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save separate checkpoints for different cities or save new checkpoints for our
New York City model if we retrain with new data. The process of applying the
model to new inputs is called inference. To create an output for a
temperature, we also apply an algorithm: subtract the parameter from the
input, and return “above” if the difference is positive.

Our temperature example is a very simple model. In machine learning, models
can be arbitrarily complex. A common type of model architecture is a neural
network, which (today) can have billions of parameters.

It is important to note that models are often embedded within software systems
that can get deployed to public-facing users. For example, GPT-4 is a
generative-AI model that is embedded within the ChatGPT system, which also has
a user interface, developer APIs, and other functionality, like input and
output filters. The other components are not part of the model itself, but can
work in concert with the model to provide overall functionality.

  28. Multimodal Generative-AI models may generate content in one modality (text, images, audio, etc.) or in multiple modalities. For example, DALL-E is a multimodal model that transforms text to images.

  29. Neural Network A neural network is a type of model architecture. Neural networks consist of layers, where the output of one layer is used as the input of the next layer. Each layer consists of a set of classifiers (neurons) that each performs a simple operation independently of one another. A neural-network model synthesizes multiple simple decisions by passing the input through a series of intermediate transformations. The outputs of all classifiers at layer $n$ are then passed to each classifier in layer $n+1$, and so forth. Each classifier in each layer has parameters that define how it responds to input.

  30. Objective Objective is a term of art in machine learning that describes a mathematical function for the reward or loss of a model. A common point of confusion is between the goal a model creator might have and the objective for a model. The goal of model training is typically to create models that generalize well. But that goal (creating models that generalize well) is not a mathematical function that can be maximized. As an example, the training objective for transformer models is typically to generate the same next token as in the training data.

  31. Parameters Parameters are numbers that define the specific behavior of a model. For example, in the linear equation model $y=mx+b$, there are two parameters: the slope $m$ and the bias (or, intercept) $b$. A more complex example might be a model that predicts the probability a person makes a bicycle trip given the current temperature and rainfall. This could have two parameters: one representing the effect of temperature and one representing the effect of rainfall. Contemporary neural network models have millions to billions of parameters. Model parameters are often interchangeably referred to as model weights. The values of parameters are saved in files called checkpoints.

For more on the distinction between parameters and hyperparameters, see
hyperparameters.

  32. Pre-Processing See data curation and pre-processing.

  33. Pre-Training and Fine-Tuning Current protocols divide training into a common pre-training phase that results in a general-purpose or base model (sometimes called a foundation or pre-trained model) and an application-specific fine-tuning phase that adapts a pre-trained model checkpoint to perform a desired task using additional data. This paradigm has become common over the last five years, especially as model architectures have become larger and larger. This is because, relative to pre-training datasets, fine-tuning datasets are smaller, which make fine-tuning faster and less expensive. In general, it is much cheaper to fine-tune an existing base model for a particular task than it is to train a new model from scratch.

As a concrete example, fine-tuning models to “follow instructions” has become
an important special case with the popularity of ChatGPT (this is called
instruction tuning). Examples of interactions in which someone makes a request
and someone else follows those instructions are relatively rare on the
Internet compared to, for example, question-and-answer forums. As a result,
such datasets are often constructed specifically for the purpose of LLM fine-
tuning, and may provide substantial practical benefits for commercial
companies.

Because pre-trained models are most useful if they provide a good basis for
many distinct applications, model builders have a strong incentive to collect
as much pre-training data from as many distinct sources as possible. Fine-
tuning results in a completely new model checkpoint (potentially gigabytes of
data that must be loaded and served separately from the original model), and
tends to require hundreds to thousands of application-specific examples.

However, the distinction between pre-training and fine-tuning is not well-
defined. Models are often trained with many (more than two) training stages.
For example, the choice to call the first two of, say three, training stages
pre-training and the last stage fine-tuning is simply a choice. Finally, pre-
training should not be confused with data curation or pre-processing.

  34. Prompt Most generative-AI systems take as input (currently, this is often some text), which is then used to condition the output. This input is called the prompt.

  35. Regurgitation See memorization.

  36. Reinforcement Learning Reinforcement learning (RL) is a type of machine learning for incorporating feedback into systems. For generative models, RL is commonly used to incorporate human feedback (HF) about whether the generations were “good” or “useful,” which can then be used to improve future generations. For example, ChatGPT collects “thumbs-up” and “thumbs-down” feedback on interactions in the system. User feedback is just one way of collecting human feedback. Model creators can also pay testers to rate generations.

  37. Reward See loss.

  38. Scale Machine-learning experts use the term scale to refer to the number of parameters in their model, the size of their training datasets (commonly measured in terms of number of examples or storage size on disk), or the computational requirements to train the model. The scale of the model’s parameter count and the training dataset size directly influence the computational requirements of training. The scale of computation needed for training can be measured in terms of the number of GPU-hours (on a given GPU type), the number of computers/GPUs involved in total, or the number of FLOPs (floating point operations).

Machine-learning practitioners will sometimes talk about scaling up a model.
This usually means figuring out a way to increase one of the properties listed
above. It can also mean figuring out how to increase the fidelity of training
examples, e.g., training on longer text sequences or on higher-resolution
images.

  39. Supply Chain Generative-AI systems are created, deployed, and used in a variety of different ways. Other work has written about how it is useful to think of these systems in terms of a supply chain that involves many different stages and actors. For more information about the generative-AI supply chain, please see Lee et al. [62].

  40. Tokenization For language models, a common pre-processing step is to break documents into segments called tokens. For example, the input “I like ice cream.” might be tokenized into [“I”, “like”, “ice”, “cream”, “.”]. The tokens can then be mapped to entries in a vocabulary. Each entry, or token, in the vocabulary is given an ID (a number representing that token). Each token in the vocabulary has a corresponding embedding that is a learned parameter. The embedding turns words into numeric representations that can be interpreted and modified by a model.

Each model family tends to share a vocabulary, which is optimized to represent
a particular training corpus. Most current models use subword tokenization to
handle words that would otherwise not be recognized. Therefore, a rare or
misspelled word might be represented by multiple tokens, for example [“seren”,
“dipity”] for “serendipity.” The number of tokens used to represent an input
is important because it determines how large the effective context window of a
model is.

Tokens are also used for other modalities, like music. Music tokens may be
semantic tokens that may be created using another neural network.

  41. Transformer A transformer is a popular model architecture for image, text, and music applications, and the transformer architecture underlies models like ChatGPT, Bard, and MusicLM. An input (text or image) is broken into segments (word tokens or image patches) as a pre-processing step. These input segments are then passed through a series of layers that generate vector representations of the segments. The model has trainable parameters that determine how much attention is paid to parts of the input. Like many other generative-AI models, the transformer model is trained with an objective that rewards reproducing a target training example.

  42. Training Machine-learning models all contain parameters. For neural networks, these parameters are typically initialized to random numbers when the network is first created. During an algorithmic process called training, these parameters are repeatedly updated based on the training data within the training dataset that the model has seen. Each update is designed to increase the chance that when a model is provided some input, it outputs a value close to the target value we would like it to output. By presenting the model with all of the examples in a dataset and updating the parameters after each presentation, the model can become quite good at doing the task we want it to do.

A common algorithm for training neural network models is stochastic gradient
descent, or SGD. Training datasets are often too large to process all at once,
so SGD operates on small batches of dozens to hundreds of examples at a time.
Upon seeing a training example, the algorithm generates the model’s output
based on the current setting of the parameters and compares that output to the
desired output from the training data. In the case of a language model, we
might ask: did we correctly choose the next word? If the output did not match,
the algorithm works backwards through the model’s layers, modifying the
model’s parameters so that the correct output becomes more likely. This
process can be thought of as leaving “echoes” of the training examples encoded
in the parameters of the model.

  43. Vector Representation See embedding.

  44. Web Crawl A web crawl is a catalog of the web pages accessible on the Internet. It is created by a web crawler, an algorithm that systematically browses the Internet, trying to reach every single web page (or a specified subset). For example, Google Search functions using a web crawl of the Internet that can be efficiently queried and ranked. Web crawls are very expensive and compute-intensive to create, and so most companies keep their crawls private. However, there is one public web crawl, called Common Crawl. Most open-source (and many closed-source) language models are trained at least in part on data extracted from the Common Crawl.

  45. Weights See parameters.

###  A.2 Open versus Closed Software

In general, an informational resource — such as software or data — is open
when it is publicly available for free reuse by others and closed when it is
not. Openness has both practical and legal dimensions. The practical dimension
is that the information must actually be available to the public. For example,
software is open in this sense when its source code is available to the
public. The legal dimension is that the public must have the legal right to
reuse the information. This legal dimension is typically ensured with an
“open-source” or “public” license that provides any member of the public with
the right to use the information.

Open versus closed is not a binary distinction. For one thing, an
informational artifact could be practically open but legally closed. For
another, there are numerous different licenses, which provide users with
different rights. Instead, it is always important to break down the specific
ways in which information is open for reuse and the ways in which it is not.
The relevant forms of openness are different for different types of
information. In this section, we discuss some of the common variations on open
and closed datasets, models, and software.

  1. Closed Dataset Many models, including open models, have been trained on non-public (i.e., closed) datasets. Though a high-level description of the dataset may have been released and some portions of it may indeed be public (e.g. nearly all large language models are trained on Wikipedia), there is insufficient public information for the dataset to be fully reproduced. For example, there might be very little information available on the curation and pre-processing techniques applied, or constituent datasets might be described in general terms such as “books” or “social media conversations” without any detail about the source of these datasets. GPT-4 and PaLM are both examples of models trained on non-public datasets.

  2. Closed Model When a model is described as closed, it might mean one of three different things. First, a model might have been described in a technical report or paper, but there is no way for members of the public to access or use the model. This is the most closed a model can be. For example, DeepMind described the Chinchilla model in a blog post and paper, but the model was never made accessible to the public [49]. Second, a model’s checkpoint may not be publicly available, but the general public may be able to access the model in a limited way via an API or a web application (often for a fee and with the requirement they must sign a Terms of Service). For example, OpenAI’s GPT-3.5 and GPT-4 have followed this paradigm. In this case, it might be possible for users to reconstruct some of the model’s characteristics, but just as with closed-source software, they do not have access to the full details. Third, the model itself may have been publicly released for inspection, but without a license that allows others to make free use of it. Practically, the license restrictions may be unenforceable against individual users, but the lack of an open license effectively prevents others from building major products using the model.

  3. Closed Software Closed-source software is any software where the source code has not been made available to the public for inspection, modification, or enhancement. It is worth noting that closed software can contain open components. For example, an overall system might be semi-closed if it releases its model, but does not disclose its dataset. Many open-source licenses, which were developed before the advent of modern generative-AI systems, do not prevent open-source software from being combined with closed components in this way.

  4. Open Dataset Saying that a dataset is open or open-source can mean one of several things. At the most open end of the spectrum, it can mean that the dataset is broadly available to the public for download and that the code and experimental settings used to create it are entirely open-source. (This is the fullest expression of the idea that making a software artifact open requires providing access to the preferred form for studying and modifying it.) In some cases, a dataset is available for download but the code and exact experimental settings used to create it are not public. In both these situations, use of the dataset is normally governed by an open-source license.

For example, one popular set of benchmark datasets for large language models
is called SuperGLUE. The licenses for its constituent datasets include BSD
2-Clause, Creative Commons Share-Alike 3.0, and the MIT License. In more
restrictive cases, the dataset is public, but users must agree to contractual
Terms of Service to access it — and those terms impose restrictions on how the
dataset can be used. Finally, many datasets are public but cost money to
access. For example, the UPenn Linguistics Data Consortium has a catalog of
hundreds of high-quality datasets, but individuals need to be affiliated with
a member institution of the consortium to access them.

  5. Open Model The machine-learning community has described a model as open-source when a trained checkpoint has been released with a license allowing anyone to download and use it, and the software package needed to load the checkpoint and perform inference with it have also been open-sourced. A model can be open-sourced even in cases where details about how the model was developed have not been made public (sometimes, such models are referred to instead as semi-closed). For example, the model creators may not have open-sourced the software package for training the model — indeed, they may have not even publicly documented the training procedure in a technical report. Furthermore, a model being open-source does not necessarily mean the training data has been made public.

However, various pre-existing open communities (including the Open Source
Initiative, which maintains the canonical Open Source Definition) have
objected to usage by the machine-learning community, arguing that it does not
capture several of the most important qualities of openness as it has been
understood by the software community for over two decades. These qualities
include the freedom to inspect the software, the freedom to use the software
for any purpose, the ability to modify the software, and the freedom to
distribute modifications to others.

  6. Open Software Open-source software is software with source code that anyone can inspect, modify, and enhance, for any purpose. Typically, such software is licensed under a standardized open-source license, such as the MIT License or the Apache license. Machine-learning systems typically consist of several relatively independent pieces of software; there is the software that builds the training dataset, the software that trains the model, and the software that does inference with the model. Each of these can be independently open-sourced.

###  A.3 Legal Concepts in Intellectual Property and Software

  1. Claims Patent claims are extremely precise statements that define the scope of protection within the patent. Patent claims are carefully written to be broad enough to encompass potential variations of the invention and specific enough to distinguish the invention from prior art.

  2. Copyright Copyright grants exclusive rights to creators of original works. For a work to be copyrightable, it must meet certain criteria: (1) it must be original, and (2) it must possess a sufficient degree of creativity. Copyright does not protect facts or concepts, but expressions of those ideas fixed in a tangible medium (e.g., the idea for a movie, if not written down or recorded in some way, is typically not copyrightable; a screenplay is typically copyrightable). Copyright laws provide protections for various forms of creative expression, including, but not limited to, literary works, artistic works, musical composition, movies, and software [65].

See idea vs. expression.

  3. Copyright Infringement Copyright infringement occurs when someone uses, reproduces, distributes, performs, or displays copyrighted materials without permission from the copyright owner. This act breaches the exclusive rights held by the copyright holder.

  4. Damages In the context of IP, damages refers to financial compensation awarded to the owner of IP for harms and losses sustained as a result of IP infringement. When IP rights such as patents, copyright, or trademarks are violated, the owner of the IP may file a legal claim for damages. These can cover lost profits, reputational damage, or licensing fees.

  5. Fair Use Fair use is a legal concept that allows limited use of copyrighted materials without permission from the copyright owner [66]. Typically, fair use applies to contexts such as teaching, research, and news reporting, and fair use analyses consider the purpose of use, scope, and the amount of material used.

  6. The Field of Intellectual Property (IP) The field of Intellectual Property (IP) refers to a set of laws that grant exclusive rights for creative and inventive works. IP laws protect and promote ideas by providing incentives for innovation and protecting owners of inventions (e.g. written works, music, designs, among others). Intellectual property laws include copyright, patents, trademarks and trade dress, and trade secrets. Intellectual property law is often the first recourse for conflicts around emerging technologies where more specific legislation has not yet crystallized. Property law is well-developed, widely applicable, and carries significant penalties including fines and forced removal or destruction of work.

  7. Harm Many areas of law only regulate actions that cause some identifiable harm to specific victims. For example, people who have not suffered individual harms may not have “standing” to bring a lawsuit in federal court. For another, damage awards and other remedies may be limited to the harms suffered by the plaintiffs, rather than dealing more broadly with the consequences of the defendant’s conduct. It is important to note that what counts as a cognizable harm is a legal question, and does not always correspond to people’s intuitive senses of when someone has suffered a harm. Physical injury is the most obvious and widely accepted type of legal harm; other widely recognized forms of harm include damage to property, economic losses, loss of liberty, restrictions on speech, and some kinds of privacy violations. But other cases have held that fear of future injury is not a present harm. Thus, having one’s personal information included in a data breach may not be a harm by itself — but out-of-pocket costs and hassle to cancel credit cards are recognized harms.

  8. Idea vs. Expression This idea vs. expression dichotomy gets at the distinction between underlying concepts (or ideas) conveyed by a work, and the specific, tangible manner in which those are expressed. An idea refers to an abstract concept or notion behind a creative work, and ideas are not subject to copyright protection. However, expressions, as tangible manifestations, are. Tangible fixed expressions of ideas include words, music, code, or art. It is important to note that within copyright law, rights are granted to expression of ideas, not ideas themselves.

See copyright.

  9. License A license gives legal permission or authorization, granted by the rights holder to others. License agreements explicitly outline rights that are granted, as well as limitations, restrictions, and other provisions related to its scope, for example, duration. Licenses are common practice within the field of IP, and are commonly used in software, music, and film industries.

  10. Non-Expressive or Non-Consumptive Certain uses of copyrighted materials can be non-expressive or non-consumptive. In such cases, copyrighted material is used in a way that does not involve expressing or displaying original work to users. Some examples include text mining, building a search engine, or various forms of computational analyses.

  11. Patent A patent confers exclusive rights to inventors, granting them the authority to prevent others from making, using, or selling their inventions without permission. Patents create incentives for innovation by providing inventors with a time-based protection from the filing date. To obtain a patent, inventions must be new, inventive, and industrially applicable. Creators apply for patents; their applications must contain claims that describe what is novel in the work.

  12. Prior Art Prior art is evidence of existing knowledge or information that is publicly available before a certain date. Prior art is critical in adjudicating the novelty and nonobviousness of a new invention and may include other patents. Patent examiners search for prior art to determine the patentability of the claimed invention. Further, prior art informs the patent’s applicability and scope.

  13. Terms of Service Terms of service (ToS) refers to a contractual agreement between the IP owner and users of licenses that govern the use and access to the protected content. ToS outline rights, restrictions, and obligations involved. ToS may specify permitted uses, licensing terms, and how IP may be copied or distributed. ToS safeguard IP owners’ rights and ensure compliance with legal standards in the use of IP.

  14. Transformative Use Expression can build on prior expression. In some cases, a new piece of copyrightable material may borrow or re-purpose material from prior work. If this new material creates something inventive, new, and substantially different from the original work, then it can be considered transformative use of the original work, as opposed to infringing on the original copyright owner’s exclusive rights. The new material may also be copyright eligible. Parody is one common type of transformative use.

###  A.4 Privacy

  1. Anonymization Anonymization is the process of removing or modifying personal data in a way that it cannot be attributed to an identifiable individual.

  2. The California Consumer Privacy Act (CCPA) The CCPA is a California state law that provides consumers with the right to know what personal information businesses collect about them, the right to request their personal information be deleted, and the right to opt-out of sales of their personal information. The CCPA applies to all businesses that operate in California, as well as those outside of California that may transfer or process the personal information of California residents.

  3. Consent Consent is the voluntary and informed agreement given by an individual for the collection, use, or disclosure of their personal information. In the context of data, consent often requires clear and specific communication about the purpose and use of collected data.

  4. Differential Privacy Differential privacy (DP) is an approach for modifying algorithms to protect the membership of a given record in a dataset [111]. Informally, these guarantees are conferred by adding small amounts of noise to the individual data examples in the dataset. Let us say that there are two version of a dataset, $D$ and $D^{\prime}$, where the former contains an example $E$ and the latter does not. If we were to run differentially private algorithms to compute statistics on the datasets $D$ and $D^{\prime}$, we would not be able to tell by those statistics which dataset contains $E$ and which does not. As a result, we can no longer use the computed statistics to infer whether or not the original training data contained the example $E$.

Differential privacy is a theoretical framework that encounters some
challenges in practice. For example, the amount of noise one must add to data
may impact the accuracy of statistics computed, or, when used for generative-
AI models, may impact performance of the model. On the other hand, someone
using a differentally private approach needs to add enough noise to ensure
that the two datasets $D$ and $D^{\prime}$ cannot be differentiated through
computed statistics. Finally, differential privacy was originally created for
tabular data and encounters challenges adapting to the unstructured data
commonly used for generative-AI models. For more on the challenges of applying
differential privacy to large language models, please see Brown et al. [13].

  5. The General Data Protection Regulation (GDPR) GDPR is a comprehensive data protection law implemented by the European Union in 2018 [41]. The GDPR governs the collection, use, storage, and protection of personal data for EU residents. The law sets out specific rights for individuals regarding their personal data, such as the right to access, rectify, and delete their data, as well as the right to know how their data is being processed. Further, the GDPR imposes obligations on organizations such as businesses that handle personal data to ensure that proper data protection measures are in place and that consent is obtained for data processing. Non-compliance results in fines and penalties.

  6. Personally Identifiable Information (PII) Personally Identifiable Information (PII) refers to data that can be used to identify an individual. PII can include names, addresses, phone numbers, social security numbers, email addresses, financial information, and biometric data. PII is sensitive, and organizations that collect PII are required to implement appropriate measures, adhering to relevant data protection laws (such as the GDPR) to safeguard its confidentiality and integrity.

  7. Privacy Policy A privacy policy consists of documents that outline how organizations collect, use, store, and protect personal information. Privacy policies are meant to inform individuals about their rights and the organization’s data processing practices.

  8. Privacy Violation A privacy violation involves unauthorized or inappropriate intrusion into an individual’s personal information or activities. Privacy violations may occur in various forms from data breaches, surveillance, identity theft, or sharing personal or sensitive information without consent. These violations may lead to significant harm such as the loss of personal autonomy, reputational damage, or financial loss.

  9. The Right to be Forgotten Some countries’ legal systems recognize a right to be forgotten that grants individuals the ability to request the removal of their personal information from online platforms or search-engine results. The idea is that the legitimate public interest in knowing about other people’s past conduct can be outweighed when the information about it is out-of-date or misleading. The European Union’s GDPR includes a form of the right to be forgotten.

  10. Tort A tort is a civil wrongdoing that causes harm or injury to another person or their property. Tort law provides remedies and compensation to individuals who suffer harm as a result of someone else’s actions or negligence.

## B Metaphors

In this Appendix, we briefly discuss several metaphors for Generative AI that
came up in the GenLaw discussions. It is worth considering why these metaphors
are helpful and where they start to break down.

#### Models are trained.

Machine-learning practitioners will often say they train models. Training
brings to mind teaching a dog to perform tricks by enforcing good behavior
with treats. Each time the dog performs the desired behavior, they get a
treat. As the dog masters one skill it may move onto another. Model training
is similar in the sense that models are optimized to maximize some
reward.313131Maximizing a reward is exactly equivalent to minimizing a loss
(except for the extra minus sign), but due to historical reasons, machine-
learning practitioners use the latter phrasing more often. This reward is
computed based on how similar the model’s outputs are to desired outputs from
the model.

However, unlike training a dog, model training does not typically have a
curriculum;323232Curriculum learning is an entire field of research in machine
learning, but it is not currently standard to use a curriculum. there is no
progression of easier to harder skills to learn, and the formula for computing
the reward remains the same throughout model training.

#### Models learn like children do.

Learning is the active verb we use to describe what a model does as it is
being trained — a model is trained, and during this process it learns. Model
learning is the most common anthropomorphic metaphor applied to machine-
learning models. The use of the word learning by machine-learning
practitioners has naturally led to comparisons between how models learn and
how human children do. Both children and machine-learning models are “skilled
imitators,” acquiring knowledge of the world by learning to imitate provided
exemplars. However, human children and Generative AI obviously use very
different mechanisms to learn. Techniques that help generative-AI systems to
learn better, such as increasing model size, have no parallels in child
development; mechanisms children use to “extract novel and abstract structures
from the environment beyond statistical patterns” have no machine-learning
comparisons [114].

#### Generations are collages.

We quote directly from discussion in Lee et al. [62, p. 58], with added links
to our glossary.

> It also may seem intuitively attractive to consider generations to be
> analogous to collages. However, while this may seem like a useful metaphor,
> it can be misleading in several ways. For one, an artist may make a collage
> by taking several works and splicing them together to form another work. In
> this sense, a generation is not a collage: a generative-AI system does not
> take several works and splice them together. Instead, …generative-AI systems
> are built with models trained on many data examples. Moreover, those data
> examples are not explicitly referred back to during the generation process.
> Instead, the extent that a generation resembles specific data examples is
> dependent on the model encoding in its parameters what the specific data
> examples look like, and then effectively recreating them. Ultimately, it is
> nevertheless possible for a generation to look like a collage of several
> different data examples; however, it is debatable whether the the process
> that produced this appearance meets the definition for a collage. There is
> no author “select[ing], coordinat[ing], or arrang[ing]”333333§ 101
> (definition of “compilation”). training examples to produce the resulting
> generation.

#### Large language models are stochastic parrots.

Bender et al. [7] describe a large language model as a stochastic parrot, a
“system for haphazardly stitching together sequences of linguistic forms it
has observed in its vast training data, according to probabilistic information
about how they combine, but without any reference to meaning.” Like parrots
mimicking the sounds that they hear around them, LLMs repeat the phrases they
are exposed to, but have no conception of the human meaning behind these
phrases.

This analogy is useful because it references the very real problem of machine-
learning models simply outputting their most frequent training data. Critics
of the stochastic-parrot analogy say that it undervalues the competencies that
state-of-the-art language models have. Some critics take this further and say
that these competencies imply models understand meaning in a human-like way
[81].343434Whether models are human-like, or the outputs are simply “really
good” is less pertinent for how generations and inputs should be regulated.
For example, proponents of this analogy might argue that Generative AI passing
a difficult standardized exam (such as the Bar Exam [56] or the GRE [77]) is
more about parroting training data than human-like skill.

#### Large language models are noisy search engines.

A search engine allows users to search for information within a large database
using natural language queries. Like a search engine, large language models
also return information in response to a natural language query. However,
while a search engine queries the entries in its database and returns the most
appropriate ones, a language model does not have direct access to its training
data and can only make predictions based on the information stored in the
model weights.353535The training data is seen during training, but models are
used separately from the training data. Most often the output will be a
mixture of information contained in many database entries. Some model outputs
may quote directly from relevant entries in the database (in the case of
memorization), but this is not reflective of the most typical outputs.

Sometimes generations from an LLM will convey similar information that one
might learn from running a search; however, sometimes it will not because the
underlying algorithm is different. Thus, while some generations answer the
prompt in a similar way to a search, we can more generally think of
generative-model outputs as a noisy version of what is actually in the
database. Currently, such outputs also tend to lack attribution to the
original data entries, and sometimes are incorrect.


# Large-scale expansion of OB stars in Cygnus

Alexis L. Quintana1 and Nicholas J. Wright1
1Astrophysics Group, Keele University, Keele ST5 5BG, UK
E-mail<EMAIL_ADDRESS>
(Accepted 2022 May 30. Received 2022 May 24; in original form 2022 March 23)

###### Abstract

The proper motions (PMs) of OB stars in Cygnus have recently been found to
exhibit two large-scale kinematic patterns suggestive of expansion. We perform
a 3D traceback on these OB stars, the newly-identified OB associations and
related open clusters in the region. We find that there are two groups of
stars, associations and clusters and that they were each more compact in the
past, reaching their closest approach $7.9^{+3.0}_{-1.8}$ and
$8.5^{+0.8}_{-2.8}$ Myr ago. We consider two main scenarios for the driver of
these large-scale expansion patterns: feedback-driven expansion from a
previous generation of massive stars, and expansion as a result of the
turbulent velocity field in the primordial molecular cloud. While it is
tempting to attribute such large-scale expansion patterns to feedback
processes, we find that the observed kinematics are fully consistent with the
turbulent origin, and therefore that the injection of further energy or
momentum from feedback is not required. Similar conclusions may be drawn for
other star forming regions with large-scale expansion patterns.

###### keywords:

stars: kinematics and dynamics - stars: early-type - stars: massive - stars:
distances - open clusters and associations: individual: Biurakan 2, Dolidze 3,
FSR 0198, NGC 6871, NGC 6910, NGC 6913.

††pubyear: 2022††pagerange: Large-scale expansion of OB stars in Cygnus–Large-
scale expansion of OB stars in Cygnus

##  1 Introduction

Many OB stars are found in groups known as OB associations (McKee & Williams,
1997), which are characterized by their unbound nature and their low-density
(< 0.1 $M_{\odot}$ pc-3, Ambartsumian, 1947; Wright, 2020). They are thought
to constitute an intermediate step between star-forming regions, many of which
are observed to be expanding (Wright et al., 2019), and the field population
of stars. They are therefore useful to understand the star formation process
and the build-up of the Galactic field (e.g., Armstrong et al., 2020).

Following star formation, stars, star clusters and OB associations disperse
from their birth place due to various processes. This can include the
intrinsic dispersion of velocities that the stars are born with, two- or
three-body interactions between stars in clusters, and changes in the local
gravitational potential (e.g., due to residual gas expulsion, Lada & Lada
2003).

The intrinsic velocity dispersion within molecular clouds sets the initial
kinematics of stars and is likely to dominate their kinematics on large
(10–100 pc) scales. This is commonly observed in the form of a power-law
relationship between the linewidth (1D velocity dispersion) and the size of
the molecular cloud. This was first observed by Larson (1981) and since
observed and refined by many studies (e.g., Solomon et al. 1987; Bolatto et
al. 2008; Miville-Deschênes et al. 2017). This relationship is attributed to
turbulence, which itself is driven by gravitational instabilities in the disk
of the galaxy, magnetorotational instabilities and stellar feedback (Miville-
Deschênes et al., 2017).

Feedback may also drive large-scale expansion patterns as energy and momentum
is injected into the molecular cloud from a previous generation of massive
stars. This feedback may be a combination of photoionization, radiation
pressure, stellar winds, outflows and supernova explosions (Dale, 2015).
Feedback is thought to be the process responsible for disrupting star
formation and dispersing giant molecular clouds (Dobbs & Pringle, 2013). It
also injects large amounts of kinetic energy and momentum into the ISM (Geen
et al., 2015; Kim & Ostriker, 2015; Walch & Naab, 2015) which may introduce
large-scale motions that are imprinted in the kinematics of future generations
of stars. Astrometry from Gaia, especially its most recent data release (Gaia
Collaboration et al., 2021), can be very powerful to identify such kinematic
patterns, as recent studies highlight (Kounkel, 2020; Drew et al., 2021;
Großschedl et al., 2021).

Figure 1: New OB associations in Cygnus identified in Quintana & Wright (2021)
and the six selected open clusters in the region, with a background map
showing the integrated extinction up to 2 kpc from Green et al. (2019). The
vectors indicate the PM of each star and open cluster subtracted by the median
PMs of all the stars. A representative 1 mas yr-1 proper motion vector is
shown at the top, equivalent a velocity of $\sim$8.5 km $s^{-1}$ at a distance
of 1.8 kpc.

The Cygnus region is a well-known region of recent massive star formation
(e.g., Reipurth & Schneider, 2008), with multiple star forming regions
(Schneider et al., 2006; Wright et al., 2012), OB associations (Humphreys,
1978) and star clusters (Cantat-Gaudin & Anders, 2020), the most prominent of
all of which is Cygnus OB2 (Wright et al., 2014; Wright et al., 2015; Wright
et al., 2016; Berlanas et al., 2019; Orellana et al., 2021). In our recent
paper, Quintana & Wright (2021), we studied the known OB associations in
Cygnus and found that the majority did not show the kinematic coherence
expected for OB associations (Cyg OB2 being the notable exception). We used
available photometry and astrometry to identify OB stars across the Cygnus
region and identified six new OB associations at distances of 1.5 - 2 kpc,
labelled A to F, which we argued should replace many of the existing OB
associations in the area. All of these new OB associations are kinematically
coherent and each is expanding in at least one dimension. We also discovered a
strong correlation between $\mu_{l}$ and $l$ for the stars in two groups of
three associations (ADF and BCE). It was hypothesised that this correlation,
indicative of a large-scale expansion pattern, could be caused by feedback
from a previous generation of stars. A similar kinematic pattern was
previously observed by Drew et al. (2021) in Carina, who concluded that it
could be due to feedback, noting that the scale of the pattern was similar to
that observed by Chevance et al. (2020) in their study of extra-galactic
molecular clouds. In this paper we follow up the work of Quintana & Wright
(2021) by performing a 3D traceback on the six new associations in Cygnus and
to study their past dynamics.

##  2 Data

This section summarises the properties of the OB associations and open
clusters in Cygnus and the data used to study them.

###  2.1 The new OB associations in Cygnus and recent refinements

Quintana & Wright (2021) identified six new kinematically-coherent OB
associations in Cygnus, replacing some of the previously identified OB
associations that were found to be kinematically incoherent. Upon further
investigation of association B we noticed a bimodal distribution to its
kinematics, and divided it into two associations, B1 (at lower longitudes and
latitudes), containing 79 of the 100 original stars, and B2 (at higher
longitudes and latitudes), with 21 stars. Furthermore, refinements to our SED
fitting tool found that $\sim$10% of the OB members of these associations are
cooler, A-type stars, but we have retained these stars because they remain
kinematic members of the associations.

###  2.2 Open clusters

Cantat-Gaudin & Anders (2020) list 31 open clusters in the Cygnus region
studied, including 17 with $d=1-2.5$ kpc. Six of these have PMs and radial
velocities (RVs) similar to our associations and therefore are likely to be
related. Table 1 lists the properties of these OCs and they are shown in
Figure 1 alongside our 7 new OB associations. Cluster mass estimates for four
of the cluster are taken from Piskunov et al. (2008) but are considered to be
conservative as higher estimates exist for NGC 6910 and NGC 6913 (Le Duigou &
Knödlseder, 2002). Dolidze 3 and FSR 0198 lack total mass estimates in the
literature and therefore we estimate masses ourselves by fitting the mass
function of SED-fitted members from Cantat-Gaudin & Anders (2020) to modelled
mass functions from Maschberger (2013).

Table 1: Properties of the six selected open clusters in Cygnus, with positions, PMs and distances from Cantat-Gaudin & Anders (2020). The labels for the references for ages, RVs and masses are: K05 = Kharchenko et al. (2005), P08 = Piskunov et al. (2008), C09 = Camargo et al. (2009), D14 = Dias et al. (2014), C17 = Conrad et al. (2017), C19 = Carrera et al. (2019), L19 = Liu & Pang (2019) and K20 = Kaur et al. (2020).  Name | $l(\circ)$ | $b(\circ)$ |  $\mu_{\alpha}$ (mas yr-1) |  $\mu_{\delta}$ (mas yr-1) |  $d$ (pc) | Age (Myr) | RV (km s-1) | Mass ($M_{\odot}$)
---|---|---|---|---|---|---|---|---
NGC 6871 | 72.66 | 2.01 | $-3.13\pm 0.01$ | $-6.44\pm 0.01$ | $1841^{+4}_{-3}$ |  $7.0\pm 0.4$ (L19) |  $-10.5\pm 2.2$ (C17) |  $1148^{+801}_{-472}$ (P08)
NGC 6910 | 78.68 | 2.01 | $-3.41\pm 0.01$ | $-5.36\pm 0.01$ | $1741^{+6}_{-7}$ |  $4.25\pm 1.5$ (L19, K20) |  $-32.7\pm 2.1$ (C17) |  $209^{+208}_{-104}$ (P08)
NGC 6913 | 76.87 | 0.61 | $-3.41\pm 0.01$ | $-5.77\pm 0.01$ | $1719\pm 7$ |  $5.0\pm 0.3$ (L19) |  $-16.9\pm 0.6$ (C17) |  $27^{+29}_{-14}$ (P08)
Biurakan 2 | 72.7 | 1.39 | $-3.17\pm 0.02$ | $-6.84\pm 0.02$ | $1751\pm 10$ | 13.8 (K05) |  $-22.0\pm 9.5$ (C17) |  $135^{+116}_{-63}$ (P08)
Dolidze 3 | 74.54 | 1.07 | $-2.87\pm 0.02$ | $-5.61\pm 0.01$ | $1907\pm 14$ |  $4.0\pm 0.2$ (L19) |  $-7.7\pm 1.9$ (C19) | $200\pm 50$
FSR 0198 | 72.18 | 2.61 | $-3.56\pm 0.03$ | $-6.61\pm 0.03$ | $1944^{+12}_{-11}$ |  $10.0\pm 5.0$ (C09) |  $-13.0\pm 3.7$ (D14) | $350\pm 100$

###  2.3 Radial velocities

To obtain 3D kinematics for our associations and open clusters we need RVs to
complement Gaia PMs. We gathered RVs from the literature, rejecting those
considered unreliable or without measured uncertainties, compiling RVs for 93
stars across our 7 new associations. Since the effects of unresolved close
binaries can cause individual measured RVs to vary significantly from the
binary system velocity, we calculated the median RV for each association and
assigned this to all stars in the association. Unfortunately none of the stars
in association B1 have measured RVs, so we took its RV to be the same as that
of association B2.

To estimate the uncertainty on the median velocity of each association we
perform a Monte Carlo simulation of an association’s velocity dispersion to
calculate the difference between a system’s central velocity and a median
derived from N velocities for stars in that association. We assume that each
group has a 1D velocity dispersion of 2 $kms^{-1}$ and sample from this
distribution. To these velocities we add randomly sampled instantaneous binary
offset velocities, assuming a 100% binary fraction (as observed in Cyg OB2,
Kiminki & Kobulnicky 2012), mass ratios from 0.005 to 1.00 with a power-law
distribution and an index of 0.1, periods from 1 to 1000 days with a power-law
distribution and an index of 0.2, and ellipticities from 0.0001 to 0.9 with a
power-law distribution and an index of -0.6 (Kiminki & Kobulnicky, 2012).
These velocity offsets are added to the calculated velocities alongside
uncertainties sampled from the observed values. We repeat this process 100,000
times and calculate uncertainties from the 16th and 84th percentile values.
The results are listed in Table 2 and show that associations with sparsely-
sampled RVs have a larger uncertainty on the median RV.

Table 2: RVs calculated for the new OB associations. $N_{stars}$ is the number of stars in the association whilst $N_{RV}$ is the number of stars with a reliable measured RV. The fourth column lists the median RV of the association, and an uncertainty calculated as described in Section 2.3. References are: (1): Hayford (1932), (2): Abt (1973), (3): Huang & Gies (2006), (4): Gontcharov (2006), , (5): Kiminki et al. (2007), (6): Huang et al. (2010), (7): Chojnowski et al. (2017), (8): Gaia Collaboration et al. (2018), (9): Holgado et al. (2018), (10): Carrera et al. (2019) Assoc. | $N_{stars}$ | $N_{RV}$ | RV (km s-1) | References
---|---|---|---|---
A | 109 | 20 | $-12.50\pm 2.77$ | (1), (2), (3), (6)
B1 | 79 | 0 |  |
B2 | 21 | 1 | $-21.00\pm 10.80$ | (4)
C | 75 | 10 | $-19.20\pm 2.98$ | (1), (3), (6), (7), (10)
D | 65 | 10 | $-7.00\pm 3.88$ | (1), (6), (10)
E | 168 | 48 | $-12.35\pm 2.06$ | (5), (11)
F | 147 | 4 | $-13.48\pm 5.06$ | (3), (8), (10)

##  3 Kinematic traceback

In this section we outline the traceback method used to study the past motion
of these associations.

Galactic space velocities $UVW$ were calculated for all stars in our 7 new OB
associations and the 6 open clusters themselves (we consider the 6 open
clusters as individual objects as they are gravitationally bound, but consider
the individual stars in our 7 new OB associations separately since the
associations are unbound). These velocities are then corrected for the motion
of the Sun $(U_{\odot},V_{\odot},W_{\odot})=(11.10,12.24,7.25)$ km s-1 from
Schönrich et al. 2010. to obtain quantities relative to the local standard of
rest.

We trace back the motions of the stars and open clusters using the epicycle
approximation from Fuchs et al. (2006), the Oort constants from Feast &
Whitelock (1997), and the local density from Holmberg & Flynn (2004). We
calculate the $XYZ$ coordinates at times, $t$, up to 20 Myr in the past, at
step times of 0.1 Myr. The projected positions of all stars and open clusters
are shown as a function of time in Figure 2, while the line of sight distances
are shown in Figure 3 (we show the median distance to each association, rather
than for individual stars, due to the large uncertainty on individual
distances).

As expected from the kinematic signature of expansion identified by Quintana &
Wright (2021) the stars in both group ADF and B1CE are closer together on the
plane of the sky in the recent past than they are at the current time. This is
the case both in the $l$ direction (where the kinematic signature of expansion
was identified), but also in the $b$ direction. Associations ADF are also
closer together along the line of sight in the recent past, however
associations B1CE move slightly further apart in the recent past (though the
uncertainties on distance and RV are so large that this is not significant).

We then calculate the distance, $d$, from each star to the central (median)
position of each group (either group ADF or group B1CE). Due to the
imprecision of the line of sight distances and RVs relative to the plane of
the sky positions and velocities, we perform this calculation only in the
plane of the sky. For each group of three associations we sum the distances at
each time step and determine the time of the most compact configuration as the
time this sum is minimised. Uncertainties were estimated using a Monte Carlo
process with 1000 iterations, randomly dispersing all measured quantities in
each iteration (including all constants used in the epicycle calculations) and
using the 16th and 84th percentile values of the resulting time distribution
as the upper and lower 1$\sigma$ uncertainties.

Figure 2: Galactic coordinates of all stars and open clusters at various times
in the past derived from traceback calculations in their reference frame,
where $l_{0}$ and $b_{0}$ stand for the median galactic coordinate of each
group.

Figure 3: Distance as a function of look-back time for the associations and
open clusters studied. Filled areas delimit the 16th and 84th percentiles of
distance at each time step. Top panel: associations A, D and F with their
related open clusters. Bottom panel: associations B1, C and E with their
related open cluster. The dashed blue line shows the time of closest approach
on the sky for each group.

The resulting times of most compact configuration are $7.9^{+3.0}_{-1.8}$ Myr
for group ADF and $8.5^{+0.8}_{-2.8}$ Myr for group B1CE and the distribution
of stars at these times are shown in Fig. 2.

##  4 Discussion

We have shown that there are two groups of three OB associations in Cygnus (as
well as multiple open clusters) whose kinematics show that they are moving
away from each other and that they can be traced back into a more compact
configuration in the past. These two groups are at their most compact 7.9 and
8.5 Myr ago, for the associations ADF and B1CE, respectively. Our calculated
traceback ages are generally larger than the evolutionary ages estimated for
these associations. Quintana & Wright (2021) estimated that associations B, C
and E are 3-5 Myr old while associations A, D and F are older, with stars aged
up to $\sim$10 Myr in them, while the open clusters that are part of these
expansion patterns have ages of 5-10 Myr (the exception to this, Biurakan 2,
has an age without an uncertainty and therefore its accuracy is unknown).
Therefore it would appear that the large-scale expansion we have identified
began before these stars and clusters formed and thus the driving force of the
expansion would have acted on the primordial molecular clouds and not the
stars we observe today. The traceback ages are also consistent with the
expansion ages for the individual OB associations estimated by Quintana &
Wright (2021, 2022), which are themselves larger than the evolutionary ages
for the associations. This suggests that the expansion of the individual OB
associations was not driven by their own (stellar) dynamics or processes such
as residual gas expulsion, but was seeded prior to their formation,
potentially by the same process responsible for the large-scale expansion
patterns studied here. A similar chronological pattern is seen in $\lambda$
Ori (Kounkel et al., 2018).

Quintana & Wright (2021) suggested that the expansion observed could be due to
feedback from a previous generation of stars, and the large-scale coherent
motions and traceback to a more compact configuration could support this.
However, the observed expansion could alternatively be the result of the
initial turbulent motion in the primordial molecular cloud (Larson, 1981). We
explore both scenarios below.

###  4.1 Feedback

One explanation is that the expansion observed could be due to two major
feedback events that occurred $\sim$8 Myr ago and drove the two primordial
molecular cloud complexes apart. It is more likely to have been two separate
feedback events, rather than a single one, as the two kinematic trends
indicative of expansion are distinct (see Figure 11 of Quintana & Wright
2021). These feedback events would have swept up the molecular gas in these
regions, possibly triggering star formation within them. As noted by
Großschedl et al. (2021), such a picture is similar to the classical feedback-
driven scenario proposed by Elmegreen & Lada (1977), albeit with an emphasis
more on ’compress and collapse’ rather than ’collect and collapse’ as the
mechanism for triggering.

To investigate this scenario we estimate how much kinetic energy and momentum
is present in the expanding motion of these stars. Since we are only able to
observe the stars and yet the energy would have been injected into the
primordial molecular clouds, we estimate the mass of these clouds by assuming
that they formed stars with a star formation efficiency (SFE) of 5% and use
the association masses estimated by Quintana & Wright (2021) and the open
cluster masses from Table 1. We calculate the velocity of each OB association
and OC relative to the mass-weighted mean velocity of each group of
associations and clusters and use these to calculate the kinetic energies and
momenta injected into each system, assuming they were previously at rest (a
highly simplistic assumption). The total kinetic energy injected is
$0.54\times 10^{50}$ erg for group ADF and $1.21\times 10^{50}$ erg for group
B1CE, while the total momentum is $0.66\times 10^{6}$ $M_{\odot}$ km s-1 for
group ADF and $1.26\times 10^{6}$ $M_{\odot}$ km s-1 for group B1CE.

The total energy output from a supernova explosion is approximately $10^{51}$
erg (see e.g. Janka 2012), a similar level to that calculated for the groups
in Cygnus. Predictions from simulations suggest that the total momentum
injected into a surrounding molecular cloud by a supernova is between 2 and
$4\times 10^{5}$ $M_{\odot}$ km s-1 (Geen et al., 2015; Kim & Ostriker, 2015;
Walch & Naab, 2015), which is between a factor 1.5 and 6 times lower than we
have calculated for the Cygnus feedback events. Kim & Ostriker (2015)
simulated the feedback generated from ten supernovae and estimated that the
final momentum would be in the range of 14 to $22\times 10^{5}M_{\odot}$ km
s-1, closer to our estimates. This all implies that either several supernovae
would have to have contributed to the potential feedback events observed or
that the motions observed are due to a combination of feedback types, such as
photo-ionization, radiation pressure, stellar winds and supernovae.

Similar kinematic patterns showing the expansion of large complexes of stars
have been observed by Kounkel (2020) and Großschedl et al. (2021) in Orion
(through respectively the 3D dynamics of stellar groups and the motion of
star-forming clouds) and Drew et al. (2021) in Carina (through the motion of
OB stars). The large-scale expansion pattern in Orion identified by Kounkel
(2020) was attributed to a supernova explosion that occurred approximately 6
Myr ago. Großschedl et al. (2021) observed the same expansion pattern in
Orion, considered various sources of feedback and concluded that a combination
of feedback sources was likely to be responsible. Großschedl et al. (2021)
estimated the total kinetic energy in the expanding structures in Orion to be
(3.5-9.6) $\times 10^{48}$ erg and the total momentum to be (0.7-1.3) $\times
10^{5}$ $M_{\odot}$ km s-1. These estimates are significantly lower than our
estimated kinetic energy and momentum, implying that both hypothetical
feedback events in Cygnus would have to be considerably more energetic than
the Orion event. This is not surprising given that the Cygnus star forming
complex is both considerably larger and more massive than the Orion region.

###  4.2 Intrinsic turbulent motions

Multiple studies have observed a power-law relationship between the physical
size of molecular clouds and the 1D velocity dispersion within them, commonly
known as Larson’s law, which has been attributed to turbulence (Larson, 1981;
Solomon et al., 1987; Bolatto et al., 2008; Heyer & Dame, 2015; Miville-
Deschênes et al., 2017). An intrinsic distribution of velocities present in
the primordial molecular cloud would presumably be passed onto the stars that
form from that cloud. If that velocity dispersion were high and there was not
a sufficiently large restoring force, this would be evident as an expansion
pattern in the stars that had formed.

To test whether this scenario could explain the observed motions, we can
compare the velocity dispersion that Larson’s law predicts for an
appropriately sized molecular cloud and the velocity dispersion of the
expanding stars in Cygnus. Fig. 2 suggests a size of $\sim$75 pc at the most
compact time for both Cygnus groups. Applying the scaling relations in these
papers we find that a molecular cloud with a size of 75 pc would be expected
to have a 1D velocity dispersion of 5.7 - 8.7 km/s, depending on the exact
relationship used (Larson, 1981; Solomon et al., 1987; Miville-Deschênes et
al., 2017). We calculate the actual 3D velocity dispersions using the UVW
velocities at the most compact time for both group ADF and B1CE and we
respectively find 7.1 and 11.3 km $s^{-1}$, equivalent to 1D velocity
dispersions of 4.1 and 6.5 km $s^{-1}$.

From these results, the velocity dispersions of both groups are perfectly
consistent with Larson’s law. This suggests that the observed expansion of
both groups of stars, associations and clusters can be explained as being due
to the intrinsic velocity dispersion in the primordial molecular cloud arising
from turbulence. Of course, stellar feedback is thought to be one of the
drivers of turbulence (Miville-Deschênes et al., 2017), and while turbulence
may have contributed to the velocity field in the primordial molecular cloud,
it appears that feedback is not required to introduce additional momentum to
generate the observed expansion pattern.

Repeating this calculation for Orion, Fig. 7 from Großschedl et al. (2021)
suggests a lower limit of $\sim$40 pc at the most compact time for the cloud
size, which implies a 1D velocity dispersion of 4.5-6.3 km $s^{-1}$. We also
perform a similar calculation for the Orion subregions in Großschedl et al.
(2021) (using their UVW velocities in the LSR from their Table 4) and found a
3D velocity dispersion of 4.8 km $s^{-1}$, equivalent to a 1D velocity
dispersion of 2.8 km $s^{-1}$. It appears that the observed motions in Orion
are also consistent with Larson’s law.

##  5 Summary

We have presented the discovery of two distinct expansion patterns in the
large-scale distribution of OB stars, associations and open clusters in
Cygnus. We have traced back the motion of OB associations and open clusters
and shown that they were more compact $\sim$8 Myr in the past as part of two
large groups. While it is tempting to attribute this expansion to a specific
driving force such as feedback from massive stars or supernovae, we find that
the observed kinematics of the expanding systems can be explained as a product
of the turbulent velocity field in the primordial molecular cloud. This is not
to say that feedback has not had some effect on the dynamics of these stars,
but that it is not necessary to search for an additional driving force of the
observed motions when they can be fully explained as a result of turbulence.
We suggest that a similar conclusion can also be drawn for other recently-
observed expansion patterns amongst young stars.

## Acknowledgements

We thank the anonymous referee for their careful reading of this manuscript
and their useful suggestions. ALQ acknowledges receipt of an STFC postgraduate
studentship. This study uses data processed by the Gaia Data Processing and
Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium) and obtained by the Gaia
mission from the European Space Agency (ESA)
(https://www.cosmos.esa.int/gaia), along with TOPCAT (Taylor, 2005), Astropy
(Astropy Collaboration et al., 2013) and the Vizier and SIMBAD database, both
operated at CDS, Strasbourg, France.

## Data Availability

The data underlying this article will be uploaded to Vizier.

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