# Collaborative Storytelling with Large-scale Neural
Language Models

Eric Nichols  Honda Research Institute Japan<EMAIL_ADDRESS>,  Leo
Gao  OrientExpress Technologies Inc<EMAIL_ADDRESS>and  Randy Gomez
Honda Research Institute Japan<EMAIL_ADDRESS>
###### Abstract.

Storytelling plays a central role in human socializing and entertainment.
However, much of the research on automatic storytelling generation assumes
that stories will be generated by an agent without any human interaction. In
this paper, we introduce the task of collaborative storytelling, where an
artificial intelligence agent and a person collaborate to create a unique
story by taking turns adding to it. We present a collaborative storytelling
system which works with a human storyteller to create a story by generating
new utterances based on the story so far. We constructed the storytelling
system by tuning a publicly-available large scale language model on a dataset
of writing prompts and their accompanying fictional works. We identify
generating sufficiently human-like utterances to be an important technical
issue and propose a sample-and-rank approach to improve utterance quality.
Quantitative evaluation shows that our approach outperforms a baseline, and we
present qualitative evaluation of our system’s capabilities.

storytelling, interactivity, language models, AI agents

††copyright: none††ccs: Human-centered computing Collaborative
interaction††ccs: Human-centered computing Natural language interfaces††ccs:
Human-centered computing Collaborative and social computing devices††ccs:
Computer systems organization Neural networks

##  1\. Introduction

Storytelling is a central part of human socialization and entertainment. Many
of the popular forms of storytelling throughout history –such as novels,
plays, television, and movies– have passive audience experiences. However,
gaming is an interesting medium because interactivity is a large part of the
entertainment experience, and interactivity and storytelling can often be in
conflict: too much player freedom means a storyline may never be explored,
while on the other hand, too many restrictions on player freedom risks
reducing gaming to a passive medium. Thus, interactivity in storytelling has
been an important challenge for gaming, with much design effort put into
striking a balance between entertaining gameplay and compelling storytelling.

As gaming technology advances, new opportunities for interactive storytelling
present themselves. Better storage technology made telling longer, more
intricate stories possible, and better graphical capabilities helped foster
more immersive gaming experiences. Advances in artificial intelligence have
lead to more challenging opponents, more realistic NPC behavior, and other
benefits. Better procedural content generation algorithms help ensure unique
gameplay experiences that stay fresh for longer. Finally, recent breakthroughs
in language modeling present a new opportunity: language, and thus stories,
can potentially be generated on demand.

In this paper, we introduce a novel game of collaborative storytelling, where
a human player and an artificial intelligence agent construct a story
together. The game starts with the AI agent reciting one of a curated set of
story starters –opening sentences meant to kick-start participants’
storytelling creativity– and the human player responds by adding a line, which
we refer to from here on out as a story continuation, to the story. The AI
agent and human player then take turns adding continuations to the story until
the human player concludes the story. The game is designed to have a few
restrictions as possible and contrasts with traditional storytelling settings
where the narrative is fixed in advance.

Figure 1. Collaborative storytelling with an AI agent.

Collaborative storytelling builds on a rich tradition of collaboration in
storytelling that includes Dungeons and Dragons, improvisational comedy, and
theater. It could be a useful tool for encouraging creativity and overcoming
writer’s block, as well as being an entertaining game in its own right.

Our end goal is to make it possible for intelligent agents, such as robot
companions and avatars (Park et al., 2019; Gomez et al., 2020), to play the
collaborative storytelling game, as shown in Figure 1.

Our primary contributions are as follows:

  * •

We introduce a novel task of collaborative storytelling, where humans and AI
agents work together to create a story.

  * •

We present a collaborative storytelling system that is constructed by tuning a
large-scale neural language model on a writing prompts story dataset.

  * •

We develop a method for ranking language model output to obtain more human-
like story continuations.

  * •

We conduct quantitative and qualitative analysis of the storytelling
capabilities of our system through collaborative storytelling with human
participants.

##  2\. Related Research

In this section, we summarize relevant research in story generation,
interactive language generation, and language modeling.

###  2.1. Story Generation

In recent years, the task of automatic story generation has gained a lot of
attention. (Fan et al., 2018) construct a corpus of stories and propose a
hierarchical story generation model. (Yao et al., 2019) approach the task by
first generating a plot outline and then filling in the language. (Gupta et
al., 2019) generate story endings by incorporating keywords and context into a
sequence-to-sequence model. (Luo et al., 2019) incorporate sentiment analysis
into story ending generation. (See et al., 2019) conduct an in-depth analysis
of the storytelling capabilities of large-scale neural language models.
However, the primary assumption of these works is that story generation is
conducted without any interaction from humans.

###  2.2. Interactive Language Generation

While research dedicated to interactive language generation games is still
sparse, there are a few notable recent developments.

AI Dungeon111https://play.aidungeon.io is a text adventure game that is
generated by a GPT-2 language model (Radford et al., 2019) tuned on a
collection of text adventure play-throughs. In the game, players assume the
first person and interact with the world by inputting commands or actions. The
language model is used to generate the world’s reaction to the player’s
actions. Our collaborative storytelling task and approach are similar to AI
Dungeon, but our task is not constrained to the genre of first-person
adventures, and we rank model output.

(Cho and May, 2020) build an improvisational theater chatbot by identifying
and collecting instances of improvisational dialogue on the Web and using it
to tune and evaluate public domain dialogue systems. Our collaborative
storytelling task is similar to improv, but stories are linguistically
different enough from improv that it would be impractical to apply their
dataset to our task. In addition, our approach employs sampling and ranking to
improve the likelihood that language model utterances are in the desired
storytelling domain, while (Cho and May, 2020) use the model’s output as-is.

Figure 2. The ranking system architecture. Collaborative Storytelling Story 1
---
Prompt: |  A man sits alone at a table, listening to the low and pleasant hum of a bassist pluck something smooth and jazzy nearby.
Human: |  He lets out a big sigh and dreamily looks at the bassist, sipping on his whisky.
System: |  The music is not too loud, just enough to drown out his worries, but still enough to cause him to feel like he has heard it before.
Human: |  The man tries his best to just immerse himself into the music until it ended.
System: |  But then the phone rang, making the man jump out of his chair.
Human: |  ”Darn it”, says the man as he frantically searches his pockets for the phone.
System: |  As the man was getting ready to answer, a beautiful lady, with long flowing blonde hair, greeted him.
Human: |  The man drowned out the constant ringing on the phone and silenced it, saying hello back to the lady.
System: |  She turns to the guy and smiles while staring him straight in the eyes.
Human: |  The man replied ”My name is Jacob… how about you”?
System: |  After a few moments of silence, she smiled and explained that the man had already lived with her for years.
Human: |  ”Huh… what do you mean I already live with you?” Jacob said in utter confusion.
System: |  She explained that she was the same age as he, and is the love of his life.
Human: |  ”No, you got to be kidding me I’m single and I come to this bar every day”, Jacob said with a quiver in his voice.
System: |  ”You know what’s funny?”
Human: |  ”Please explain, and are you just a stranger playing a joke on me?”
System: |  She handed him a picture of her and a girl.
Human: |  Her thumb was covering another person, and she slowly uncovered it as Jacob looked at the picture.
System: |  ”Look at me, ” said the girl.
Human: |  ”This… picture shows me, you, and a child… but why?” Jacob started to tear up.
System: |  ”Just a moment, it will all make sense soon enough.”
Collaborative Storytelling Story 2
Prompt: |  The garage door lurched open and my face turned from joy to agonizing surprise.
Human: |  A small squirrel leaped from behind my car, likely as shocked to see me as I was him.
System: |  ”I’m so sorry, I didn’t mean to scare you.”
Human: |  He tilted his head to the side, almost indicating he understood my words.
System: |  ”You don’t scare me.”
Human: |  Completely floored that this squirrel can speak English, I fumbled myself into asking ”Are you real? This can’t be real!”
System: |  ”Yes, this is real, and I have been waiting for you for quite some time.”
Human: |  I asked him ”What have you been waiting for? Some peanuts from the kitchen?!”
System: |  ”No, I can answer all your questions with just one sentence!”
Human: |  He leaned against the tire of my car with a sly look on his face, ”I’m madly in love with Penny, your cat, and I’d like to take her to dinner tonight!”
System: |  I sat there confused for a good thirty seconds before I snapped out of it.
Human: |  ”Have you been spying on my house cat!?”
System: |  The squirrel cocked his head to the side and shrugged, as if he had no response to what I had just said.
Human: |  ”Well I’ll have you know that I am not okay with you romantically pursuing my poor Penny!”
System: |  This time, the squirrel cracked his knuckles and the look in his eyes made me question everything I was hearing.
Human: |  ”Look Mr, all I want to do here is show her a good time and maybe be a part of the family!”
System: |  I was dumbfounded.
Human: |  I felt a slight lump in my throat realizing that maybe this squirrel was lonely and just wanted a good home and asked ”Well, I guess if you insist, where did you want to take her to dinner?”
System: |  ”To my favorite fishing spot!”
Human: |  The squirrel chuckled, pulled out a teeny tiny fishing rod, slapped on a little fishing hat and started making his way inside to ask my soon to be very confused cat out on a date.
System: |  Thank you for reading!
Table 1. Example stories generated by the tuned system with a human through
the collaborative storytelling annotation task.

###  2.3. Language Models

In order for an AI agent to participate in collaborative storytelling, it must
be able to generate story continuations. A language model (LM) is a
mathematical model that assigns likelihoods to sequences of words where
sequences that are more likely in a target language are given higher scores.
Such a model can be used to generate text.

More precisely, a language model provides a probability distribution $P(x)$
over all sequences of tokens $x$. Sampling from the LM distribution is
equivalent to generating text, motivating the approximation of the value of
$P(x)$ using a universal function approximator, like an artificial neural
network. Specifically, autoregressive LMs predict the next token given all
previous tokens; this is equivalent to factoring the probability $P(x)$ as as
a product of conditional probabilities of each token $x_{i}$ given previous
tokens $x_{<i}$:

$P(x)=\prod_{i=0}^{n}P(x_{i}|x_{<i})$

The autoregressive formulation facilitates text generation as previous tokens
are used to predict a distribution over potential next tokens, from which a
token can be sampled and appended to the sequence. In other words, at each
timestep an autoregressive LM predicts the next token given the sequence of
previous tokens.

Early language models estimated token sequence likelihood based on token
sequence counts taken from large collections of text together with various
smoothing methods to handle novel token sequences (Ney et al., 1994). Later,
RNNs and other sequential neural networks models became popular due to their
ability to apply distributed word representations (Bengio et al., 2003;
Mikolov et al., 2011; Sutskever et al., 2011), but RNNs have issues with
vanishing gradients and modelling long-term dependencies found in text.

The recent transformer architecture (Vaswani et al., 2017) uses attention
layers to model long-term dependencies by greatly increasing the model’s
visible context. Transformers have been shown to perform well in a variety of
tasks, including machine translation (Vaswani et al., 2017) and a variety of
language understanding (Radford et al., 2019) and language generation tasks
(Zhang et al., 2019). A notable transformer model is BERT (Devlin et al.,
2018). However, as it is a bidirectional model, BERT and its variants are
rarely used for text generation, due to the necessity for computationally-
expensive Gibbs sampling (Wang and Cho, 2019).

The model we use as a basis for our system, GPT-2 (Radford et al., 2019), is a
large-scale neural network using the transformer architecture, and it has been
applied successfully in a variety of language generation tasks ranging from
news article generation to dialog. GPT-2 is a general purpose auto-regressive
LM trained on a large corpus of internet text and its pretraining has been
shown to be effective for transfer learning to novel domains.

Figure 3. Web interface for collaborative storytelling annotation task.
Participants select from amongst ten possible story continuations generated by
the system before adding their own line to the story.

##  3\. Approach

Our approach to collaborative storytelling is simple: a Generator model that
is a large-scale neural language model tuned on storytelling data to generate
story continuation candidates is combined with a Ranking model that is trained
on human storyteller preferences to score them and select the highest quality
continuation.

###  3.1. Generation

The Generator is a unidirectional autoregressive language model which is
sampled from multiple times to generate candidate story continuations. We used
the publicly-available pretrained 774M parameter GPT-2-large
model222https://github.com/openai/gpt-2 tuned on our WritingPrompts dataset.

One issue with using an LM for generation is the output may be ill-formed or
lacking in logical coherence. The main solutions for this issue are the use of
larger models, the use of different sampling methods, and the use of various
methods of traversing the search space of possible sentences. However, larger
models are at greater risk of over-fitting and result in large increases in
memory usage for modest gains in quality, which makes them impractical to use.
As such, we focused on sampling and searching through ranking.

###  3.2. Sampling

The most popular approaches for sampling from autoregressive models have
predominantly focused on techniques for truncating the low-quality tail of the
model distribution, like top-k and nucleus sampling (Holtzman et al., 2019).
Sampling is used in most GPT-2 based text generation systems, superseding
greedy or untruncated sampling. In all experiments, we use nucleus sampling
with $p=0.9$.

###  3.3. Ranking

The Ranker model scores each story continuation candidate and selects the
highest scoring one. It is a standard GPT-2-large model with a final
classification head consisting of a linear layer outputting a single scalar
for each token. The input format to the model is:
(context)<|endoftext|>(choice)<|endoftext|>.

The <|endoftext|> token is used because it is guaranteed not to occur
elsewhere in the input. As GPT-2 is unidirectional, the embedding of the final
token integrates information from the entire input context window; this is
similar to the use of the [CLS] token in BERT. Thus we execute the Ranker
model once for each choice, keep only the outputs from the last token of the
final layer for each choice as the logit score of each choice, and compute a
softmax over them. The Ranking model architecture is shown in Figure 2.

We chose a neural network-based Ranker model to select the best story
completion from the Generator output because it offers us control over the
trade-off between text generation quality and computational demand, while
avoiding the significantly increased memory footprint and inflexibility in
computational cost of using a larger language model. The amount of
computational resources used is easily adjustable by changing the number of
rollouts considered by the Ranker. This serves as a middle ground between the
intractable extreme of searching the entire space of all
$\mathrm{vocab}^{\mathrm{length}}$ possible sentences, and the computation-
efficient but suboptimal solution of sampling without any branching or
backtracking.

One popular alternative search solution making a similar trade-off is beam
search, which keeps a dynamic list of generation candidates. Beam search has
been applied in many language generation tasks, including machine translation
(Tillmann and Ney, 2003). However, sampling from an LM using beam search can
lead to degenerate text (which is typically repetitive and uninteresting), in
an open-ended task such as storytelling. (Holtzman et al., 2019) These issues
are avoided using a neural network-based Ranker model because it has richer
text representations, it scores full text utterances rather than incomplete
text fragments, and it can incorporate additional information about the
storytelling domain from its training data.

System | Dataset | Accuracy
---|---|---
tuned+ranked | validation | 22.9% | (229 / 1000)
tuned+ranked | test | 23.3% | (233 / 1000)
random baseline | - | 10.0% |

Table 2. Accuracy of the tuned+ranked model at predicting the story
continuation that was selected by the Mechanical Turker who constructed the
story. Note that a random baseline would pick the correct continuation 1 out
of 10 times.

System | Acceptability
---|---
untuned | 33.9% | (305 / 900)
tuned | 39.8% | (358 / 900)
tuned+ranker | 62% | ( 62 / 100)

Table 3. Mean acceptability of story continuations in the test set. To
evaluate untuned and tuned, acceptability is calculated over all 9
continuations from each system, while tuned+ranked uses the Ranker to consider
only the best one.

###  3.4. Datasets

In this section we describe our datasets: (i) a collaborative storytelling
dataset constructed by crowdsourcing workers interacting with our
collaborative storytelling system that are used to train the Ranker model and
for evaluation, and (ii) a writing prompts dataset comprised of short stories
written in response to writing prompts posted to a Web forum that are used to
train the Generator model.

####  3.4.1. Collaborative Storytelling Dataset

We collected collaborative stories using Mechanical Turk, each consisting of
20 interactions in response to a provided story starter (which is sampled from
the initial sentences of stories in the WritingPrompts dataset described in
Section 3.4.2). The interactions in the story alternate between choice type
interactions, in which a human participant chooses from 10 story continuations
that are generated by out collaborative storytelling system, and freeform type
interactions, in which the human participant is able to provide a complete
sentence response. The Web interface for this task in shown in Figure 3.

In order to ensure data quality, one of the continuations in the choice type
interaction is a distractor which is made by concatenating randomly sampled
words. The distractors are also filtered through Mechanical Turk beforehand by
asking workers whether the sentences are coherent or not, and only the ones
labelled incoherent by workers are used. As a quality check, if a worker
selects a distractor during a choice type interaction, the story is discarded.

We collected a total of 2,200 stories, which we randomly partitioned into a
training split of 2,000 stories, and validation and test splits of 100 stories
each. Some example stories generated by human participants together with our
system are shown in Table 1.

####  3.4.2. Writing Prompts Dataset

We constructed a dataset of stories from the r/WritingPrompts
subreddit333https://www.reddit.com/r/WritingPrompts/, consisting of all posts
with score greater than 3 made before 2019-11-24, amounting to 140k stories in
total. Some heuristics were used to clean the stories444We removed smart
quotes, links and user/subreddit mentions, and all HTML entities and markdown
formatting.. This data was used to train the Generator model.

To train the Ranker model, stories with less than 100 characters or 35
sentences were also removed. This data is then used to generate synthetic
collaborative storytelling data. The first sentence of the story is used as
the story starter, and the next 20 sentences are all used as the preferred
story continuations of choice type interactions, where the other 9 incorrect
choices are sampled from the 25th and subsequent sentences of the story.

We chose to collect our own WritingPrompts dataset instead of using the FAIR
WritingPrompts dataset (Fan et al., 2018), because it gave us the flexibility
to filter stories by custom score thresholds, as well as to perform the
different preprocessing necessary for GPT-2. Our dataset also contains more
than an additional year’s worth of data compared to the FAIR dataset.

###  3.5. Story Continuation Sampling and Ranking

To generate story continuations from our system, sentences are generated from
the Generator model and filtered using a set of cleanliness heuristics until
the desired number of samples is achieved. Our heuristic rejected sentences
with less than 60% alphabetic characters, unbalanced quotations, select
profanity, or words like “chapter” that are not typically part of the story.

For systems using ranking, the Ranker model computes a score for each story
continuation and selects the highest scoring one.

###  3.6. Training

The Generator model is trained with a maximum likelihood estimation loss
function using Adafactor (Shazeer and Stern, 2018) with a learning rate of
5e-5 on a weighted mixture of the WritingPrompts and BookCorpus (Zhu et al.,
2015) datasets. The addition of BookCorpus helps reduce the risk of over-
fitting on the comparatively smaller WritingPrompts dataset.

The Ranking model is trained using Adam (Kingma and Ba, 2014) with a maximum
learning rate of 1e-5. The entire model is trained; no layers are frozen. The
checkpoint is resumed from a GPT-2 text generation model that was tuned on the
BookCorpus and WritingPrompts datasets in the same way as the Generator model.

The Ranking model is trained on the WritingPrompts dataset and 8 copies of the
training split of the Collaborative Storytelling dataset, shuffled at the
story level. Each batch for the Ranking model consists of 20 sentences taken
from a single story. To ensure that the model fits in memory, only the
sentences that fit within 400 tokens are used, resulting in some batches with
less than 20 sentences. The majority of stories do not have to be truncated.

Figure 4. Web interface for storytelling system preference evaluation.  Characteristic | Question
---|---
Engagingness | Who would you prefer to collaborate with for a long story?
Interestingness | If you had to say one of these storytellers is interesting and one is boring, who would you say is more interesting?
Humanness | Which storyteller sounds more human?
Story Preference | Which of these stories do you like better?
Table 4. Questions asked to human evaluators of collaborative storytelling
systems. Characteristics and questions are based on the PersonaChat evaluation
metric of (Li et al., 2019), with minor changes to wording to reflect the
task’s storytelling nature. EngagingnessInterestingnessHumannessStory
Preference050100$63$$52$$60$$57$$37$$48$$40$$43$# of
participantsuntunedtunedtuned+rankedEngagingnessInterestingnessHumannessStory
Preference050100$65$$57$$54$$65$$35$$43$$46$$35$# of participants Figure 5.
Human evaluation of collaborative storytelling systems. We compare the pairs
(untuned, tuned) and (tuned, tuned+ranking). Each bar graph shows a comparison
of two different systems generating stories through self chat. A larger
portion of the bar indicates that system was preferred by evaluators.

##  4\. Evaluation

We evaluate our collaborative storytelling system through a combination of
qualitative and quantitative metrics. To understand how well our system
replicates human preferences, we measure story continuation ranking accuracy
and story continuation acceptability. To gain insights into the
characteristics that people feel our system has, we adapt the Acute-eval
chatbot evaluation metric (Li et al., 2019) to collaborative storytelling
evaluation.

The three systems we evaluate are (i) untuned (pretrained GPT-2) as a
baseline, (ii) tuned (GPT-2 tuned on storytelling data), and (iii)
tuned+ranker (GPT-2 tuned on storytelling data with a single story
continuation selected by the Ranker model).

###  4.1. Story Continuation Prediction Accuracy

Story continuation prediction accuracy measures the accuracy of the Ranker
model at predicting the continuation chosen by the Mechanical Turk worker that
interacted with the model to produce the story. This metric is a proxy for how
often the tuned+ranked picks the best continuation of the story, but its
usefulness is diminished by variance in human annotators and the possibility
of multiple equally good continuations. The results are summarized in Table 3.
Nonetheless, we find that our Ranker model outperforms chance by a factor of
over two, providing evidence that it is able to capture the preferences of
human annotators to an extent.

Self-chat tuned+ranked Story 1
---
A: |  The clock finally struck 10am and the massive archway gates were slowly pulled open with the sound of a grinding mechanism.
B: |  I stood before the immense bronze doors, arms crossed, awaiting the fate of the two evil Dictators.
A: |  “Ladies and gentlemen of the land” a soft yet authoritative voice boomed through the doors.
B: |  “We are here for your arrival” a commanding and officious voice echoed through the halls.
A: |  A slow breath tickled my lips as I was finally allowed inside.
B: |  The archway was brimming with people, many in red, with metal cufflinks, and most in ornate black garb.
A: |  I stepped forward into the main audience hall, pausing to take in my surroundings.
B: |  The ceiling was made of rough jagged glass panels; out in the back stood eight shiny and elaborately painted metal ladders.
A: |  The stately mahogany wooden podium was suspended from the ceiling, very tall and proud.
B: |  The four different Dictators circled the podium with their various groups in the room.
A: |  The oldest of the Dictators stood, hands together in front of him, on his magnificent golden podium.
B: |  He seemed more imposing than the rest, holding a bony silver sword by the hilt in his shining gold hand.
A: |  “Hallowed be the name of his majesty, King Gautir” the King boomed through the open archway.
B: |  The King was a corpulent, middle aged man with his long white hair growing out of his crown, nearly the size of his small face.
A: |  I could see that his eyes were piercing like the flaming sun.
B: |  The King’s long, white robes seemed long like a black robe worn by someone with a wide girth.
A: |  His sneering smile was reflected in his large, deep blue eyes.
B: |  “Today, we greet you both, members of the committee, from the Holy Empire of All Flame and Sound.”
A: |  The King’s voice boomed as the rest of the Dictators turned and stepped towards the podium, stopping on their footsteps.
B: |  “Welcome to this evening’s meeting” the King announced to us.
A: |  “You two can either choose to remain in your chambers or come out and face the Committee” The King said in a commanding tone.
Self-chat tuned+ranked Story 2
A: |  Have you ever wondered what exactly goes into making our favorite foods?
B: |  You know, the big baked potato with oil and salt, the slushy that’s savory enough to eat for lunch every day?
A: |  The answer is simple: the food industry.
B: |  It’s a fairly big industry, you see.
A: |  It’s sort of estimated that five hundred different corporations control 70% of the world’s food supply.
B: |  If you were to think of it in simple terms, that’s right: almost everyone on the planet eats food produced by a food corporation.
A: |  As you might imagine, the world is full of giant corporations and a huge amount of money being made through the food industry.
B: |  We’ve all heard the expression “money talks, money does.”
A: |  What do you think happens when that money goes through the food industry?
B: |  It goes into the mouths of politicians and it goes into the mouths of stockholders.
A: |  This whole industry is very complicated, although people never seem to come up with any clear-cut answers for it.
B: |  But, really, the only thing that people seem to have a handle on about the food industry is that it’s a big financial mess.
A: |  When you think about it, this seems pretty clear.
B: |  Let me explain.
A: |  In order to make money, companies have to produce enough food to feed a population.
B: |  When a company creates more food than it can eat, it has to buy more food, so that it can keep producing more food.
A: |  More food means more food prices, so that the corporation can make more money.
B: |  So how does the food industry achieve this?
A: |  The answer to this is pretty simple.
B: |  In the world of food production, companies come up with marketing schemes that manipulate people’s tastes.
A: |  Using a carrot for example, a company might work to improve a persons’ reaction to carrots.
Table 5. Example stories generated by self-chat with the tuned+ranked system.

###  4.2. Story Continuation Acceptability

As an additional measure of our systems’ capacity to generate story
continuations that match human preferences, we formulate the story
continuation acceptability task. In this task, each story continuation
generated by a system is classified as either acceptable or unacceptable, and
we compare their mean acceptability precision.

We annotated the acceptability of candidate story continuations by asking
Mechanical Turk workers to classify each continuation given the context of the
story generated so far. To ensure annotation quality, we have 3 workers
evaluate each choice interaction per story from both the validation and test
sets and take the majority vote across the three labels as the final
label555The workers reached unanimous agreement 41.9% of the time on the test
data.. These choice interactions consist of 9 story continuations generated by
the system and 1 incoherent distractor. If a worker labels a distractor
acceptable, their annotations are discarded. We use this method to evaluate
how often each model produces outputs that are an acceptable continuation of
the story, rather than the best continuation.

Since the tuned and tuned+ranked systems use the same language model samples,
we use the test set to evaluate their performance, considering the mean
acceptability of all of the sampled continuations from tuned and the
acceptability of the single continuation selected by tuned+ranked for each
choice interaction in the datasets. To evaluate the untuned system, we gather
and evaluate 100 choice interactions by having Mechanical Turkers construct
stories with the untuned system.

The results are summarized in Table 3. As we can see, the tuned system
outperforms the untuned system, showing that tuning the language model on
storytelling data is important in improving generation quality. We also find
that tuned+ranked greatly outperforms the other two systems, providing
supporting evidence that our Ranking model is effective at helping our
language model produce story continuations that are likely to be preferred by
humans.

###  4.3. Human Annotator Story Preferences

Conducting qualitative evaluation of collaborative storytelling is challenging
because the highly interactive nature of the task means that the influence of
human participants makes it difficult to isolate the performance of the
system. Ideally we would like to conduct subjective evaluation of
participants’ collaborative storytelling experience with an intelligent agent,
but this is left for future work.

Instead, since collaborative storytelling involves language exchange between
entities with turn taking, we take inspiration from dialogue system evaluation
methodology. Faced with the challenge of comparing multiple dialogue systems,
(Li et al., 2019) developed a method of comparing conversation pairs that
instructs evaluators to only pay attention to the contributions of a single
specified speaker in the conversation. In addition, their evaluation method,
known as Acute-eval, allowed them to evaluate the contributions of a given
dialogue system in terms of characteristics, such as engagingness,
interestingness, humanness, and knowledgeability. Finally, to evaluate
different dialogue systems without requiring a human to chat with them, they
apply the self-chat technique of (Ghandeharioun et al., 2019) and generate
conversations for evaluation by having dialogue systems talk to themselves.

We create our own evaluation metric based on the characteristics targeted by
the PersonaChat metric of ACUTE-Eval666We exclude the Wizard of Wikipedia
metric because knowledgeability is not directly relevant to our collaborative
storytelling setting.. For each target characteristic, we take the question
that (Li et al., 2019) identified as most likely to differentiate between the
evaluation of two systems and reword it to fit the collaborative storytelling
setting. Finally, we add a question to measure overall story preference. The
resulting evaluation metric is shown in Table 4.

We created a Mechanical Turk task to determine relative pairwise user
preferences using our evaluation metric. To eliminate variance from human
storytellers, we use the self-chat setting of (Li et al., 2019), where each
model converses with itself. Some example stories are shown in Table 5. We
compare the untuned and tuned+ranked models against the tuned model. For each
pair of models, we collect 100 comparisons per question, and we instruct
workers to provide short justifications for their decisions. The Web interface
shown to workers is given in Figure 4.

The results of the evaluation are summarized in Figure 5. For each
characteristic evaluated, the pairs of models are shown as stacked bar graphs,
where a larger portion represents a stronger preference for that system. As
can be seen, tuned is preferred over untuned, and tuned+ranked is preferred
over tuned for all characteristics and overall story preferences, providing
evidence that tuning the language model on storytelling data and ranking the
generated story continuations make complementary contributions to our
collaborative storytelling system’s performance.

##  5\. Discussion

In this section, we discuss the advantages and limitations of our approach to
collaborative storytelling.

###  5.1. Advantages

The advantages of our approach are that our storytelling system can produce
well-formed story contributions that display creativity and react to the
contributions made by human storytellers. In Collaborative Storytelling Story
1 from Table 1, we see an example of that creativity, when our system
introduces the plot twist that the man and women not only know each other but
have been living together for year. In Story 2 from the same table, we see our
system’s ability to play along with a human storyteller when the system
accepts its collaborator’s assertion that the squirrel can speak English and
starts crafting dialogue for it.

###  5.2. Limitations

The limitations of our approach are that our storytelling system has a very
shallow model of the world, which can lead to incoherent output. This is
illustrated by the self-chat Story 2 in Figure 4: the narrative makes jarring
shifts in setting and lacks overall cohesion. Such problems in cohesion are
often amplified in self-chat settings, as the model lacks human input to reign
it in.

In addition, because the storytelling model lacks explicit story structure, it
can be hard to steer toward desired output, such as a human-preferred genre or
mood, or generation of story endings on demand. We plan to address these
issues in future work by adding more structure to the data used to train our
models.

Finally, evaluation of this task is challenging: because interaction with
human players introduces variance into the output, it is difficult to directly
compare generated stories, but at the same time, evaluation limited to self-
chat is not fully reflective of our desired task setting. Once our system has
been implemented in a suitable agent, we plan to carry out detailed subjective
evaluation of the collaborative storytelling experience of volunteers to gain
further insights about our task and approach.

##  6\. Conclusion

In this paper, we introduced the novel task of collaborative storytelling,
where humans and AI agents work together to make stories. We presented a
collaborative storytelling system that tunes a large-scale neural LM on
storytelling data and uses a sampling-and-ranking approach to select more
human-preferred story continuations. Quantitative evaluation of our system
found that tuning and ranking both greatly contribute to its capability to
generate story continuations that human evaluators prefer and consider
acceptable. Qualitative evaluation of human evaluator preferences showed that
humans found tuned+ranked more preferable than tuned and tuned more preferable
than untuned in terms of engagingness, interestingness, and humanness metrics,
as well as overall story quality preferences. Finally, we identified areas for
potential future work, including evaluation of stories produced by humans and
our system, integration of our system into intelligent agents such as robots
and avatars, and improvement of generated story continuation quality by
allowing genres or moods to be targeted.

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# Lattice quantum gravity with scalar fields

, Jack Laiho, Judah Unmuth-Yockey
Department of Physics, Syracuse University, Syracuse, NY 13244, USA
E-mail:

###### Abstract:

We consider the four-dimensional Euclidean dynamical triangulations lattice
model of quantum gravity based on triangulations of $S^{4}$. We couple it
minimally to a scalar field in the quenched approximation. Our results suggest
a multiplicative renormalization for the mass of the scalar field which is
consistent with the shift symmetry of the discretized lattice action. We
discuss the possibility of measuring the mass anomalous dimension and the
gravitational binding energy between two scalar test particles, where a
negative bound state energy would imply that this model has an attractive
gravitational force.

##  1 Introduction

The problem of constructing a quantum theory of gravity in four dimensions is
notoriously difficult because the theory is perturbatively non-renormalizable
in four dimensions. However, it was conjectured by Weinberg in [1] that the
quantum theory of gravity might be asymptotically safe in the ultraviolet (UV)
by possessing an interacting fixed point with finite dimensional critical
surface. There is no proof that this is true, but there is non-trivial
evidence in its support ; see [2, 3] and references therein. However, there
are arguments that argue that gravity cannot be described by a renormalizable
quantum field theory in four dimensions based on the inconsistency between
entropy scaling of black holes in the high-energy spectrum and that of a scale
invariant theory [4, 5]. The argument goes that the entropy of a
renormalizable theory must scale as $S\sim E^{\frac{d-1}{d}}$. For gravity,
the high-energy spectrum must be dominated by black holes. The black hole
entropy area law tells us that $S\sim E^{\frac{d-2}{d-3}}$. However, these
scalings are consistent for the value $d=3/2$, which curiously is also the
value of the fractal (spectral) dimension obtained from lattice gravity
simulations at short distances in both Euclidean dynamical triangulations
(EDT) and Causal dynamical triangulations (CDT) [6, 7].

In this proceedings, we work under the assumption that there is merit in
understanding gravity as a quantum field theory in four dimensions. In the
1990s, using the discretization of the Einstein-Hilbert action due to Regge,
the phase diagram of dynamical triangulations was explored and it was hoped
that one would find a second-order critical point, which could be identified
as the asymptotically safe fixed point of Weinberg’s conjecture. This is
crucial for the continuum extrapolation of the lattice model. However, the
order of the phase transition turned out to be first-order [8, 9]. The
approach we follow here introduces a non-trivial measure term which alters the
structure of the phase diagram where it appears that the continuum limit can
be taken.

##  2 Action and discretization

The Einstein-Hilbert action for a metric $g_{\mu\nu}$ has the form,

$S_{E}[g]=\frac{1}{16\pi G}\int d^{4}x\sqrt{-g}\left(2\Lambda-R\right)$ (1)

where R is the Ricci scalar and $\Lambda$ and G are the cosmological constant
and Newton’s constant respectively. On a triangulation, we discretize the
volume according to

$V_{4}=\int d^{4}x\sqrt{-g}\rightarrow N_{4}[T]$ (2)

The Euclidean Einstein-Regge discrete action is given by :

$S_{ER}=-\kappa_{2}N_{2}+\kappa_{4}N_{4}$ (3)

where $N_{i}$ is the number of simplices of dimension $i$, $\kappa_{2}$ and
$\kappa_{4}$ are related to Newton’s constant $G$ and the cosmological
constant $\Lambda$. In our lattice simulations, $\kappa_{4}$ must be tuned to
a critical value such that an infinite lattice volume can be taken. This
leaves two parameters in the theory, $\kappa_{2}$ and $\beta$. Note that for a
fixed topology $S^{4}$ with fixed four-volume $N_{4}$, the number of
0-simplices and 2-simplices i.e $N_{0}$ and $N_{2}$ are not independent but
related by

$N_{2}=2N_{0}+2N_{4}-2\chi~{}~{},$

where $\chi=N_{0}-N_{1}+N_{2}-N_{3}+N_{4}$ is the Euler characteristic. It is
customary to start with the discrete Euclidean-Regge action [10]

$S_{ER}=-\kappa\sum V_{2}\left(2\pi-\sum\theta\right)+\lambda\sum V_{4}$ (4)

where $\kappa=\frac{1}{8\pi G}$, $\theta=\mathrm{cos}^{-1}(1/4)$ and
$\lambda=\kappa\Lambda$. Also, the volume of a d-simplex is given by :

$V_{d}=l^{d}\frac{\sqrt{d+1}}{\sqrt{2^{d}}d!}.$ (5)

Rewriting $V_{2}$ and $V_{4}$ above in terms of $N_{2}$ and $N_{4}$ and using
the relation between them ($N_{2}=10N_{4}$) and using Eq. (5), we can write
Eq. (4) as,

$S_{ER}=-\frac{\sqrt{3}}{2}\pi\kappa
N_{2}+N_{4}\left(\kappa\frac{5\sqrt{3}}{2}\mathrm{cos}^{-1}\left(\frac{1}{4}\right)+\frac{\sqrt{5}}{96}\lambda\right)$
(6)

Defining new variables $\kappa_{2}=\frac{\sqrt{3}}{2}\pi\kappa$ and
$\kappa_{4}$ = $\kappa$
$\frac{5\sqrt{3}}{2}\mathrm{cos}^{-1}(\frac{1}{4})+\frac{\sqrt{5}}{96}$
$\lambda$, we recover the form written above in Eq. (3). The continuum path
integral can be written as,

$Z=\int\mathscr{D}[g]e^{-S_{ER}[g]}$ (7)

which we discretize by writing the grand canonical (i.e. volume can fluctuate)
partition function as,

$Z=\sum_{\mathcal{T}}\frac{1}{C(\mathcal{T})}\Bigg{[}\prod_{i=1}^{N_{2}}\mathcal{O}(t_{i})^{\beta}\Bigg{]}e^{-S_{ER}[\mathcal{T}]}$
(8)

where $C(\mathcal{T})$ is a symmetry factor which mods out the number of
equivalent ways of labelling the vertices in a given triangulation
$\mathcal{T}$. Note that the term in paranthesis is the contribution from a
non-trivial measure term. It was shown [11] that this term is crucial in four
dimensions unlike in lower dimensions. This term was absent in much of past
work [12] which implicitly assumed $\beta=0$ triangulations. Another
difference from what was done in the past is that we use degenerate
triangulations [13] as opposed to the combinatorial ones used in [12]. The
reason we employ degenerate triangulations is that it leads to a substantial
reduction in finite-size effects compared to combinatorial triangulations.

##  3 Coupling to the scalar field

We introduce the scalar field $\Phi$ as a matter field minimally coupled to
gravity. In the continuum, the action coupled to the scalar field ignoring the
self-interaction terms can be written as

$S=S_{ER}[g]+S[g,\Phi]$ (9)

where,

$S[g,\Phi]=\int
d^{4}x\sqrt{-g}~{}\bigg{(}g^{\mu\nu}\partial_{\mu}\Phi\partial_{\nu}\Phi+m_{0}^{2}\Phi^{2}\bigg{)}$
(10)

Here, $\Phi$ is a test particle and the back reaction of the metric is
ignored. The notion of distance is non-trivial to define on the lattice that
itself is dynamical, but the geodesic distance can be understood via the
propagation of massive particle as suggested in [14, 15] The propagator for
the scalar field in a _fixed background_ of constant curvature decays as,

$G_{\mathrm{xy}}(r)=A(r)e^{-mr}$ (11)

where $r$ is the geodesic distance between two points. It is noted that $m$,
is the physical mass of the particle with _multiplicative gravitational
renormalization_. The multiplicative renormalization follows from the shift
symmetry of the discrete lattice action [16] and can be seen as follows,

$\displaystyle S_{\mathrm{lat}}$ $\displaystyle=$
$\displaystyle\sum_{\langle\mathrm{xy}\rangle}\bigg{(}(\Phi_{x}-\Phi_{y})^{2}+\sum_{x}m_{0}^{2}\Phi_{x}^{2}\bigg{)}$
(12) $\displaystyle=$
$\displaystyle\sum_{\langle\mathrm{xy}\rangle}\bigg{(}(\text{D}+1+m_{0}^{2})\delta_{xy}-C_{xy}\bigg{)}\Phi_{\mathrm{x}}\Phi_{\mathrm{y}}$
(13)

where $C_{\mathrm{xy}}$ is the simplex neighbor (or connectivity) matrix,
$m_{0}$ is the bare mass and $D$ is the space-time dimension. For zero bare
mass, there is a shift symmetry, $\Phi\to\Phi+c$, which implies that the
renormalized mass should vanish in the limit that the bare mass is sent to
zero.

##  4 Computation and results

We restrict our analysis to the ensembles close to the critical line of the
phase transition, where it was shown that the geometry has semi-classical
properties, and on each degenerate dynamical triangulation, we calculate the
propagator using,

$G_{\mathrm{xy}}=(-\Box+m_{0}^{2})^{-1}_{\mathrm{xy}}$ (14)

The definition of the discrete Laplacian is given by,

Figure 1: Left: $G(r)$ for different volumes at $\beta=0$. Right: The
renormalized mass versus the bare mass for different lattice volumes
($i.e.~{}N_{4}$) with $\beta=0$. Bottom: The $\beta$ dependence on a fixed
lattice volume. The range used for fitting the data $r\in(24,28)$ for $16$k,
$r\in(19,23)$ for 8k and $r\in(16,20)$ for 4k respectively.

$-\Box_{\mathrm{xy}}=\hskip 17.07164pt\begin{cases}D+1\hskip
14.22636pt\text{if x = y}\quad\phantom{0}\\\ -1\hskip 28.45274pt\text{if x \&
y are nearest neighbors}\\\ 0\hskip 36.98857pt\text{otherwise}\end{cases}$
(15)

Here, $D+1$ is the coordination number of a $D$-simplex, which is 5 in our
case. Unlike the combinatorial case studied in [12, 17], here we study
degenerate triangulations. In such a setting, a given four-simplex can have
non-unique neighbors. This enables us to construct the laplacian for
configurations such that the sum of any particular row is just $m_{0}^{2}$. In
the limit of vanishing bare mass ($m_{0}\to 0$), we have an exact zero mode of
the operator corresponding to the zero eigenvalue of the Laplacian. It should
be noted that there exists an alternate geometric description of the laplacian
in terms of boundary ($\partial$) 111The action of $\partial$ on a given
p-simplex yields an directed sum of (p - 1)-simplices on its boundary,
whereas, $\overline{\partial}$ yields directed sum of (p + 1)-simplices and
co-boundary operators ($\overline{\partial}$). We can then write the laplacian
as,
$\Box=-\partial\overline{\partial}-\overline{\partial}\partial=(\partial-\overline{\partial})^{2}$,
where we have used $\partial^{2}=\overline{\partial}^{2}=0$. See [18] for
details and its role in gravitational systems coupled to fermions.

Similar to the continuum definition of the massive lattice scalar propagator,
we can define the same quantity on the lattice as,

$\displaystyle G_{\mathrm{xy}}(r)$ $\displaystyle=$
$\displaystyle\bigg{[}\frac{1}{(-\Box+m_{0}^{2})}\bigg{]}_{\mathrm{xy}}$ (16)
$\displaystyle\propto$ $\displaystyle e^{-mr}$ (17)

where, $m$ is the renormalized mass. Unlike the previous study [12], we have
not used smeared sources for the inversion of the matrix. However, it might be
crucial for the future calculation of binding energy. In calculating the
propagator over all configurations, we have considered five sources
($N_{\text{src}}=5$) per configuration and checked that our results are
unaffected by this choice.

$a_{\rm rel}$ | $\beta$ | $\kappa_{2}$ | $N_{4}$ | Physical volume
---|---|---|---|---
1.47(10) | 1.5 | 0.5886 |  4000 | 0.054
1 | 0.0 | 1.669 |  4000 | 0.25
1 | 0.0 | 1.7024 |  8000 | 0.125
1 | 0.0 | 1.7325 |  16000 | 0.0625
Table 1: The ensembles used in this work. There are several other ensembles
that we have generated but are not included in this proceedings. See [19] for
details.

###  4.1 Binding energy and Mass anomalous dimension of scalar fields

The calculation of the one-particle and two-particle propagators on generated
ensembles can be fitted to the form as given below

$\displaystyle G(r)$ $\displaystyle=$ $\displaystyle Ar^{\alpha}e^{-mr}$ (18)
$\displaystyle G^{(2)}(r)$ $\displaystyle=$ $\displaystyle Br^{\beta}e^{-Mr}$
(19)

where $M$ is the energy of the two-particle state. The coefficient of the fits
can then be used to calculate the binding energy associated as

$\displaystyle E_{b}(r)$ $\displaystyle=$
$\displaystyle\frac{1}{r}~{}\text{ln}\Bigg{(}\frac{G(r)^{2}}{G^{(2)}(r)}\Bigg{)}$
(20)

such that at long distances, _i.e._ $r\to\infty$, the negative value of the
binding energy, $E_{b}(r\to\infty)=M-2m$ would represent an attractive force.

We now discuss the calculation of the mass anomalous dimension from a
determination of the mass renormalization factor at the same physical volume
but different lattice spacings. The bare and renormalized lagrangians are

$\displaystyle
L_{b}=\dfrac{1}{2}\partial_{\mu}\varphi_{0}\partial^{\mu}\varphi_{0}-\dfrac{1}{2}m_{0}^{2}\varphi_{0}^{2}$
(21) $\displaystyle
L_{r}=\dfrac{1}{2}Z_{\varphi}\partial_{\mu}\varphi\partial^{\mu}\varphi-\dfrac{1}{2}Z_{m}m^{2}\varphi^{2}.$
(22)

Comparing them we get,

$\varphi_{0}\left(x\right)=Z_{\varphi}^{1/2}\varphi\left(x\right)$ (23)

and,

$m=\sqrt{\frac{Z_{\varphi}}{Z_{m}}}~{}m_{0}$ (24)

Taking the log of ( 24) and then taking the derivative with respect to
$\ln\mu$ and identifying $\mu=1/a$, we get:

$\frac{d\ln(m)}{d\ln a}=\dfrac{1}{2}\Big{(}\frac{d\ln F}{d\ln a}\Big{)}$ (25)

where we have used the shorthand $F=Z_{\varphi}/Z_{m}$. Then, the mass
anomalous dimension is given by,

$\gamma_{m}=-\dfrac{1}{2}\Big{(}\frac{d\ln F}{d\ln a}\Big{)}$ (26)

In the future, we will explore additional volumes and lattice spacings and
report on the results for gravitational binding energy and anomalous
dimensions.

Acknowledgments: This research was supported by the US Department of Energy
(DOE), Office of Science, Office of High Energy Physics, under Award Number
DE-SC0009998.

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