreme quiescent
+galaxies, or to confirm whether any exist at earlier times. Here, we report the
+spectroscopic confirmation of a quiescent galaxy, GS-9209, at a new redshift
+record of 4.658, just 1.25 billion years after the Big Bang, using the NIRSpec
+instrument on JWST. The transformative power of JWST allows us to char-
+acterise the physical properties of this early massive galaxy in unprecedented
+detail. GS-9209 has a stellar mass of M∗ = 4.1 ± 0.2 × 1010 M⊙, and quenched
+star formation at z = 6.7 ± 0.3, when the Universe was ≃ 800 million years
+old. This intriguing object offers perhaps our deepest insight yet into massive
+galaxy formation and quenching during the first billion years of cosmic history.
+2 Results
+GS-9209 was first highlighted in the early 2000s as an object with red optical
+to near-infrared colours and a photometric redshift of z ≃ 4.5 [11]. An optical
+spectrum was taken in the mid-2010s as part of the VIMOS Ultra Deep Sur-
+vey (VUDS) [12], showing tentative evidence for a Lyman break at λ ≃ 7000˚A,
+but no Lyman α emission. During the past 5 years, several studies have iden-
+tified GS-9209 as a candidate high-redshift massive quiescent galaxy [13, 14],
+based on its blue colours at wavelengths, λ = 2 − 8µm and non-detection at
+millimetre wavelengths [15]. GS-9209 is also not detected in X-rays [16], at
+radio wavelengths [17], or at λ = 24µm [18]. The faint, red nature of the source
+(with magnitudes HAB = 24.7 and KAB = 23.6) means that near-infrared
+spectroscopy with ground-based instrumentation is prohibitively expensive.
+
+Springer Nature 2021 LATEX template
+A massive quiescent galaxy at redshift 4.658
+3
+2.0
+2.5
+3.0
+3.5
+4.0
+4.5
+5.0
+Observed Wavelength / µm
+0.0
+0.3
+0.6
+0.9
+1.2
+1.5
+fλ / 10−19 erg s−1 cm−2 ˚A−1
+F170LP + G235M
+F290LP + G395M
+2.0
+2.2
+2.4
+2.6
+λ / µm
+0.3
+0.6
+0.9
+1.2
+fλ / 10−19 erg s−1 cm−2 ˚A−1
+Hγ
+Hδ
+Hζ
+Hη
+Ca k
+Ca h
+Hϵ
++
+[O ii]
+Fitted model
+0.4
+0.5
+0.6
+0.7
+0.8
+Rest-frame Wavelength / µm
+Fig. 1 JWST NIRSpec observations of GS-9209. Data were taken using the G235M and
+G395M gratings (R = 1000), providing wavelength coverage from λ = 1.7 − 5.1µm. The
+galaxy is at z = 4.658, and exhibits extremely deep Balmer absorption lines, similar to lower
+redshift post-starburst galaxies, clearly indicating this galaxy experienced a significant, rapid
+drop in star-formation rate (SFR) within the past few hundred million years. The spectral
+region from λ = 2.6 − 4.0µm, containing Hβ and Hα, is shown at a larger scale in Fig. 2.
+2.1 Spectroscopic data
+On 16th November 2022, we obtained medium-resolution spectroscopy (R =
+λ/∆λ = 1000) through the JWST NIRSpec fixed slit, integrating for 3 hours
+with the G235M grism and 2 hours with the G395M grism, providing con-
+tinuous wavelength coverage from λ = 1.7 − 5.1µm. These data, shown in
+Fig. 1, reveal a full suite of extremely deep Balmer absorption features, from
+which we measure a spectroscopic redshift of 4.6582 ± 0.0002, consistent with
+previous photometric data and the VUDS spectrum. The spectrum strongly
+resembles that of an A-type star, and is reminiscent of lower-redshift post-
+starburst galaxies [19–21], with a Hδ equivalent width (EW), as measured by
+the HδA Lick index, of 7.9 ± 0.3˚A, comparable to the most extreme values
+observed in the local Universe [22]. These spectral features strongly indicate
+this galaxy has undergone a sharp decline in star-formation rate (SFR) during
+the preceding few hundred Myr.
+The observed continuum is relatively smooth, as is the case for A-type
+stars, with only two clearly detected metal absorption features: the Ca k line
+at 3934˚A and the Na d feature at 5895˚A. The Ca h line at 3969˚A is blended
+with the much stronger Hϵ Balmer line. The spectrum exhibits only the merest
+suspicion of [O ii] 3727˚A and [O iii] 4959˚A, 5007˚A emission, and no apparent
+infilling of Hβ or any of the higher-order Balmer absorption lines. However,
+as can be seen in Fig. 2, both Hα and [Nii] 6584˚A are clearly albeit weakly
+detected in emission, with Hα also exhibiting an obvious broad component.
+This broad component, along with the relative strength of [N ii] compared
+with the narrow Hα line indicate the presence of an accreting supermassive
+
+Springer Nature 2021 LATEX template
+4
+A massive quiescent galaxy at redshift 4.658
+2.6
+2.8
+3.0
+3.2
+3.4
+3.6
+3.8
+4.0
+Observed Wavelength / µm
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+fλ / 10−19 erg s−1 cm−2 ˚A−1
+Hβ
+Hα
+Mg i
+Na d
+[N ii]
+Fe i
+[O iii]
+[O iii]
+Bagpipes full fitted model
+Bagpipes AGN component
+Narrow line model
+0.50
+0.55
+0.60
+0.65
+0.70
+Rest-frame Wavelength / µm
+Observed fluxes
+Observed flux errors
+Fig. 2 JWST NIRSpec observations of GS-9209: zoom in on Hβ and Hα. Data are shown
+in blue, with their associated uncertainties visible at the bottom in purple. The full Bagpipes
+fitted model is shown in black, with the AGN component shown in red. The narrow Hα and
+[N ii] lines were masked during the Bagpipes fitting process, and subsequently fitted with
+Gaussian functions, shown in green. Key emission and absorption features are also marked.
+black hole: an active galactic nucleus (AGN). However, the extreme EWs of
+the observed Balmer absorption features indicate that the continuum emission
+must be strongly dominated by the stellar component. Nevertheless, the AGN
+contribution to GS-9209 must be carefully modelled when fitting the spectrum
+of this source to extract reliable stellar population properties (see Section 4.3).
+2.2 Full spectral fitting
+To measure the stellar population properties of GS-9209, we perform full spec-
+trophotometric fitting using the Bagpipes code. Full details of the methodology
+we employ are given in Section 4.3. Briefly, we combine our spectroscopic
+data with previously available CANDELS photometry, as well as new JWST
+NIRCam medium-band imaging in 5 filters from the Ultra Deep Field
+Medium-Band Survey (Programme ID: 1963; PI: Williams). We first mask the
+wavelengths corresponding to [O ii], [O iii], narrow Hα and [N ii], due to likely
+AGN contributions. We discuss the properties of these lines and their likely
+origin in Section 2.5. We then fit a 22-parameter model for the stellar, dust,
+nebular and AGN components, as well as spectrophotometric calibration.
+The resulting posterior median model is shown in black in Figs 1 and 2. We
+obtain a stellar mass of log10(M∗/M⊙) = 10.61±0.02, under the assumption of
+a Kroupa initial mass function (IMF) [23]. We additionally recover a very low
+level of dust attenuation, with AV = 0.04+0.05
+−0.03. The SFR we measure averaged
+over the past 100 Myr is consistent with zero, with a very stringent upper
+bound, though this is largely a result of our chosen star-formation history
+(SFH) parameterisation [24]. We report a more-realistic upper bound on the
+SFR in Section 2.5 based on the narrow Hα line.
+
+Springer Nature 2021 LATEX template
+A massive quiescent galaxy at redshift 4.658
+5
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+1.2
+Age of Universe / Gyr
+0.0
+1.0
+2.0
+3.0
+log10(SFR/yr−1)
+SFRpeak = 530+840
+−310 M⊙ yr−1
+tform = 0.71+0.3
+−0.2 Gyr
+2σ
+1σ
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+1.2
+Age of Universe / Gyr
+9.0
+9.5
+10.0
+10.5
+11.0
+log10(M∗/M⊙)
+Labbe et al. (2022)
+5
+6
+8
+12
+30
+Redshift
+5
+6
+8
+12
+30
+Redshift
+Fig. 3 The star-formation history of GS-9209. The SFR as a function of time is shown in
+the left panel, with the stellar mass as a function of time shown in the right panel. The blue
+lines show the posterior medians, with the darker and lighter shaded regions showing the 1σ
+and 2σ confidence intervals respectively. We find a formation redshift, zform = 7.3 ± 0.2 and
+a quenching redshift, zquench = 6.7 ± 0.3. The sample of massive z ≃ 8 galaxy candidates
+from JWST CEERS reported by [7] is also shown in the right panel, demonstrating that
+these candidates are plausible progenitors for GS-9209.
+2.3 Star-formation history
+The star-formation history (SFH) we recover is shown in Fig. 3. We find that
+GS-9209 formed its stellar population largely during a ≃ 200 Myr period, from
+around 600 − 800 Myr after the Big Bang (z ≃ 7 − 8). We recover a mass-
+weighted mean formation time, tform = 0.71+0.03
+−0.02 Gyr after the Big Bang,
+corresponding to a formation redshift, zform = 7.3 ± 0.2. This is the redshift
+at which GS-9209 would have had half its current stellar mass, approximately
+log10(M∗/M⊙) = 10.3. We find that GS-9209 quenched (which we define as
+the time at which its sSFR fell below 0.2 divided by the Hubble time, e.g.,
+[25]) at time tquench = 0.79+0.06
+−0.04 Gyr after the Big Bang, corresponding to a
+quenching redshift, zquench = 6.7 ± 0.3.
+Our model predicts that the peak historical SFR for GS-9209 (at approx-
+imately zform) was within the range SFRpeak = 530+840
+−310 M⊙ yr−1. This is
+similar to the SFRs of bright submillimetre galaxies (SMGs). The number den-
+sity of SMGs with SFR > 300 M⊙ yr−1 at 5 < z < 6 has been estimated to
+be ≃ 3×10−6 Mpc−3 [26]. Extrapolation then suggests that the SMG number
+density at z ≃ 7 is ≃ 1 × 10−6 Mpc−3, which equates to ≃ 1 SMG at z ≃ 7
+over the ≃ 400 square arcmin area from which GS-9209 and one other z > 4
+quiescent galaxy were selected [14]. This broadly consistent number density
+suggests it is entirely plausible that GS-9209 went through a SMG phase at
+z ≃ 7, shortly before quenching.
+In the right panel of Fig. 3, we show the positions of the massive, high-
+redshift galaxies recently reported by [7] in the first imaging release from the
+JWST CEERS survey. It can be seen that the positions of these galaxies are
+
+Springer Nature 2021 LATEX template
+6
+A massive quiescent galaxy at redshift 4.658
+broadly consistent with the SFH of GS-9209 at z ≃ 8. It should however be
+noted that, as previously discussed, GS-9209 was selected as one of only two
+robustly identified z > 4 massive quiescent galaxies in an area roughly 10 times
+the size of the initial CEERS imaging area [14]. It therefore seems unlikely
+that a large fraction of the objects reported by [7] will evolve in a similar way
+to GS-9209 over the redshift interval from z ≃ 5 − 8.
+2.4 Stellar metallicity
+We obtain a relatively low stellar metallicity for GS-9209 of log10(Z∗/Z⊙) =
+−0.97+0.06
+−0.07 (where we adopt a value of Z⊙=0.0142 [27]). By re-running our
+fitting procedure at a range of fixed metallicity values, we find that metallicity
+is constrained mainly by the shape of the stellar continuum emission above
+the Balmer break (the λ = 2.0 − 2.6µm region shown in the inset panel of
+Fig. 1), which is strongly incompatible with models at higher metallicities.
+This UV continuum shape is mostly sensitive to the Fe abundance [28, 29],
+and we therefore associate our measured Z∗ value with the Fe abundance,
+[Fe/H] = −0.97+0.06
+−0.07. This is ≃ 0.4 dex below the mean z ≃ 3.5 stellar mass vs
+iron abundance relationship for star-forming galaxies [30]. Given that GS-9209
+formed its stellar population at z ≃ 7, our result suggests that the stellar mass
+vs iron abundance relation continues to trend downwards over the redshift
+interval from z ≃ 3.5−7, as is observed between the local Universe and z ≃ 3.5.
+As can be seen from Figs 1 and 2, we do not obtain a good fit to either the
+Ca k or Na d absorption features, with our model significantly under-predicting
+the depths of both. Stellar populations that form and quench rapidly are known
+to be α-enhanced [31], whereas the stellar population models we fit assume a
+fixed scaled-Solar abundance pattern (see Section 4.3). We therefore provision-
+ally attribute the failure of our model to reproduce these α-element absorption
+features to significant α-enhancement in GS-9209. It should be noted however
+that both of these features (in particular Na d) can also arise from interstellar
+medium (ISM) absorption, though the low dust attenuation we infer from our
+spectral fit might be taken to suggest this effect should be small.
+Unfortunately, reliable empirical α-enhanced models are not currently
+available for stellar populations with ages less than 1 Gyr. Therefore, to test
+this α-enhancement hypothesis, we first measure the EWs of these two fea-
+tures from our data (see Section 4), obtaining a Ca k EW of 2.15 ± 0.25˚A,
+and a Na d EW of 2.09 ± 0.46˚A. For comparison, our posterior median model
+predicts values of 1.12˚A and 0.41˚A respectively. We then scale up the metallic-
+ity of our model, keeping all other parameters fixed, until the predicted EWs
+match our data. By this process, we obtain [Ca/Fe] = 0.67+0.25
+−0.15. We are how-
+ever unable to reproduce the observed depth of Na d via this process, which
+we attribute to the known strong ISM component of this absorption feature
+[29, 32]. The Ca abundance we calculate is however fully consistent with both
+theoretical predictions [33] and observational evidence [34] for α-enhancement
+in extreme stellar populations. In particular, [3] report a consistent value of
+[Ca/Fe] = 0.59 ± 0.07 for an extreme massive quiescent galaxy at z = 2.1.
+
+Springer Nature 2021 LATEX template
+A massive quiescent galaxy at redshift 4.658
+7
+We therefore adopt our measured Ca abundance as our best estimate of the
+α-enhancement of GS-9209, [α/Fe] = 0.67+0.25
+−0.15. This extreme α-enhancement
+supports our finding of an extremely short, ≲ 200 Myr formation timescale
+[31], as shown in Fig. 3. We caution however that this value could be artificially
+boosted by an ISM contribution to the Ca k absorption line.
+2.5 Evidence for AGN activity
+From our Bagpipes full spectral fit, we measure an observed broad Hα flux of
+fHα, broad = 1.26±0.08×10−17 = erg s−1 cm−2 and full width at half maximum
+(FWHM) of 10800±600 km s−1 in the rest frame. This line width, whilst very
+broad, is consistent with rest-frame UV broad line widths measured for some
+z = 6 quasars (e.g., [35, 36]).
+We also recover an observed AGN continuum flux at rest-frame wave-
+length, λrest = 5100˚A of f5100 = 0.040 ± 0.004 × 10−19 erg s−1 cm−2 ˚A−1.
+This is approximately 5 per cent of the total observed flux from GS-9209 at
+λ = 2.9µm. We measure a power-law index for the AGN continuum emission
+of αλ = −1.36±0.08 at λrest < 5000˚A, and αλ = 0.69±0.14 at λrest > 5000˚A.
+These indices are broadly consistent with the average values observed for local
+quasars [37]. In combination with the non-detection of GS-9209 at longer wave-
+lengths (see Section 2), this suggests the AGN component in GS-9209 is not
+significantly reddened. The AGN contribution to the continuum flux from GS-
+9209 rises to ≃ 15 per cent at the blue end of our spectrum (λ = 1.7µm),
+and ≃ 20 per cent at the red end (λ = 5µm). Just above the Lyman break at
+λ ≃ 7000˚A, the AGN contribution is ≃ 35 per cent of the observed flux.
+Given our measured fHα, broad, which is more direct than our AGN con-
+tinuum measurement, the average relation for local AGN presented by [38]
+predicts f5100 to be ≃ 0.4 dex brighter than we measure. However, given the
+intrinsic scatter of 0.2 dex they report, our measured f5100 is only 2σ below
+the mean relation. The extreme equivalent widths of the observed Balmer
+absorption features firmly disfavour stronger AGN continuum emission.
+We fit the narrow Hα and [N ii] lines in our spectrum as follows. We first
+subtract from our observed spectrum the posterior median Bagpipes model
+from our full spectral fitting, described in Section 2.2. We then simultaneously
+fit Gaussian components to both lines, assuming the same velocity width for
+both, which is allowed to vary. This process is visualised in Fig. 2. We also
+show the broad Hβ line in our AGN model, for which we assume the same
+width as broad Hα, as well as Case B recombination. It can be seen that the
+broad Hβ line peaks at around the noise level in our spectrum, and is hence
+too weak to be clearly observed in our data.
+We obtain a Hα narrow-line flux of 1.58 ± 0.10 × 10−18 erg s−1 cm−2
+and a [N ii] flux of 1.56 ± 0.10 × 10−18 erg s−1 cm−2, giving a line ratio of
+log10([N ii]/Hα) = −0.01 ± 0.04. This line ratio is significantly higher than
+would be expected as a result of ongoing star formation, and is consistent
+with excitation due to an AGN or shocks resulting from galactic outflows [39].
+Such outflows are commonly observed in post-starburst galaxies at z ≳ 1 [40]
+
+Springer Nature 2021 LATEX template
+8
+A massive quiescent galaxy at redshift 4.658
+Fig. 4 JWST NIRCam imaging of GS-9209. Each cutout image shows an area of 1.5′′×1.5′′.
+The RGB image in the first (leftmost) panel is constructed with F430M as red, F210M as
+green and F182M as blue. The second panel shows the F210M image, with our posterior
+median PetroFit model shown in the third panel. The residuals between model and data are
+shown in the right panel, on the same colour scale as the middle two panels.
+without corresponding AGN signatures, suggesting either that these outflows
+are driven by stellar feedback, or that the AGN activity responsible for the
+outflow has since shut down.
+Even if we assume all the narrow Hα emission is driven by ongoing
+star formation, we obtain SFR = 1.9 ± 0.1 M⊙ yr−1 [41], corresponding to
+log10(sSFR/yr−1) = −10.3±0.1. This is under the assumption that dust atten-
+uation is negligible, based on our finding of a very low AV from full spectral
+fitting in Section 2.2. This is well below the commonly applied sSFR threshold
+for defining quiescent galaxies at this redshift [25], log10(sSFRthreshold/yr−1) =
+0.2/tH = −9.8, where tH is the age of the Universe. Given the multiple lines
+of evidence we uncover for a significant non-stellar component to this line, it
+is likely that the SFR of GS-9209 is considerably lower than this estimate.
+We estimate the black-hole mass for GS-9209, M•, from our combined
+Hα flux and broad-line width, using the relation presented in Equation 6
+of [38], obtaining log10(M•/M⊙) = 8.7 ± 0.1. From our Bagpipes full spec-
+tral fit, we infer a stellar velocity dispersion, σ = 247 ± 16 km s−1 for
+GS-9209, after correcting for the intrinsic dispersion of our template set,
+as well as instrumental dispersion. Given this measurement, the relationship
+between velocity dispersion and black-hole mass presented by [42] predicts
+log10(M•/M⊙) = 8.9 ± 0.1.
+Given the broad agreement between these estimators, it seems reasonable
+to conclude that GS-9209 contains a supermassive black hole with a mass of
+approximately half a billion to a billion Solar masses. It is interesting to note
+that this is ≃ 4 − 5 times the black-hole mass that would be expected given
+the stellar mass of the galaxy, assuming this is equivalent to the bulge mass.
+This is consistent with the observed increase in the average black-hole to bulge
+mass ratio for massive galaxies from 0 < z < 2 [43]. This large amount of
+historical AGN accretion relative to star formation strongly implies that AGN
+feedback may be responsible for quenching this galaxy.
+2.6 Size measurement and dynamical mass
+GS-9209 is an extremely compact source, which is only marginally resolved in
+the highest-resolution available imaging data. The CANDELS/3DHST team
+
+RGB
+F210M Data
+Model
+Residual
+1.5"×Springer Nature 2021 LATEX template
+A massive quiescent galaxy at redshift 4.658
+9
+[44] measured an effective radius, re = 0.029 ± 0.002′′ for GS-9209 in the HST
+F125W filter via S´ersic fitting, along with a S´ersic index, n = 6.0 ± 0.8. At
+z = 4.658, this corresponds to re = 189 ± 13 parsecs.
+We update this size measurement using the newly available JWST NIR-
+Cam F210M-band imaging, which has a FWHM of ≃ 0.07′′ (see Section 4.4).
+Accounting for the AGN point-source contribution, we measure an effective
+radius, re = 0.033 ± 0.003′′ for the stellar component of GS-9209, along with
+a S´ersic index, n = 2.3 ± 0.3. At z = 4.658, this corresponds to re = 215 ± 20
+parsecs. This is consistent with the CANDELS/3DHST measurement, and is
+≃ 0.7 dex below the mean relationship between re and stellar mass for qui-
+escent galaxies at z ≃ 1 [44, 45]. This is interesting given that post-starburst
+galaxies z ≃ 1 are known to be more compact than is typical for the wider
+quiescent population [46]. We calculate a stellar-mass surface density within
+re of log10(Σeff/M⊙ kpc−2) = 11.15 ± 0.08, consistent with the densest stel-
+lar systems in the Universe [47]. We show the F210M data for GS-9209, along
+with our posterior-median model in Fig. 4.
+We estimate the dynamical mass using our size and velocity dispersion
+measurements (e.g., [40]), obtaining a value of log10(Mdyn/M⊙) = 10.3 ± 0.1.
+This is ≃ 0.3 dex lower than the stellar mass we measure. As GS-9209 is only
+marginally resolved, even in JWST imaging data, and due to the presence
+of the AGN component, it is plausible that our measured re may be subject
+to systematic uncertainties. Deeper imaging data in the F200W or F277W
+bands (e.g., from the JWST Advanced Deep Extragalactic Survey; JADES)
+will provide a useful check on this, particularly given the lower AGN fraction
+in the F277W band. Furthermore, since the pixel scale of NIRSpec is 0.1′′,
+our velocity dispersion measurement may not accurately represent the central
+velocity dispersion of GS-9209, leading to an underestimated dynamical mass.
+It should also be noted that the stellar mass we measure is strongly dependent
+on our assumed IMF.
+A final, intriguing possibility would be a high level of rotational support in
+GS-9209, as has been observed for quiescent galaxies at 2 < z < 3 [48]. Unfor-
+tunately, the extremely compact nature of the source makes any attempt at
+resolved studies extremely challenging, even with the JWST NIRSpec integral
+field unit. Resolved kinematics for this galaxy would be a clear use case for the
+High Angular Resolution Monolithic Optical and Near-infrared Integral field
+spectrograph (HARMONI) planned for the Extremely Large Telescope (ELT).
+3 Conclusion
+We report the spectroscopic confirmation of a massive quiescent galaxy, GS-
+9209 at a new redshift record of z = 4.6582 ± 0.002, with a stellar mass
+of log10(M∗/M⊙) = 10.61 ± 0.02. This galaxy formed its stellar popula-
+tion over a ≃ 200 Myr period, approximately 600 − 800 Myr after the Big
+Bang (zform = 7.3 ± 0.2), before quenching at zquench = 6.7 ± 0.3. GS-9209
+demonstrates unambiguously that massive galaxy formation was already well
+
+Springer Nature 2021 LATEX template
+10
+A massive quiescent galaxy at redshift 4.658
+underway within the first billion years of cosmic history, with this object having
+reached log10(M∗/M⊙) > 10.3 by z = 7. This galaxy also clearly demonstrates
+that the earliest onset of galaxy quenching was no later than ≃ 800 Myr after
+the Big Bang.
+We estimate the iron abundance and α-enhancement of GS-9209, finding
+[Fe/H] = −0.97+0.06
+−0.07 and [α/Fe] = 0.67+0.25
+−0.15, suggesting the stellar mass vs
+iron abundance relation at z ≃ 7, when this object formed most of its stars,
+was ≃ 0.4 dex lower than at z ≃ 3.5 [30]. Whilst its spectrum is dominated by
+stellar emission, GS-9209 also hosts an AGN, for which we measure a black-hole
+mass of log10(M•/M⊙) = 8.7 ± 0.1 from the observed broad and narrow Hα
+emission [38]. We also predict a consistent value of log10(M•/M⊙) = 8.9 ± 0.1
+based on the stellar velocity dispersion of GS-9209 [42]. Whilst large-scale star
+formation in GS-9209 has been quenched for almost half a billion years, the
+significant integrated quantity of AGN accretion implied by this large black-
+hole mass (≃ 4 − 5 times what would be expected given the stellar mass of
+this galaxy) suggests that AGN activity plausibly played a significant role in
+quenching star formation in this galaxy.
+Based on the properties we measure, GS-9209 seems likely to be associated
+with the most extreme galaxy populations currently known at z > 5, such as
+the highest-redshift submillimetre galaxies and quasars (e.g., [36, 49, 50]). GS-
+9209 is also plausibly descended from an object similar to the z ≃ 8 massive
+galaxy candidates recently reported in the first data from the JWST CEERS
+programme [7], though the number density of these candidates is significantly
+higher than that of z > 4 quiescent galaxies. GS-9209 and similar objects (e.g.,
+[9]) are also likely progenitors for the dense, ancient cores of the most massive
+galaxies in the local Universe.
+This study, which makes use of just 5 hours of on-source integration time,
+demonstrates the huge potential of JWST for revolutionising our understand-
+ing of the high-redshift Universe. It seems clear that this work will be followed
+rapidly by the confirmation and detailed spectroscopic exploration of large
+samples of z > 4 quiescent galaxies, to build up a detailed understanding of
+massive galaxy formation and quenching during the first billion years.
+4 Methods
+4.1 Spectroscopic data reduction
+We reduce our NIRSpec data using the JWST Science Calibration Pipeline
+v1.8.4, using version 1017 of the JWST calibration reference data. To improve
+the spectrophotometric calibration of our data, we also reduce observations
+of the A-type standard star 2MASS J18083474+6927286 [51], taken as part
+of JWST commissioning programme 1128 (PI: L¨utzgendorf) [52] using the
+same instrument modes. We compare the resulting stellar spectrum against
+a spectral model for this star from the CALSPEC library [53] to construct a
+calibration function, which we then apply to our observations of GS-9209.
+
+Springer Nature 2021 LATEX template
+A massive quiescent galaxy at redshift 4.658
+11
+4.2 Photometric data reduction
+The majority of our photometric data are taken directly from the CANDELS
+GOODS South catalogue [54]. We supplement this with new JWST NIRCam
+photometric data taken as part of the Ultra Deep Field Medium-Band Survey
+[55] (Programme ID: 1963; PI: Williams). Data are available in the F182M,
+F210M, F430M, F460M and F480M bands. We reduce these data using the
+PRIMER Enhanced NIRCam Image-processing Library (PENCIL, e.g., [8]), a
+custom version of the JWST Science Calibration Pipeline (v1.8.0), and using
+version 1011 of the JWST calibration reference data. We measure photometric
+fluxes for GS-9209 in large, 1′′-diameter apertures to ensure we measure the
+total flux in each band (the object is isolated, with no other sources within
+this radius, see Fig. 4). We measure uncertainties as the standard deviation of
+flux values in the nearest 100 blank-sky apertures, masking out nearby objects
+(e.g., [56]).
+4.3 Bagpipes full spectral fitting
+We fit the available photometry in parallel with our new spectroscopic data
+using the Bagpipes code [57]. Our model has a total of 22 free parameters,
+describing the stellar, dust, nebular and AGN components of the spectrum.
+A full list of these parameters, along with their associated priors, is given in
+Table 1. We fit our model to the data using the MultiNest nested sampling
+algorithm [58–60].
+We use the 2016 updated version of the BC03 [61, 62] stellar population
+models, using the MILES stellar spectral library [63] and updated stellar evolu-
+tionary tracks [64, 65]. We assume a double-power-law star-formation-history
+model (e.g., [24, 57]). We allow the logarithm of the stellar metallicity, Z∗ to
+vary freely from log10(Z∗/Z⊙) = −2.45 to 0.55. These are the limits of the
+range spanned by the BC03 model grid relative to our adopted Solar metallicity
+value (Z⊙ = 0.0142 [27]).
+We mask out the narrow emission lines in our spectrum during our Bag-
+pipes fitting due to likely AGN contributions, whereas Bagpipes is only capable
+of modelling emission lines from star-forming regions. We do however still
+include a nebular model in our Bagpipes fit to allow for the possibility of
+nebular continuum emission from star-forming regions. We assume a stellar-
+birth-cloud lifetime of 10 Myr, and vary the logarithm of the ionization
+parameter, U, from log10(U) = −4 to −2. We also allow the logarithm of the
+gas-phase metallicity, Zg, to vary freely from log10(Zg/Z⊙) = −2.45 to 0.55.
+Because our eventual fitted model only includes an extremely small amount
+of star formation within the last 10 Myr for GS-9209, this nebular component
+makes a negligible contribution to the fitted model spectrum.
+We model attenuation of the above components by dust using the model
+of [66, 67], which is parameterised as a power-law deviation from the Calzetti
+dust attenuation law [68], and also includes a Drude profile to model the 2175˚A
+bump. We allow the V −band attenuation, AV to vary from 0 − 4 magnitudes.
+
+Springer Nature 2021 LATEX template
+12
+A massive quiescent galaxy at redshift 4.658
+Table 1 The 22 free parameters of the Bagpipes model we fit to our spectroscopic and photometric data (see Sections 2.2 and 4.3), along with their
+associated prior distributions. The upper limit on τ, tobs, is the age of the Universe as a function of redshift. Logarithmic priors are all applied in
+base ten. For parameters with Gaussian priors, the mean is µ and the standard deviation is σ.
+Component Parameter
+Symbol / Unit
+Range
+Prior
+Hyper-parameters
+General
+Redshift
+z
+(4.6, 4.7)
+Gaussian
+µ = 4.66
+σ = 0.01
+Stellar velocity dispersion
+σ / km s−1
+(50, 500)
+Logarithmic
+SFH
+Total stellar mass formed
+M∗ / M⊙
+(1, 1013)
+Logarithmic
+Stellar metallicity
+Z∗ / Z⊙
+(0.00355, 3.55)
+Logarithmic
+Double-power-law falling slope
+α
+(0.01, 1000)
+Logarithmic
+Double-power-law rising slope
+β
+(0.01, 1000)
+Logarithmic
+Double-power-law turnover time
+τ / Gyr
+(0.1, tobs)
+Uniform
+Dust
+V −band attenuation
+AV / mag
+(0, 4)
+Uniform
+Deviation from Calzetti slope
+δ
+(−0.3, 0.3)
+Gaussian
+µ = 0
+σ = 0.1
+Strength of 2175˚A bump
+B
+(0, 5)
+Uniform
+Attenuation ratio for birth clouds ϵ
+(1, 5)
+Uniform
+AGN
+Power law slope (λ < 5000˚A)
+αλ<5000˚
+A
+(−2.5, −0.5)
+Gaussian
+µ = −1.5 σ = 0.1
+Power law slope (λ > 5000˚A)
+αλ>5000˚
+A
+(−0.5, 1.5)
+Gaussian
+µ = 0.5
+σ = 0.2
+Hα broad-line flux
+fHα, broad / erg s−1 cm−2
+(0, 2.5 × 10−17) Uniform
+Hα broad-line velocity dispersion
+σHα, broad / km s−1
+(1000, 5000)
+Logarithmic
+Continuum flux at λ = 5100˚A
+f5100 / erg s−1 cm−2 ˚A−1 (0, 10−19)
+Uniform
+Nebular
+Ionization parameter
+U
+(10−4, 10−2)
+Logarithmic
+Gas-phase metallicity
+Zg / Z⊙
+(0.00355, 3.55)
+Logarithmic
+Calibration Zero order
+P0
+(0.75, 1.25)
+Gaussian
+µ = 1
+σ = 0.1
+First order
+P1
+(−0.25, 0.25)
+Gaussian
+µ = 0
+σ = 0.1
+Second order
+P2
+(−0.25, 0.25)
+Gaussian
+µ = 0
+σ = 0.1
+Noise
+White noise scaling
+a
+(0.1, 10)
+logarithmic
+
+Springer Nature 2021 LATEX template
+A massive quiescent galaxy at redshift 4.658
+13
+We further assume that attenuation is multiplied by an additional factor for
+all stars with ages below 10 Myr, and resulting nebular emission. This factor
+is commonly assumed to be 2, however we allow this to vary from 1 to 5.
+We allow redshift to vary, using a narrow Gaussian prior with a mean of 4.66
+and standard deviation of 0.01. We additionally convolve the spectral model
+with a Gaussian kernel in velocity space, to account for velocity dispersion in
+our target galaxy. The width of this kernel is allowed to vary with a logarithmic
+prior across a range from 50 − 500 km s−1.
+Separately from the above components, we also include a model for AGN
+continuum, broad Hα and Hβ emission. Following [37], we model AGN contin-
+uum emission with a broken power law, with two spectral indices and a break
+at λrest = 5000˚A in the rest frame. We vary the spectral index at λrest < 5000˚A
+using a Gaussian prior with a mean value of αλ = −1.5 (αν = −0.5) and stan-
+dard deviation of 0.1. We also vary the spectral index at λrest > 5000˚A using
+a Gaussian prior with a mean value of αλ = 0.5 (αν = −2.5) and standard
+deviation of 0.2. We parameterise the normalisation of the AGN continuum
+component using f5100, the flux at rest-frame 5100˚A, which we allow to vary
+with a linear prior from 0 to 10−19 erg s−1 cm−2 ˚A−1.
+We model broad Hα with a Gaussian component, varying the normalisation
+from 0 to 2.5 × 10−17 erg s−1 cm−2 using a linear prior, and the velocity
+dispersion from 1000 − 5000 km s−1 in the rest frame using a logarithmic
+prior. We also include a broad Hβ component in the model, which has the
+same parameters as the broad Hα line, but with normalisation divided by the
+standard 2.86 ratio from Case B recombination theory. However, as shown in
+Fig. 2, this Hβ model peaks at around the noise level in our spectrum, and
+the line is therefore plausible in not being obviously detected in the observed
+spectrum.
+We include intergalactic medium (IGM) absorption using the model of
+[69]. To allow for imperfect spectrophotometric calibration of our spectroscopic
+data, we also include a second-order Chebyshev polynomial (e.g., [70, 71]),
+which the above components of our combined model are all divided by before
+being compared with our spectroscopic data. We finally fit an additional white
+noise term, which multiplies the spectroscopic uncertainties from the JWST
+pipeline by a factor, a, which we vary with a logarithmic prior from 1 − 10.
+4.4 Size measurement from F210M-band imaging
+We model the light distribution of GS-9209 in the JWST NIRCam F210M
+imaging data using PetroFit [72]. We fit these PetroFit models to our data
+using the MultiNest nested sampling algorithm [58–60]. We use F210M in
+preference to the F182M band due to the smaller AGN contribution in
+F210M and the fact that it sits above the Balmer break, therefore being
+more representative of the stellar mass present rather than any ongoing star
+formation.
+
+Springer Nature 2021 LATEX template
+14
+A massive quiescent galaxy at redshift 4.658
+As our spectroscopic data contains strong evidence for an AGN, we fit both
+S´ersic and delta-function components simultaneously, convolved by an empir-
+ically estimated PSF, derived by stacking bright stars. In preliminary fitting,
+we find that the relative fluxes of these two components are entirely degen-
+erate with the S´ersic parameters. We therefore predict the AGN contribution
+to the flux in this band based on our full-spectral-fitting result, obtaining a
+value of 8 ± 1 per cent. We then impose this as a Gaussian prior on the rela-
+tive contributions from the S´ersic and delta function components. The 11 free
+parameters of our model are the overall flux normalisation, which we fit with a
+logarithmic prior, the effective radius, re, S´ersic index, n, ellipticity and posi-
+tion angle of the S´ersic component, the x and y centroids of both components,
+the position angle of the point spread function, and the fraction of light in the
+delta-function component, which we fit with a Gaussian prior with a mean of
+8 per cent and standard deviation of 1 per cent, based on our full spectral
+fitting result.
+Acknowledgements
+The authors would like to thank James Aird for helpful discussions. A. C.
+Carnall thanks the Leverhulme Trust for their support via a Leverhulme
+Early Career Fellowship. R. J. McLure, J. S. Dunlop, D. J. McLeod, V. Wild,
+R. Begley, C. T. Donnan and M. L. Hamadouche acknowledge the support
+of the Science and Technology Facilities Council. F. Cullen acknowledges
+support from a UKRI Frontier Research Guarantee Grant (grant reference
+EP/X021025/1). A. Cimatti acknowledges support from the grant PRIN
+MIUR 2017 - 20173ML3WW 001.
+Statement of Author Contributions
+ACC led the preparation of the observing proposal, reduction and analysis of
+the data, and preparation of the manuscript. RJM, JSD, VW, FC and AC
+provided advice and assistance with data reduction, analysis and interpreta-
+tion, as well as consulting on the preparation of the observing proposal. DJM,
+DM, RB and CTD reduced the JWST imaging data and prepared the empir-
+ical PSF. DJM, MLH and SMJ assisted with measurement of the size and
+morphology of GS-9209. SW assisted with selection of GS-9209 from the CAN-
+DELS catalogues prior to the observing proposal being submitted. All authors
+assisted with preparation of the final published manuscript.
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