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[orcid=0009-0002-7185-7186<EMAIL_ADDRESS>]

[orcid=0000-0002-8436-8974<EMAIL_ADDRESS>]

[orcid=0000-0003-2919-3566<EMAIL_ADDRESS>url=https://webpages.charlotte.edu/rbunescu, ] [1]

[1]Corresponding author.

# Extraction of Atypical Aspects from Customer Reviews: Datasets and
Experiments with Language Models

Smita Nannaware  Department of Computer Science, University of North Carolina
at Charlotte, Charlotte, NC 28223, USA  Erfan Al-Hossami  Razvan Bunescu

(2023)

###### Abstract

A restaurant dinner may become a memorable experience due to an unexpected
aspect enjoyed by the customer, such as an origami-making station in the
waiting area. If aspects that are atypical for a restaurant experience were
known in advance, they could be leveraged to make recommendations that have
the potential to engender serendipitous experiences, further increasing user
satisfaction. Although relatively rare, whenever encountered, atypical aspects
often end up being mentioned in reviews due to their memorable quality.
Correspondingly, in this paper we introduce the task of detecting atypical
aspects in customer reviews. To facilitate the development of extraction
models, we manually annotate benchmark datasets of reviews in three domains –
restaurants, hotels, and hair salons, which we use to evaluate a number of
language models, ranging from fine-tuning the instruction-based text-to-text
transformer Flan-T5 to zero-shot and few-shot prompting of GPT-3.5.

###### keywords:

surprise, serendipity, customer reviews, language models

##  1 Introduction

When looking for a restaurant or a hotel, people are often faced with an
overwhelming number of options matching their search constraints. Even when
ranked by their average review scores, there may be numerous high quality
choices that satisfy the basic search criteria, especially in a metropolitan
area. This may lead to choice overload, or overchoice [1, 2], where an
individual is presented with a large number of choices that are too difficult
to compare, particularly under time constraints [3]. Making a decision in the
presence of overchoice becomes mentally exhausting and can lead to subsequent
impaired self-regulation [4], decision paralysis, and anxiety [5]. The level
of satisfaction that people experience when faced with an increasing number of
choices has been observed to follow the well-known Wundt curve [6], an
inverted U-shape curve originally relating stimulus intensity with its
pleasantness. According to this functional dependency, as the number of
choices goes up, satisfaction initially increases and then decreases [7, 8].
In this context, choice overload can be alleviated by reducing the number of
consumer choices [9] or by making one option stand out and appear better than
the others [10]. To this end, we propose that recommender systems emphasize
options that possess aspects with the potential to surprise the user in a
positive way, i.e., serendipity. Figure 1 illustrates an example where a user
Jane is looking for a ramen restaurant in her locality. The system knows that
she has been passionate about creating crafts from paper since childhood. Upon
being asked for recommendations, the system finds a number of highly rated
ramen restaurants, of which Nikita Ramen stands out because it has an origami
making station, an atypical aspect for a restaurant, in its waiting area. The
system recommends this restaurant to Jane, importantly without telling her
about the origami station. Upon entering the restaurant, she is very
pleasantly surprised to see the origami making station in the waiting area,
which brings feelings of nostalgia and happy memories from childhood. She
takes some time making various origami figures, before being seated at her
table. This serendipitous experience was facilitated by the fact that an
origami making station is an atypical aspect for a restaurant, hence it would
be experienced as surprising. After the dinner event, the system further
confounds her expectations by asking her if she enjoyed the origami making
station, which surprises her because she did not expect that the system was
responsible for the initial serendipity.

To enable such recommendations with potential for serendipity, the input would
ideally consist of three parts:

  1. 1.

The user’s query, be it a standalone request or a turn in a longer
conversation. This would be used to find the initial, often large set of items
that satisfy the user’s information need.

  2. 2.

The item’s data, including not only information about the typical aspects of
items from the same category, but also atypical aspects that may generate
surprise.

  3. 3.

The user’s data, especially in terms of their interests, their likes and
dislikes. This would be useful for determining if an atypical aspect would be
enjoyed by the user, i.e. serendipitous.

To increase the chance of serendipity, the system would need to (i) have
knowledge about the user preferences, and (ii) also ensure that the user
notices / takes advantage of the atypical aspect, e.g. estimating that there
will be some wait involved in the origami example.

Figure 1: Example of an interaction with the recommender system showing the
potential for serendipity of atypical aspects. The user profile on the left
shows a user interest (crafts) that is relevant for the atypical aspect
(origami) shown on the right.

In this paper, we introduce a more focused task where we assume that the
category of items requested in the user’s query is known, e.g. restaurants,
and the task is confined to using the item’s data to extract aspects that are
atypical for its category, e.g. origami station for restaurants. Because
users’ expectations are shaped by what they think is common for the category
of interest in their query, atypical aspects are likely to confound
expectations, and hence be perceived as surprising. Henceforth, we will use
the term surprising aspects to refer solely to atypical aspects. Whenever
atypical aspects are observed for an item, they tend to be more noticeable and
often lead to more memorable experiences. As such, they are likely to be
mentioned in customer reviews of that item. Therefore, we use customer reviews
as the source of an item’s data. At this time, no user data is used as input,
which means that the atypical aspects that are extracted, while surprising for
the user searching for that particular category of items, cannot be said for
sure to lead to serendipity due to unknown user preferences. In short, the
task is that of extracting atypical aspects from customer reviews, where
atypical is defined to be relative to a predefined item category. To the best
of our knowledge, no prior work has looked into extracting atypical aspects
from reviews or any other types of item data.

The rest of the paper proceeds as follows. Section 2 introduces the task of
atypical aspect extraction from customer reviews. Section 3 details the
development of benchmark datasets of customer reviews that are manually
annotated for atypical aspects with respect to three categories: restaurants,
hotels, and hair salons. In Section 4 we describe a number of extraction
approaches that rely on language models (LM), ranging from Flan-T5 [11, 12]
and ChatGPT [13] in zero-shot or few-shot setting, to fine-tuning of Flan-T5.
Experimental evaluations of these models in both extractive and abstractive
settings are detailed in Section 5. The paper ends with related work in
Section 6 and concluding remarks.

##  2 Task Definition and Guidelines

$\blacktriangleright$ A group of work friends and I stumbled upon Upper Deck a
little over a year ago and everyone from our office has turned Upper Deck into
our local watering hole ever since. Their happy hour special is unbeatable,
they have a good selection of draft beers, and the food is out of this world
good. The stand out feature of Upper Deck is the offering of life size beer
pong at their outside patio. This takes traditional beer pong and substitutes
solo cups with garbage cans (painted to look like solo cups) and Ping Pong
balls with dodgeballs They also have a pool table and recently added arcade
games (nfl blitz 99 beats madden 15 all day). Get some friends and bring your
appetites and some quarters, you won’t be disappointed.
---
[1pt/2.5pt] The restaurant offers life size beer pong at their outside patio.
They have a pool table. They recently added arcade games, such as nfl blitz 99
and madden 15.
$\blacktriangleright$ The big draw of this place is the excellent pizza, which
you can have with beer on an outside deck with a view of the parklands. It’s a
nice place to hang out on a sunny afternoon. You can even go for a walk in the
Goose Creek Park behind the restaurant afterwards to burn off the calories you
just consumed. The big minus is that if you go for lunch or in early
afternoon, the menu is really limited. This place also seems to attract a
goodly number of families with kids at lunch times, probably because it serves
pizza and there’s a playground in the adjoining park,
[1pt/2.5pt] The restaurant has an outside deck with a view of the parklands.
Customers can go for a walk in the Goose Creek Park behind the restaurant.
There’s a playground in the adjoining park.
$\blacktriangleright$ Classic West Philly spot where you can see local
wildlife. Everyone from moms to anarchists to hackers to organic gardeners to
activists hangs out there. The coffee is excellent, the baked goods are great
as well, and if you’re working on something, you might run into a possible
collaborator there. If you’re thinking of moving to West Philly, definitely
check out Satellite and the farmer’s market. They’ve replaced the cracked and
chipped cups with awesome new cups, which are awesome.
[1pt/2.5pt] In this restaurant you can see local wildlife. Everyone from moms
to anarchists to hackers to organic gardeners to activists hangs out there.
$\blacktriangleright$ This is such a cool place! Three words was all it took
to add this gem to my list of places to visit while in St. Louis - "Good
Burger Car!!" YES! They have the car from the movie Good Burger! A movie I was
obsessed with as a child & have since gotten my kids to love just as much! The
place is made out of cool, colorful shipping containers with many neat
decorations, what looks like an alien spaceship from Toy Story with a laser on
it adorned the top of the place along with a cow. Now, on to the food. They
have many different options to choose from including create-your-own burgers &
many of their own creations, sandwiches, salads, sides, kid’s meals, & shakes
& floats … Such a unique place & worth a visit! They also sell souvenir
T-shirts & hats, & my fiance had to get himself a "HI AF" shirt. The shirts
were heavily influenced by the movie Good Burger & there was one in particular
I had my heart set on, unfortunately they did not have it in my size.
[1pt/2.5pt] The restaurant has the car from the movie Good Burger. They sell
souvenir T-shirts and hats, and a customer got a "HI AF" shirt. The shirts are
heavily influenced by the movie Good Burger.
The place is made out of cool, colorful shipping containers, with many neat
decorations, what looks like an alien spaceship from Toy Story with a laser on
it adorned the top of the place along with a cow.
Table 1: Examples of extractive and abstractive annotations of customer
reviews in the restaurants domain. Secondary or optional annotations are shown
in blue.

Given a domain category, e.g. restaurants, and a customer review of a
particular item in that category, e.g. a restaurant, the task is to extract
aspects of that particular item that are atypical of items in its category.
Throughout most of this paper we will use the category of restaurants as an
example. All aspects that are related to the core business of a restaurant,
including but not limited to food, service, price, opening hours, parking, are
considered typical aspects and are not annotated. Conversely, we define and
annotate an aspect as atypical if it is not related to the core business of
restaurants, yet it belongs to or is a feature of the restaurant (restaurants
refers generically [14] to the restaurant category, whereas the restaurant
refers to a specific restaurant). Correspondingly, in Table 1 we show samples
taken from 4 reviews, illustrating two types of manual annotations, extractive
and abstractive, analogous to the extractive [15, 16] and abstractive [17, 18]
annotation schemes widely used in summarization
datasets111https://duc.nist.gov, https://tac.nist.gov. A special case is made
of aspects related to the ambience or atmosphere of a restaurant: while
ambience might be considered as an important part of, and thus subordinated
to, the core business of restaurants, there are cases where ambience aspects
stand out and become an attraction on their own. When that happens, we
annotate them on a secondary, optional layer.

In the extractive annotation, only base noun phrases referring to atypical
aspects are annotated. If multiple phrases refer to the same atypical aspects,
we only annotate the grounding instance of the coreference chain. For example,
the noun phrase "adjoining park" in the second review is not annotated, as it
refers to the "Goose Creek Park" which is already annotated. However, if a
review mentions an atypical category, such as "arcade games" in the first
review or "local wildlife" in the third review, any category instance that is
mentioned will also be annotated as atypical, such as "nfl blitz 99" in the
first review or "anarchists" in the third review, respectively. If the
atypical aspect is a more complex noun phrase, we only annotate the base noun
phrase that expresses the semantic core (often the syntactic head), as in "the
Goose Creek Park behind the restaurant". The extractive annotation is meant to
be used together with the original review in downstream applications, which
makes it acceptable to annotate only the most important part of the phrase.

In the abstractive annotation, one or more sentences are generated that
enumerate the atypical aspects mentioned in the review. The formulation is
kept as close as possible to the original text while maintaining naturalness.
The generated sentences are intended to be concise, usually maintaining
details that are expressed in the same sentence in the review, however keeping
out unimportant information about the atypical aspect that is mentioned in
other sentences, or details that are vague or uncertain. Sentiment words are
maintained only if it helps keep the text natural and faithful to the
original. The abstractive annotation is meant to be standalone and used
without the original review in downstream tasks, as such it may require some
minimal rewriting of the original review formulation, e.g. adding the phrase
"the restaurant", or removing opinion words such as "beats" in the first
example. Sometimes reviewers use metaphors to refer to atypical aspects, in
which case it is important that the abstractive version preserves the
metaphorical meaning. This is the case for "local wildlife" in the third
review, which refers metaphorically to types of customers that are seen
relatively less often in that context.

In many aspect-based sentiment analysis approaches [19], identifying typical
aspects that are mentioned in a review is done explicitly as aspect term
extraction. However, the task of extracting atypical aspects, as introduced
above, cannot be solved simply by first (a) identifying all typical aspects of
restaurants that are mentioned in a review, followed by (b) extracting all
other noun phrases, i.e. phrases that do not refer to a typical aspect of a
restaurant. In their reviews, people often mention entities or events that are
not associated with the restaurant, such as "our office" in the first review,
or "the farmer’s market" in the third review, and these phrases should not be
extracted either. Thus, it is important that the noun phrase refers to an
aspect that is associated with the reviewed restaurant, and that at the same
time is atypical of restaurants (or unexpected for a restaurant). Finally,
while Table 1 may induce the perception that atypical aspects are common, the
opposite is actually true. As will be detailed in Section 3 below, it takes
going through at least 50 reviews in order to find one review that mentions an
atypical aspect. The difficulty of manually finding this "needle in a
haystack" further motivates the development of automated approaches for
surprising aspect extraction.

##  3 Manually Annotated Datasets

We used the Yelp dataset [20] as a source of reviews for the 3 target
categories: Restaurant ($\sim$5M reviews), Hotel ($\sim$190K reviews), and
Hair Salon ($\sim$115K reviews). Because most aspects are expressed as nouns
and less frequently as verbs, we use spaCy [21] to collect lemmas of all nouns
and verbs and compute their frequencies for each domain. We rank words in
ascending order based on their counts and filter out words that appear with
very low frequency, e.g., less than 10 times for the Restaurant domain, as
these tend to be spelling mistakes or interjections that are purposely
misspelled for extra emphasis, e.g., "amaazzing". We then consider the
remaining rare words in ascending order of their frequency as candidate
atypical words, extract the reviews that mention them, and read these reviews
to determine which occurrences truly refer to an atypical aspect. When reading
a review, all atypical aspects are annotated, not only the ones corresponding
to the search word. Notwithstanding the heuristic selection of reviews based
on the occurrence of rare words, overall this was still a very time-consuming
process, because rare words very often appear in a review without necessarily
referring to atypical aspects. For example, out of the 43 restaurant reviews
that contain the lemma "poncho", in only 1 review the word "ponchos" was
deemed to refer to an atypical aspect (the restaurant was selling them). The
other 42 reviews contained references to ponchos that were not associated with
the restaurants itself, e.g. staff helping customers put their ponchos on a
rainy day, or customers describing their arrival at the restaurant on a rainy
day. As we went down the list of rare words, their frequency increased,
resulting in a larger number of reviews to skim through for each rare word.
Overall, for the Restaurant dataset, we used as search words the rare words
that appeared with a frequency of up to 187. Upon semi-automatically sifting
through the $\sim$97K reviews found to contain these words, we were able to
collect 114 reviews that contained atypical aspects. On average, one hour of
following this process led to finding between 2 and 3 reviews containing
atypical aspects for the restaurant category, whereas for the hair salon
category it took on average two hours to find 1 atypical reviews. Henceforth
the term atypical review will be used to refer to a review that contains one
or more atypical aspects; analogously, the term typical review will be used to
refer to reviews that do not contain any atypical aspect.

As illustrated in the examples from Section 2, we organize annotations of
atypical aspects on two layers:

  * •

A primary layer that contains atypical aspects that are clearly not connected
to any core feature of that domain.

  * •

A secondary layer that contains atypical aspects that are related to a typical
aspect, such as ambiance or location, but that stand out and are interesting
on their own, separate from the core features of the domain.

For example, ’I was even encouraged to visit their petting zoo in the back’
would be considered a primary atypical aspect in any of the 3 categories,
whereas ’There is an interesting giant stuffed spider that goes up and down
when the door leading to the bathrooms opens and closes’ would be annotated as
a secondary atypical aspect.

Table 2 shows summary statistics for the 3 datasets, one for each domain
(category), split between data used for training and testing, and data used
for development. Under the Primary column, we show the number of atypical
reviews and atypical aspect annotations contained in them. The next column
shows the same statistics for when both primary and secondary atypical aspects
are considered. The total number of reviews in each dataset, shown in the
third column, is about double the number of primary atypical reviews,
reflecting a balanced dataset where the number of typical reviews was selected
to be about the same as the number of atypical reviews.

We computed inter-annotator agreement (ITA) on both the extractive and
abstractive annotations in the development sets of the Restaurant and Hair
Salon domains. The ITA metrics are shown in Table 3 and are calculated by
assuming one annotator provides the ground truth while the other annotator is
considered as the system.

Table 2: Statistics for the 3 datasets, split between Train+Test and Development (Dev). The number of atypical reviews and atypical aspects are presented separately for primary (Primary) vs. both primary and secondary atypical aspects ($+$ Secondary). Domain | Dataset split |  | Primary
---
|  $+$ Secondary
---
| Total
---
|  | # reviews | # aspects | # reviews | # aspects | reviews
Restaurant | Train+Test | 100 | 253 | 107 | 340 | 200
Dev | 14 | 32 | 16 | 46 | 28
Hotel | Train+Test | 69 | 274 | 85 | 401 | 150
Dev | 10 | 33 | 11 | 49 | 20
Hair Salon | Train+Test | 45 | 147 | 48 | 181 | 90
Dev | 5 | 24 | 5 | 29 | 10

##  4 LM-based Approaches

This section describes our Language Model (LM) based approaches to detecting
surprising aspects in customer reviews. We experimented with 2 language
models: Flan-T5 and ChatGPT. The 3 billion parameter FLAN-T5 is an encoder-
decoder transformer based on the T5 model [22] that was further instruction-
tuned on the FLAN dataset [11, 12]. We decided to use the FLAN-T5 model due to
its exposure to narratives in the style of reviews, e.g., blog posts, during
pre-training on the C4 corpus [22], and also due to its instruction-tuning on
summarization and sentiment analysis tasks. We also experimented with zero-
shot and few-shot prompting of the much larger ChatGPT (gpt-3.5) [13] in order
to evaluate the performance of a state-of-the-art language model without any
fine tuning.

LMs are known to be sensitive to word choices [23]. In the case of zero-
shot/few-shot experiments, we tried between 10 and 20 different prompts for
each type of annotation and selected the ones that performed the best on the
development data. We noticed that, given the description of the task along
with examples of typical aspects in the prompt helped model to identify the
multiple atypical aspects present in a review. We also observed that the more
examples of typical aspects were given in the prompt the easier it was for the
model to identify atypical aspects. We also had to try multiple prompt
formulations to instruct the LM to align with an expected output format. For
5-shot experiments, various sets of 5 examples from the development set were
first selected at random, then manually checked for diversity in terms of
difficulty, number, and types of atypical aspects. Of these, we selected the
5-shot examples that yielded the highest performance on the development set.

With the exception of abstractive generation for Hotels, which did not benefit
from a prompt, the FLAN-T5 fine-tuning experiments employed the following
prompts:

  * $\blacktriangleright$

Fine-tuning FLAN-T5 Extractive Prompt: question: Based on the following
restaurant review, list aspects that are atypical for a restaurant. Separate
them using commas. context: {{Review}}

  * $\blacktriangleright$

Fine-tuning FLAN-T5 Abstractive Prompt: question: Based on the following
restaurant review, what are the atypical aspects for a restaurant? context:
{{Review}}

In the 0-shot setup for ChatGPT, we include an instruction to either extract
lists of atypical aspects (extractive) or to generate naturally sounding text
about the atypical aspects in the review (abstractive):

  * $\blacktriangleright$

0-shot ChatGPT Extractive Prompt: Given the following restaurant review, can
you list atypical aspects for a restaurant? Atypical aspects are not related
to service, food, drinks, location, price, menu, discounts, policies, staff,
customer satisfaction, or other items commonly associated with a restaurant.
Please be precise in your response; it should contain only atypical aspects
associated with the restaurant that is reviewed. Extract base noun phrases in
the output format: ’Atypical aspects: aspect 1, aspect 2, aspect 3.’ Output
$\langle$None$\langle$ if there are no atypical aspects. Please follow the
output format strictly.
Passage:  {{Review}}

  * $\blacktriangleright$

0-shot ChatGPT Abstractive Prompt: Which aspects mentioned in the review are
atypical for a restaurant? Unlike common aspects such as service, food,
drinks, location, price, menu, discounts, policies, staff, or customer
satisfaction, atypical aspects are not commonly associated with a restaurant.
In the output, formulate each aspect as sentences, e.g., "Atypical aspects: –
The restaurant has $\langle$aspect 1$\rangle$. – The restaurant has
$\langle$aspect 2$\rangle$. – The restaurant has $\langle$aspect 3$\rangle$."
If there are no atypical aspects, output "None".
Passage:  {{Review}}

In the few-shot setup for ChatGPT, we include in the prompt both the
instruction and 5 worked-out examples:

  * $\blacktriangleright$

Few-shot ChatGPT Extractive and Abstractive Prompt: Given the following
restaurant review, can you list atypical aspects for a restaurant? Atypical
aspects are not related to service, food, drinks, location, price, menu,
discounts, policies, staff, customer satisfaction or other types of items that
are commonly associated with a restaurant. Please be precise in your response,
which should contain only atypical aspects that are associated with the
restaurant that is reviewed. Output  <None> if there are no atypical aspects.

    * Example 1: {{Example Review 1}} Atypical aspects: {{comma-separated extractive annotations OR bullet-listed abstractive sentences}} … Examples 2, 3, 4, 5

    * Can you try for the review below? {{Review}}

We use the Hugging Face Transformers package [24] for fine-tuning Flan-T5 with
the following hyper-parameters: an effective batch size of 32, a number of
epochs of 30, a learning rate of 3e-5 for Restaurants and 5e-5 for Hotels and
Hair Salons, a weight decay of 0.001, and a generation max length set to 512.
Those hyper-parameter values were found through tuning on the development
portion of each dataset. We perform the fine-tuning experiments on a high-
performance computing cluster using $8$ CPU cores, $128$ GB RAM, and 2 A100 80
GB GPUs, for around 96 hours. We use the OpenAI API Python package [25] for
ChatGPT, where we do greedy decoding by setting the temperature parameter to
0.

##  5 Experimental Evaluations

Table 3: Extractive (exact vs. partial match) and abstractive results (%), on primary (default) and primary + secondary atypical aspects across the 3 domains. Precision (P), Recall (R), and F1 are reported for the extractive setting. F1 for Rouge-1 (R-1), Rouge-2 (R-2), rougeLsum (RLS) and BERTScore is reported for the abstractive setting. Best results in each domain are in bold. Language Model & |  |  Exact Match
---
| Partial Match
---
| Abstractive
---
Experimental Setup | P | R | F1 | P | R | F1 | R-1 | R-2 | RLS | BERT
|  |  |  | Restaurants |  |  |  |
ChatGPT (0-shot) | 22.0 | 37.7 | 27.7 | 27.9 | 56.8 | 37.4 | 35.0 | 24.0 | 52.0 | 66.0
\+ secondary | 25.1 | 35.2 | 29.3 | 32.5 | 56.0 | 41.2 | 42.0 | 29.0 | 53.0 | 68.0
ChatGPT (5-shot) | 33.0 | 43.6 | 37.6 | 39.3 | 61.7 | 48.0 | 42.0 | 31.0 | 59.0 | 71.0
\+ secondary | 26.8 | 38.9 | 31.7 | 33.5 | 60.7 | 43.2 | 46.0 | 36.0 | 57.0 | 70.0
FLAN-T5 (0-shot) | 28.9 | 23.5 | 25.9 | 32.4 | 28.7 | 30.5 | 32.0 | 24.0 | 44.0 | 54.0
\+ secondary | 27.9 | 18.5 | 22.3 | 32.3 | 23.9 | 27.4 | 30.0 | 22.0 | 44.0 | 56.0
FLAN-T5 (fine-tuned) | 67.5 | 60.2 | 63.4 | 72.9 | 65.3 | 68.6 | 58.0 | 50.0 | 73.0 | 79.0
\+ secondary | 57.7 | 58.6 | 56.4 | 64.2 | 64.4 | 62.3 | 56.0 | 48.0 | 68.0 | 75.0
Human ITA (est.) | 80.0 | 78.26 | 79.12 | 85.56 | 82.61 | 84.06 | 65.0 | 51.0 | 75.0 | 80.0
\+ secondary | 75.4 | 79.3 | 77.3 | 82.4 | 86.8 | 84.5 | 71.0 | 54.0 | 76.0 | 86.0
|  |  |  | Hotels |  |  |  |
ChatGPT (5-shot) | 30.5 | 35.2 | 32.7 | 34.8 | 46.9 | 39.9 | 34.0 | 26.0 | 56.0 | 65.0
FLAN-T5 (fine-tuned) | 60.2 | 54.9 | 55.9 | 63.8 | 57.6 | 59.0 | 34.0 | 26.0 | 59.0 | 63.0
|  |  |  | Hair Salons |  |  |  |
ChatGPT (5-shot) | 34.7 | 43.2 | 38.5 | 42.4 | 61.1 | 50.1 | 48.0 | 37.0 | 57.0 | 69.0
FLAN-T5 (fine-tuned) | 66.6 | 62.9 | 63.9 | 75.1 | 69.1 | 71.1 | 38.0 | 33.0 | 61.0 | 65.0
Human ITA (est.) | 92.3 | 82.8 | 87.3 | 94.2 | 85.1 | 89.4 | 59.0 | 41.0 | 78.0 | 91.0
\+ secondary | 74.2 | 67.6 | 70.8 | 79.0 | 71.8 | 75.3 | 65.0 | 47.0 | 77.0 | 91.0

The LM-based approaches are evaluated in a 10-fold scenario where the
Train+Test reviews dataset is partitioned into 10 folds, 9 folds are used for
training and 1 fold is used for testing. This process is repeated 10 times
until each fold in the dataset is used as a test fold. The metrics computed
across the 10 folds are then micro-averaged yielding the final evaluation
metric. For the extractive evaluation, we report the precision, recall, and
$F_{1}$ scores for the exact and partial matches of the extracted base noun
phrase (BNP) with the ground truth phrase.

In the exact match method, an extracted phrase is considered correct if and
only if it matches exactly a ground truth (gold) phrase. Precision (P) and
Recall (R) are then computed as follows:

  * $P=\\#\mbox{\it{correct extracted BNPs}}\;/\;\\#\mbox{\it{extracted BNPs}}$

  * $R=\\#\mbox{\it{correct extracted BNPs}}\;/\;\\#\mbox{\it{gold BNPs}}$

In the partial match method, we use the greedy method shown in Algorithm 1 to
compute a bipartite matching between gold phrases $gp$ and extracted phrases
$ep$ that aimed at maximizing their word overlap $|ep\cap gp|$ in total. The
overlaps between extracted and gold phrases are then used to compute
precision, recall, and $F_{1}$.

1

Input : Gold Phrases $GP$, Extracted Phrases $EP$

Output : Precision (P), Recall (R), and $F_{1}$

2 // $TPe$ = # True Positives w.r.t $EP$

3 // $TPg$ = # True Positives w.r.t $GP$

4 // $FP$ = # False Positives

5 // $FN$ = # False Negatives

6 for  _gp in GP_ do

7 if  _EP is empty_ then

8 $FN\leftarrow FN+|gp|/|gp|$

9 else

10 Find $ep\in EP$ that has maximum Jaccard similarity with $gp$

11 $TPe\leftarrow TPe+|ep\cap gp|/|ep|$

12 $TPg\leftarrow TPg+|ep\cap gp|/|gp|$

13 $FP\leftarrow FP+|ep-gp|/|ep|$

14 $FN\leftarrow FN+|gp-ep|/|gp|$

15

16 Remove $ep$ from the set $EP$

17for  _ep in EP_ do

18 $FP\leftarrow FP+|ep|/|ep|$

19$P\leftarrow TPe/(TPe+FP)$, $R\leftarrow TPg/(TPg+FN)$

return _$P,\;R,\;F_{1}\leftarrow 2PR/(P+R)$_

Algorithm 1 PartialMatchMetrics($GP$, $EP$)

For the abstractive evaluation, we follow prior work in summarization [26, 27,
28] and compare the generated output with the ground truth using BERT F1 Score
[29] instantiated with DeBERTa [30], Rouge-1, Rouge-2, and Rouge-L-Sum [31].
In the case of typical reviews, the prediction, i.e. the generated text,
should be empty, reflecting no atypical aspect. When using RougeLsum and
BERTScore to evaluate the model output on a typical review, $F_{1}$ is
calculated as 1.0 if the model generates an empty text, and 0.0 if it
generates a non-empty text.

The overall experimental results are shown in Table 3. For Restaurants, we
show results on extracting primary atypical aspects as well as results on
extracting both primary and secondary atypical aspects. Since fine-tuned
Flan-T5 and ChatGPT (5-shot) obtained the best results on Restaurants, they
were selected to be evaluated on the other two domains, using solely primary
atypical aspects. Fine-tuning FLAN-T5 yields the best performance in the
extractive task across all domains. While we observe a big performance gap
between ChatGPT and fine-tuned FLAN-T5 in the extractive setting, that gap
shrinks considerably in the abstractive setting for Hotels and Hair Salons,
where ChatGPT (5-shot) occasionally outperforms FLAN-T5 on some of the
metrics. For both LMs, the Hotel domain appears to be more challenging.
Compared to the other domains, atypical aspects are more common and more
diverse in hotels, likely because hotels try to differentiate themselves from
other hotels more than restaurants or hair salons do. Table 2 shows that
indeed there are more primary and secondary atypical aspects per review in the
hotel domain.

To determine how well Flan-T5 generalizes to unseen atypical aspects in the
Restaurant domain, we manually created groupings of atypical aspects where
semantically similar atypical aspects, e.g. greeting cards and anniversary
gifts, are grouped together, such that aspects in different groups are
semantically very different. We then partition the set of groups into 10 folds
of groups, which ensures that the atypical aspects that the language model
sees in the test fold have not been seen during training (either literally or
semantically similar). Upon fine-tuning and evaluating FLAN-T5 on this
dataset, we observe a similar precision as reported in Table 3, however, there
is a significant drop in recall from 60.2 to 46.1 for primary atypical aspects
and from 58.6 to 49.3 when extracting both primary and secondary atypical
aspects. Improving generalization to semantically novel atypical aspects is
therefore an interesting avenue for future work.

To get a sense of the real performance in the abstractive setting for primary
aspects, we also performed a manual evaluation of the fine-tuned Flan-T5 and
5-shot ChatGPT outputs. To enable calculation of precision and recall, we
manually label and count the following: (A) Atypical aspects from the model
output that are semantically similar to gold aspects; (B) Gold aspects that
are missing from the model output; (C) Typical aspects or other types of
entities that should not have been extracted as atypical; (D) Extra details
about atypical aspects; (E) Secondary atypical aspects; (F) Typical reviews
for which the model correctly generates an empty string. The first 4 types are
illustrated on the example below, where A = 2, B = 1, C = 1, D = 1, and E = 1:

  * •

Gold = ["On the weekends kids can experience ’Mark the Balloon Guy’ at the
restaurant. They have stuffed animal/puppets for sale at the front.B", "The
restaurant has therapeutic sketching at every table."]

  * •

Output = ["The restaurant has a balloon artist on weekends.A The restaurant
has traditional wooden baseball stadium seats for waiting.E", "The restaurant
offers therapeutic sketching at every table.A If your sketch is good, it will
be on the wall.D The restaurant has limited menu options before 4:30 pm.C"]

These counts are then used to compute a lenient precision as $P=(A+F)/(A+F+C)$
and a strict precision as $P=(A+F)/(A+F+C+D+E)$, whereas recall is computed as
$R=(A+F)/(A+F+B)$. Correspondingly, the fine-tuned Flan-T5 obtains a lenient
and strict $F_{1}$ of 77.5% and 76.5%, respectively, whereas ChatGPT obtains a
lenient and strict $F_{1}$ of 71.3% and 65.9%, respectively. Looking at Table
3, the strict $F_{1}$ is in between RLS and BERT, further supporting the use
of these automated metrics. Overall, manual evaluation shows that models
perform better in the abstractive vs. extractive setting.

Error analysis reveals that fine-tuned Flan-T5 is more succinct in its
answers, leading it to sometimes ignore atypical aspects in its response.
Conversely, ChatGPT tends to be more verbose, often generating unnecessary
details about the atypical aspects that it extracts, or mistaking typical for
atypical aspects. For instance, ChatGPT extracted a food-related aspect in the
second sentence in "The restaurant has an annual Valentine’s Date Night with
table service, a caricature artist, and a piano player. The restaurant offers
in-house made chocolate-covered strawberries.". ChatGPT also tends to extract
one-time customer experiences which are not atypical aspects of a restaurant,
as shown in the second sentence in "The restaurant has a sister restaurant
next door with a lively fun band. The server, Peter, gave very helpful
suggestions.". On the other hand, fine-tuned FLAN-T5 mistakenly considers
"farmer’s market" to be an atypical aspect in the third review from Table 1.
Also, when the sole atypical aspect of a business is in its proximity, the
fine-tuned FLAN-T5 tends to not extract it, as in the model failing to
generate the ground truth abstractive sentences "They are close to a dock area
where customers can board paddle cruises." , "Customers can catch an airboat
ride down the road."

##  6 Related Work

Addressing overchoice is a core focus of recommender systems and it is
typically addressed by recommending between 5 to 20 attractive and diverse
items [32], based on user preferences [33, 34], user ratings, item attributes,
or user reviews [35, 36, 37]. Recommending items with potential for
serendipity is one way of diversifying an item set. In [38], unexpectedness is
defined as the distance of an item from a set of obvious items for that user,
relative to the user’s preferred level of unexpectedness. Li et al. [39]
recommended unexpected items by modeling user interests as clusters of
historical data in a latent space and calculating the weighted distance
between a new item and the clusters of interests. Kotkov et al. [40] crowd-
sourced serendipity labels for a movie dataset using multiple definitions of
serendipity.

User reviews have been used to learn latent features of users [37], extract
sentiment [36], derive user preferences [34], or to perform aspect-based
sentiment analysis in order to recommend better quality products with aspects
relevant to the user [35]. Conversational recommender systems use reviews to
provide explanations [41], to maintain fluency in conversation [42], or to
understand the user’s requirements by asking questions about aspects mentioned
in reviews [43].

Aspect-based sentiment analysis (ABSA) is a technique that aims to extract
topic-specific aspects mentioned in a review, together with any associated
sentiment. There are different approaches to extracting aspect terms, with
some focusing on using term frequency in the corpus [44, 45] or using semantic
clustering of prominent aspects [46]. Qiu et al. [47] only extract aspects
that have an expressed opinion, using expanded opinion lexicons containing
adjectives. As detailed at the end of Section 2, extracting atypical aspects
cannot be addressed simply as the logical complement of ABSA.

Prior work investigated using Language Models (LMs) in recommender systems.
Zhang et al. [48] investigate using LMs as a recommender system by formulating
a movie recommendation task as a multi-token cloze task and find that LMs
underperform traditional recommender systems such as GRU4Rec in both zero-shot
and fine-tuned settings. LMs have also been used to elicit user preferences in
natural language given historical interactions and prior selections for more
personalized recommendations [49]. Such a model can benefit a complete
implementation of the system illustrated in Figure 1, where it would
automatically infer Jane’s interests. Furthermore, LMs have been used for
explaining why a specific recommendation was made to the user [50].

Atypical aspects are valuable due to their potential to create serendipity,
i.e. experiences that are both unexpected (surprising) and relevant (positive)
for the user. Unlike Kotkov et al. [40], we do not consider novelty to be a
required dimension of serendipity. Finally, surprise can appear from other
sources, be it the experience of a typical aspect that stands out (such as a
unique dish offered by a restaurant), or the accidental discovery of a
restaurant as shown in the first sentence in Table 1 and studied in [51]. All
of these different sources of surprise have great potential for setting up
serendipity.

##  7 Conclusion and Future Work

We introduced the new task of extracting atypical aspects from customer
reviews. To enable training and evaluation of atypical aspect extraction
models, we manually annotated two layers of atypical aspects in customer
reviews from three domains. While experimental evaluations using few-shot
prompting of ChatGPT and fine-tuning of Flan-T5 show promising results, there
is still a substantial gap relative to human performance, as shown by the
higher ITA. Future work includes enhancing reproducibility by using open-
source LMs [52], prototyping a recommender system that leverages atypical
aspects, and a user study verifying their utility.

To facilitate reproducibility and future progress, we make the code and the
datasets publicly available at https://github.com/smitanannaware/XtrAtA.

###### Acknowledgements.

This research was partly supported by the United States Air Force (USAF) under
Contract No. FA8750-21-C-0075.

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SV}_{w,i}(z,\bar{z})$, where $w$ labels its element, and an extra index $i$
distinguishes different basis elements with the same weight. The range of $i$
depends on the value of $w$, and its specific counting up to weight $6$ can be
found in, e.g. Table 1 of [26].

We also further divide the basis into two disjoint sets, according to whether
the letter $z-\bar{z}$ is contained in their symbols. Those without
$z-\bar{z}$ are in fact known as single-valued harmonic polylogarithms
(SVHPLs) [55, 56], and correspondingly we also denote them as $H^{\rm
SV}_{w,i}\equiv G^{\rm SV}_{w,i}$. Up to weight $2$ these elements can be
selected as

$\begin{split}&H_{0,1}^{\rm SV}=1,\quad H_{1,1}^{\rm SV}=\log{u},\quad
H_{1,2}^{\rm SV}=\log{v},\\\ &H_{2,1}^{\rm SV}=\zeta_{2},\quad H_{2,2}^{\rm
SV}=\log^{2}{u},\quad H_{2,3}^{\rm SV}=\log{u}\log{v},\quad H_{2,4}^{\rm
SV}=\log^{2}{v},\\\ &H_{2,5}^{\rm SV}\equiv
W_{2}(z,\bar{z})=\mathrm{Li}_{2}(z)-\mathrm{Li}_{2}(\bar{z})+\frac{1}{2}\log{u}\log\frac{1-z}{1-\bar{z}}.\end{split}$
(A.7)

In the above expression we explicitly see that some of the basis elements at a
given weight can be simply constructed from products of $H^{\rm SV}$’s at
lower weights. On the other hand, we name elements with $z-\bar{z}$ as
$Q_{w,i}$. They do not show up until weight $3$. At weight $3$ there is a
unique element of this type, $Q_{3}\equiv Q_{3,1}$ (up to additive terms whose
symbols are free of the letter $z-\bar{z}$). A choice of $Q_{3}$ that is
convenient for the presentation of $\mathcal{H}^{(2)}$ was already listed in
(4.25). At weight $4$ two of the $Q$ elements can be identified as products

$Q_{4,1}=Q_{3}H^{\rm SV}_{1,1},\quad Q_{4,2}=Q_{3}H^{\rm SV}_{1,2},$ (A.8)

and in addition to these there are three new elements $Q_{4,3}$, $Q_{4,4}$ and
$Q_{4,5}$. $Q$ elements at higher weights are not needed except for
$Q_{6,1}=\zeta_{3}\mathcal{Q}_{3}$. In summary, our SVMPL basis $G^{\rm SV}$
includes

$G^{\rm SV}\equiv H^{\rm
SV}\sqcup\\{\mathcal{Q}_{3},\mathcal{Q}_{4,1},\mathcal{Q}_{4,2},\mathcal{Q}_{4,3},\mathcal{Q}_{4,4},\mathcal{Q}_{4,5},\mathcal{Q}_{6,1}\\}.$
(A.9)

We use $G^{\rm SV}_{A}(z,\bar{z})$ to denote functions in $G^{\rm SV}$, and we
use $\sum_{A\leq n}$ to represent sum over all possible $G^{\rm
SV}_{A}(z,\bar{z})$ with weight $w\leq n$.

Our computation of both MPLs and their symbols utilizes the PolyLogTools
Mathematica package introduced in [53].

##  Appendix B Analytic result of the one-loop reduced correlator

This appendix contains the analytic expression for the full one-loop reduced
correlator $\mathcal{H}^{(2)}$. In terms of the color factors defined in
Section 4.1 it is decomposed as

$\mathcal{H}^{(2)}(z,\bar{z})=\mathtt{d}_{st}\mathcal{H}^{(2)}_{st}(z,\bar{z})+\mathtt{d}_{su}\mathcal{H}^{(2)}_{su}(z,\bar{z})+\mathtt{d}_{tu}\mathcal{H}^{(2)}_{tu}(z,\bar{z})+a_{0}\mathcal{H}^{(2)}_{\rm
c},$ (B.1)

where the counterterm $\mathcal{H}^{(2)}_{\rm c}$ was already recorded in
(4.19). Bose symmetry implies that the three components are related by

$\displaystyle\mathcal{H}^{(2)}_{st}(z,\bar{z})$
$\displaystyle=\mathcal{H}^{(2)}_{su}\left(\frac{z}{z-1},\frac{\bar{z}}{\bar{z}-1}\right),$
(B.2a) $\displaystyle\mathcal{H}_{tu}^{(2)}(z,\bar{z})$
$\displaystyle=\frac{u^{3}}{v^{3}}\mathcal{H}_{su}^{(2)}(1-z,1-\bar{z}).$
(B.2b)

Therefore it suffices to explicitly give the analytic result for one of the
components. In the following we provide the expression for
$\mathcal{H}_{su}^{(2)}(z,\bar{z})$, organized by transcendental weights. For
convenience we use the variable $y\equiv u-v$ and $\delta\equiv\bar{z}-z$. At
weight $4$

$\begin{split}&\left.u^{-3}\mathcal{H}_{su}^{(2)}(z,\bar{z})\right|_{\text{weight
}4}=\\\
&\left(-\frac{7+11y}{4\delta^{3}}+\frac{67+165y+261y^{2}+163y^{3}}{12\delta^{5}}-\frac{5(1+y)^{3}(27-30y+47y^{2})}{12\delta^{7}}\right.\\\
&\left.\quad+\frac{35(1-y)^{2}(1+y)^{5}}{4\delta^{9}}\right)W_{4}(z,\bar{z}).\end{split}$
(B.3)

At weight $3$

$\begin{split}&\left.u^{-3}\mathcal{H}_{su}^{(2)}(z,\bar{z})\right|_{\text{weight
}3}=\\\
&\left(-\frac{8}{9\delta^{2}}+\frac{129+318y+317y^{2}}{36\delta^{4}}-\frac{5(1+y)^{2}(5-4y+10y^{2})}{3\delta^{6}}+\frac{35(1-y)^{2}(1+y)^{4}}{4\delta^{8}}\right)W_{3}(z,\bar{z})\\\
&+\left(-\frac{1}{8\delta}-\frac{1-27y^{2}}{18\delta^{3}}-\frac{1-26y^{2}+49y^{4}}{12\delta^{5}}+\frac{5(1-y^{2})^{2}(1+5y^{2})}{6\delta^{7}}-\frac{35(1-y^{2})^{4}}{24\delta^{9}}\right)\\\
&\quad\times\left(Q_{3}(z,\bar{z})-W_{2}(z,\bar{z})\log{u}+\frac{1}{2}W_{2}(z,\bar{z})\log{v}\right)\\\
&+\left(-\frac{2+15y}{36\delta^{3}}-\frac{7+27y-63y^{2}-155y^{3}}{72\delta^{5}}+\frac{5(1+y)^{2}(6-13y+30y^{2}-23y^{3})}{36\delta^{7}}\right.\\\
&\left.\qquad-\frac{35(1-y)^{3}(1+y)^{4}}{24\delta^{9}}\right)W_{2}(z,\bar{z})\log{u}.\end{split}$
(B.4)

At weight $2$

$\begin{split}&\left.u^{-3}\mathcal{H}_{su}^{(2)}(z,\bar{z})\right|_{\text{weight
}2}=\\\
&\left(-\frac{19}{96\delta}+\frac{271+486y+405y^{2}}{216\delta^{3}}-\frac{407+364y+654y^{2}+884y^{3}+643y^{4}}{144\delta^{5}}\right.\\\
&\left.\quad+\frac{(1-y^{2})^{2}(411+280y+295y^{2})}{72\delta^{7}}-\frac{377(1-y^{2})^{4}}{288\delta^{9}}\right)W_{2}(z,\bar{z})\\\
&+\left(-\frac{83+165y}{432\delta^{2}}+\frac{231+479y+893y^{2}+645y^{3}}{432\delta^{4}}-\frac{5(1+y)^{3}(33-42y+53y^{2})}{144\delta^{6}}\right.\\\
&\left.\qquad+\frac{35(1-y)^{2}(1+y)^{5}}{48\delta^{8}}\right)\log{u}\left(\log{u}-\log{v}\right)\\\
&+\left(\frac{75+157y}{108\delta^{4}}-\frac{5(3+3y+8y^{2}+8y^{3})}{9\delta^{6}}+\frac{35(1-y)^{2}(1+y)^{3}}{12\delta^{8}}\right)\log{u}\log{v}.\end{split}$
(B.5)

At weight $1$

$\begin{split}&\left.u^{-3}\mathcal{H}_{su}^{(2)}(z,\bar{z})\right|_{\text{weight
}1}=\\\
&\left(\frac{31}{48\delta^{2}}+\frac{365+160y-3297y^{2}}{432\delta^{4}}-\frac{365+1858y-2223y^{4}}{144\delta^{6}}+\frac{1217(1-y^{2})^{3}}{144\delta^{8}}\right)\log{u}\\\
&+\left(-\frac{163-1941y}{864\delta^{2}}-\frac{773-1105y-2761y^{2}+7533y^{3}}{864\delta^{4}}\right.\\\
&\left.\qquad+\frac{(1-y)^{2}(505+1503y+4079y^{2}+3081y^{3})}{288\delta^{6}}-\frac{1217(1-y)^{4}(1+y)^{3}}{288\delta^{8}}\right)\left(\log{u}-\log{v}\right).\end{split}$
(B.6)

And finally at weight $0$

$\begin{split}&\left.u^{-3}\mathcal{H}_{su}^{(2)}(z,\bar{z})\right|_{\text{weight
}0}=\frac{43}{24\delta^{2}}+\frac{56-28y-471y^{2}}{54\delta^{4}}+\frac{499(1-y^{2})^{2}}{72\delta^{6}}.\end{split}$
(B.7)

##  Appendix C Bulk-point limit

In the bulk-point limit $\mathcal{H}^{(3)}$ is expected to match the flat-
space four-point scattering amplitude $\mathcal{A}^{\text{2-loop}}$ of the
maximal supersymmetric Yang–Mills (SYM) in 8d [13]. This comparison in the
physical region should provide non-trivial constraints to our bootstrap
computation at two loops. For convenience of this comparison we define a
reduced amplitude $\tilde{\mathcal{A}}^{\text{2-loop}}$ by

$\mathcal{A}^{\text{2-loop}}=stA_{1234}^{\rm
tree}\tilde{\mathcal{A}}^{\text{2-loop}},$ (C.1)

where $A_{1234}^{\rm tree}$ is the so-called partial amplitude with cyclic
ordering $(1234)$ appearing in the color trace decomposition of the tree-level
SYM amplitude ($T^{I}$ being generators in the adjoint representation of the
color group)

$\mathcal{A}^{\rm tree}=\sum_{\rho\in
S_{4}/Z_{4}}\mathrm{Tr}\quantity(T^{I_{\rho(1)}}T^{I_{\rho(2)}}T^{I_{\rho(3)}}T^{I_{\rho(4)}})A_{\rho}^{\rm
tree}.$ (C.2)

The combination $stA_{1234}^{\rm tree}$ is invariant under $S_{4}$ permutation
of the particles and encodes the full dependence on the polarization vectors,
so that the reduced amplitude $\tilde{\mathcal{A}}^{\text{2-loop}}$ is a
permutation invariant scalar quantity.

As studied in [57] by unitarity cuts in generic dimensions, the two-loop four-
point maximal SYM amplitude receives a decomposition onto planar and non-
planar double boxes. In terms of the reduced amplitude
$\tilde{\mathcal{A}}^{\text{2-loop}}$ and the color structures defined in
Section 5.1 this decomposition reads

$\begin{split}\tilde{\mathcal{A}}^{\text{2-loop}}=&\mathtt{e}_{s_{1}}\,sI_{1234}^{\rm
pdb}+\mathtt{e}_{s_{2}}\,sI_{1243}^{\rm
pdb}+\mathtt{e}_{t_{1}}\,tI_{1432}^{\rm
pdb}+\mathtt{e}_{t_{2}}\,tI_{1423}^{\rm
pdb}+\mathtt{e}_{u_{1}}\,uI_{1324}^{\rm
pdb}+\mathtt{e}_{u_{2}}\,uI_{1342}^{\rm pdb}\\\
&+2\mathtt{f}_{s}\,sI_{1234}^{\rm ndb}+2\mathtt{f}_{t}\,tI_{1423}^{\rm
ndb}+2\mathtt{f}_{u}\,uI_{1324}^{\rm nbd}.\end{split}$ (C.3)

Here $I_{abcd}^{\rm pdb}$ and $I_{abcd}^{\rm ndb}$ are Feynman integrals
associated to planar and non-planar double boxes, defined by

$\begin{split}I_{abcd}^{\rm pdb}&=\parbox{85.35826pt}{ \leavevmode\hbox
to75.44pt{\vbox to47.75pt{\pgfpicture\makeatletter\hbox{\hskip
37.75964pt\lower-23.87704pt\hbox to0.0pt{\pgfsys@beginscope\pgfsys@invoke{
}\definecolor{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@rgb@stroke{0}{0}{0}\pgfsys@invoke{
}\pgfsys@color@rgb@fill{0}{0}{0}\pgfsys@invoke{
}\pgfsys@setlinewidth{0.4pt}\pgfsys@invoke{
}\nullfont\pgfsys@beginscope\pgfsys@invoke{ }\pgfsys@invoke{\lxSVG@closescope
}\pgfsys@endscope\hbox to0.0pt{\pgfsys@beginscope\pgfsys@invoke{
}{\pgfsys@beginscope\pgfsys@invoke{ }{{}} {}{{}}{}
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} \pgfsys@invoke{\lxSVG@closescope }\pgfsys@endscope{}{{}}{}
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{{}}\hbox{\hbox{{\pgfsys@beginscope\pgfsys@invoke{ }{{}{}{{{}{}}}{{}{}}
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}\hbox{{\definecolor{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@rgb@stroke{0}{0}{0}\pgfsys@invoke{
}\pgfsys@color@rgb@fill{0}{0}{0}\pgfsys@invoke{ }\hbox{{$b$}}
}}\pgfsys@invoke{\lxSVG@closescope }\pgfsys@endscope}}}
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\pgfsys@invoke{\lxSVG@closescope }\pgfsys@endscope}
\pgfsys@invoke{\lxSVG@closescope
}\pgfsys@endscope{}{}{}\hss}\pgfsys@discardpath\pgfsys@invoke{\lxSVG@closescope
}\pgfsys@endscope\hss}}\lxSVG@closescope\endpgfpicture}}}\\\
&\equiv\int\frac{\mathrm{d}^{8-2\epsilon}\ell_{1}}{(2\pi)^{8-2\epsilon}}\frac{\mathrm{d}^{8-2\epsilon}\ell_{2}}{(2\pi)^{8-2\epsilon}}\frac{1}{\ell_{1}^{2}(\ell_{1}+p_{a})^{2}(\ell_{1}+p_{a}+p_{b})^{2}\ell_{2}^{2}(\ell_{1}-\ell_{2})^{2}(\ell_{2}-p_{d})^{2}(\ell_{2}-p_{c}-p_{d})^{2}},\end{split}$
(C.4)

and

$\begin{split}I_{abcd}^{\rm ndb}&=\parbox{85.35826pt}{ \leavevmode\hbox
to75.44pt{\vbox to47.75pt{\pgfpicture\makeatletter\hbox{\hskip
37.75964pt\lower-23.87704pt\hbox to0.0pt{\pgfsys@beginscope\pgfsys@invoke{
}\definecolor{pgfstrokecolor}{rgb}{0,0,0}\pgfsys@color@rgb@stroke{0}{0}{0}\pgfsys@invoke{
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&\equiv\int\frac{\mathrm{d}^{8-2\epsilon}\ell_{1}}{(2\pi)^{8-2\epsilon}}\frac{\mathrm{d}^{8-2\epsilon}\ell_{2}}{(2\pi)^{8-2\epsilon}}\frac{1}{\ell_{1}^{2}(\ell_{1}+p_{a})^{2}(\ell_{1}+p_{a}+p_{b})^{2}\ell_{2}^{2}(\ell_{1}-\ell_{2})^{2}(\ell_{2}-p_{d})^{2}(\ell_{1}-\ell_{2}-p_{c})^{2}},\end{split}$
(C.5)

These integrals can be computed by solving similar integrals by in
$4-2\epsilon$ dimensions using differential equations [58, 59, 60, 61, 62],
and then lifting to $8-2\epsilon$ dimensions by dimensional recurrence
relations [63, 64, 65] 151515The authors are grateful to Lilin Yang for
sharing data for these integrals in $4-2\epsilon$ dimensions, together with a
set of master integrals needed for dimensional recursion which were selected
following [66, 67]. The dimensional recursion is performed using the
Mathematica package LiteRed [68].. In the region $s,t<0$ and $u>0$, the final
result for the planar double box integral $I_{1234}^{\rm pdb}$ in
$8-2\epsilon$ dimensions reads

$\begin{split}I_{1234}^{\rm
pdb}=&(-s)^{1-2\epsilon}\Bigg{(}\frac{1}{144}\frac{1}{\epsilon^{2}}+\frac{79+2x}{1728}\frac{1}{\epsilon}+\frac{-48+3303x+242x^{2}}{20736x}\\\
&+\frac{(1+x)(2-15x+x^{2})}{432x^{2}}\quantity(G_{0}-G_{1})+\frac{(1-6x+34x^{2}+67x^{3})\pi^{2}}{2592(x-1)x^{3}}\\\
&-\frac{1-5x+25x^{2}+3x^{3}}{216x^{3}}\quantity(G_{0,0}-G_{0,1}-G_{1,0}+G_{1,1}+\frac{5\pi^{2}}{12})\\\
&-\frac{-1+8x+17x^{2}}{108(x-1)x^{2}}\quantity(G_{0,0,0}-G_{0,0,1}-G_{0,1,0}+G_{0,1,1}+\frac{\pi^{2}}{6}\quantity(2G_{0}+G_{1})-\zeta_{3})\\\
&-\frac{3+x}{18(x-1)^{2}}\bigg{(}G_{0,0,0,0}-G_{0,0,0,1}-G_{0,0,1,0}+G_{0,0,1,1}+\frac{\pi^{2}}{6}\quantity(2G_{0,0}+G_{0,1})-\zeta_{3}G_{0}+\frac{17\pi^{4}}{360}\Big{)}\Bigg{)},\end{split}$
(C.6)

where we use the abbreviation $G_{\vec{a}}\equiv G_{\vec{a}}(x^{-1})$, and the
dimensionless parameter $x$ is related to the Mandelstam variables $s,t$ or
the scattering angle $\theta$ by

$x\equiv 1+\frac{t}{s}=\frac{1+\cos\theta}{2}.$ (C.7)

In the same region the result for the non-planar double box integral
$I_{1234}^{\rm ndb}$ reads

$\begin{split}I_{1234}^{\rm
ndb}=&(-s)^{1-2\epsilon}\Bigg{(}\frac{1}{288}\frac{1}{\epsilon^{2}}+\frac{37}{1728}\frac{1}{\epsilon}+\frac{-60-3607x+3625x^{2}-36x^{3}+18x^{4}}{51840(x-1)x}\\\
&+\frac{(-12+42x-47x^{2}+2x^{3}-63x^{4}+18x^{5})}{25920(x-1)^{2}}\quantity(G_{1}+i\pi)\\\
&-\frac{60-328x+727x^{2}-798x^{3}+399x^{4}}{25920(x-1)^{2}x^{2}}\quantity(G_{0}-G_{1})+\frac{\pi^{2}}{1728}\\\
&-\frac{30-173x+428x^{2}-600x^{3}+525x^{4}-270x^{5}+90x^{6}}{12960(x-1)^{3}x^{3}}\quantity(G_{0,0}+i\pi
G_{0})\\\
&+\frac{30-113x+160x^{2}-107x^{3}+36x^{4}+6x^{5}}{12960(x-1)x^{3}}\quantity(G_{0,1}+G_{1,0}+i\pi\quantity(G_{0}+G_{1})-\frac{\pi^{2}}{2})\\\
&+\frac{(x-1)^{3}(-30-7x+4x^{2}+9x^{3}+9x^{4})}{12960x^{3}}\quantity(G_{1,1}+i\pi
G_{1})-\frac{(3x-2)(3x-1)\zeta_{3}}{720(x-1)^{2}x^{2}}\\\
&+\frac{(2x-1)(2-5x+5x^{2})}{2160(-1+x)^{2}x^{2}}\quantity(G_{0,0,1}+G_{0,1,0}-2G_{1,0,0}+i\pi\quantity(G_{0,0}+G_{0,1}-2G_{1,0})-\frac{\pi^{2}}{2}G_{0}+\frac{i\pi^{3}}{2})\\\
&+\frac{(x-1)^{3}(2+x)}{2160x^{2}}\quantity(G_{1,0,1}+G_{1,1,0}-2G_{0,1,1}+i\pi\quantity(G_{1,0}+G_{1,1}-2G_{0,1})-\frac{\pi^{2}}{2}G_{1})\Bigg{)}.\end{split}$
(C.8)

The remaining integrals in (C.3) can be obtained from (C.6) and (C.8) by
permuting the particle labels. For readers’ convenience we also record these
results in the ancillary file. Note that the expressions from permutations may
live in different physical regions, and so before assembling them together one
needs to analytically continued the Mandelstam variables to the same region
following the standard $i\varepsilon$ prescription. For our computation we
finally lands on the region $s,t<0$ and $u>0$, in which (C.6) and (C.8)
directly apply.

In order to perform the comparison in the bulk-point limit we need to
analytically continue our ansatz for the correlator from Euclidean region to
physical region as well. Following [27], our prescription is to continue $z$
counter-clockwisely around 0 and $\bar{z}$ clockwisely around $1$, and then
set $z=\bar{z}+2\omega\bar{z}\sqrt{1-\bar{z}}$. The bulk-point limit
$z\to\bar{z}$ is then reached by setting $\omega\to 0$. As was already pointed
out in Section 5.2, when taking this limit at two loops
$[\Delta^{(4)}]^{2}\mathcal{L}^{(3)}$ dominates over the modification terms,
and the action of $\Delta^{(4)}$ reduces to a simple multiplication factor.
Therefore it suffices to compare $\mathcal{A}^{\text{2-loop}}$ with the pre-
correlator $\mathcal{L}^{(3)}$. The detailed connection between these two
objects is

$\lim_{\omega\to
0}\left.(z-\bar{z})^{5}\mathcal{L}^{(3)}\left(z^{\circlearrowleft_{0}},\bar{z}^{\circlearrowleft_{1}}\right)\right|_{z=\bar{z}+2\omega\bar{z}\sqrt{1-\bar{z}}}=\left.48\pi^{2}(1-\bar{z})^{2}\bar{z}^{6}s^{-2}\tilde{\mathcal{A}}^{\text{2-loop}}(x)\right|_{x=1/\bar{z}},$
(C.9)

Note the above relation is already expressed in terms of the reduced amplitude
$\tilde{\mathcal{A}}^{\text{2-loop}}$. Although the full amplitude
$\mathcal{A}^{\text{2-loop}}$ contains an extra factor $stA^{\rm tree}_{1234}$
including polarization vectors, in practical computation we do not have to
bother manipulating it. The reason is that comparison with the leading log
data in (5.15) already fully determines contributions of some MPLs of highest
transcendental weight, and matching them with the corresponding MPL
contributions in $\tilde{\mathcal{A}}^{\text{2-loop}}$ easily determines the
factors appearing in the above relation (C.9) (e.g., matching coefficients of
$G_{0,0,0,0}$ or $G_{1,1,1,1}$ in the limit). Comparison between the remaining
contributions then generates constraints for the undetermined variables in the
ansatz.

[46] proposed a simpler connection than (C.9), the relation between
discontinuities $\operatorname{dDisc}\mathcal{H}$ and
$\operatorname{Disc}\mathcal{A}$, in the context of graviton scattering.
Similar connection should also apply to the gluon scattering studied here.
Ideally one would not expect much difference between the comparison at the
level of the full correlator and that of the discontinuity, because in
principle the correlator $\mathcal{H}$ can be reconstructed from its double
discontinuity $\operatorname{dDisc}\mathcal{H}$ through Lorentz inversion
[47], which is the CFT counterpart of the dispersion relation relating
$\mathcal{A}$ and its discontinuity $\operatorname{Disc}\mathcal{A}$ in flat
space. However, at loop level these dispersion relations can be polluted by
the presence of finite spin contributions to the correlator/amplitude, which
imposes extra data in addition to the discontinuities. Therefore one expects
that constraints from (C.9) are stronger.

##  Appendix D Recursion of twist-4 data at $\log^{2}u$

The reduced correlator $\mathcal{H}$ can be organized in terms of power
expansions in $\log u$ in the small $u$ limit, where the power of $\log u$
goes up to $n+1$ at $n$ loops. The coefficient functions of these $\log u$
powers encode different combinations of the expansion coefficients of the CFT
data with respect to $a_{F}$, which are schematically listed in Table 2. The
goal of this appendix is to compute the combination $\langle
a_{\mathbf{a}}^{(1)}(\gamma_{\mathbf{a}}^{(1)})^{2}+2a_{\mathbf{a}}^{(0)}\gamma_{\mathbf{a}}^{(1)}\gamma_{\mathbf{a}}^{(2)}\rangle$
for twist-4 operators. This data contributes to the two-loop correlator in the
$\log^{2}u$ coefficient, as explicitly shown in (5.22), and we use them as one
of the inputs in our bootstrap algorithm. As is clear from the expression,
only tree-level and one-loop correlators are needed. Moreover, the twist-4
operators are free of operator mixing. This fact makes it possible to extract
their CFT data from just the $\mathcal{O}_{2}$ correlators alone. The angle
brackets $\langle\ldots\rangle$ will also be dropped as they are no longer
necessary in this case.

order | $a^{1}_{F}$ | $a^{2}_{F}$ | $a^{3}_{F}$ |
---|---|---|---|---
$\;\log(u)^{0}\;$ | $\langle a_{\mathbf{a}}^{(1)}\rangle$ | $\langle a_{\mathbf{a}}^{(2)}\rangle$ | $\langle a_{\mathbf{a}}^{(3)}\rangle$ |
$\log(u)^{1}$ | $\langle a_{\mathbf{a}}^{(0)}\gamma_{\mathbf{a}}^{(1)}\rangle$ | $\langle a_{\mathbf{a}}^{(1)}\gamma_{\mathbf{a}}^{(1)}+a_{\mathbf{a}}^{(0)}\gamma^{(2)}\rangle$ | $\;\langle a_{\mathbf{a}}^{(2)}\gamma_{\mathbf{a}}^{(1)}+a_{\mathbf{a}}^{(1)}\gamma_{\mathbf{a}}^{(2)}+a_{\mathbf{a}}^{(0)}\gamma_{\mathbf{a}}^{(3)}\rangle\;$ |
$\log(u)^{2}$ |  | $\langle a_{\mathbf{a}}^{(0)}(\gamma_{\mathbf{a}}^{(1)})^{2}\rangle$ | $\;\langle a^{(1)}(\gamma_{\mathbf{a}}^{(1)})^{2}+2a_{\mathbf{a}}^{(0)}\gamma_{\mathbf{a}}^{(1)}\gamma_{\mathbf{a}}^{(2)}\rangle\;$ |
$\log(u)^{3}$ |  |  | $\;\langle a_{\mathbf{a}}^{(0)}(\gamma_{\mathbf{a}}^{(1)})^{3}\rangle\;$ |
Table 2: The OPE data encoded in the coefficient functions of different $\log
u$ powers for correlators up to two loops.

The most efficient way to extract the CFT data from explicit correlators is to
use the Lorentzian inversion formula [47]. Applying it to the tree-level
correlator $\mathcal{H}^{(1)}$ as well as the $a_{F}^{1}$ term in
$\mathcal{G}_{0}$, we obtain the following data for the twist-4 operator with
spin $\ell$

$\displaystyle a_{\mathbf{a}}^{(0)}\gamma_{\mathbf{a}}^{(1)}=$
$\displaystyle(-\mathtt{c}_{t}+(-1)^{\ell}\mathtt{c}_{u})_{\mathbf{a}}\
\frac{2\Gamma(\ell+3)^{2}}{\Gamma(2\ell+5)}\;,$ (D.1) $\displaystyle
a_{\mathbf{a}}^{(1)}=$
$\displaystyle(-\mathtt{c}_{t}+(-1)^{\ell}\mathtt{c}_{u})_{\mathbf{a}}\
\frac{\Gamma(\ell+3)^{2}}{\Gamma(2\ell+5)}\left[2\psi^{(0)}(\ell+3)-2\psi^{(0)}(2\ell+5)+\frac{1}{2}\right]\;.$
(D.2)

Here for the color part $(\\#)_{\mathbf{a}}$ is defined by projectors as in
(2.20). Similarly, from the one-loop correlator $\mathcal{H}^{(2)}$, we can
extract the following combinations

$\displaystyle a_{\mathbf{a}}^{(0)}(\gamma_{\mathbf{a}}^{(1)})^{2}=$
$\displaystyle(\mathtt{d}_{st}+(-1)^{\ell}\mathtt{d}_{su})_{\mathbf{a}}\
\frac{\Gamma(\ell+3)^{2}}{\Gamma(2\ell+5)}\frac{8}{(\ell+1)(\ell+4)}\;,$ (D.3)
$\displaystyle\begin{split}a_{\mathbf{a}}^{(1)}\gamma_{\mathbf{a}}^{(1)}+a_{\mathbf{a}}^{(0)}\gamma_{\mathbf{a}}^{(2)}=&(\mathtt{d}_{st}+(-1)^{\ell}\mathtt{d}_{su})_{\mathbf{a}}\
\frac{\Gamma(\ell+3)^{2}}{\Gamma(2\ell+5)}\left[-\frac{4\left(2\ell^{3}+23\ell^{2}+65\ell+32\right)}{\ell(\ell+1)^{2}(\ell+4)^{2}(\ell+5)}\right.\\\
&\qquad+\left.\frac{2\left(12\psi^{(0)}(\ell+3)-12\psi^{(0)}(2\ell+5)+11\right)}{3(\ell+1)(\ell+4)}\right]\\\
&-(1+(-1)^{\ell})(\mathtt{d}_{tu})_{\mathbf{a}}\
\frac{\Gamma(\ell+3)^{2}}{\Gamma(2\ell+5)}\frac{2\left(5\ell^{2}+25\ell+24\right)}{3\ell(\ell+1)(\ell+4)(\ell+5)}\;.\end{split}$
(D.4)

By comparing (D.1) and (D.3), we get

$\gamma_{\mathbf{a}}^{(1)}=(-\mathtt{c}_{t}+(-1)^{\ell}\mathtt{c}_{u})_{\mathbf{a}}\
\frac{2}{(\ell+1)(\ell+4)}\;.$ (D.5)

We could also solve for
$a_{\mathbf{a}}^{(0)},a_{\mathbf{a}}^{(1)},\gamma_{\mathbf{a}}^{(2)}$.
However, to compute the wanted data it is sufficient to consider the following
combination

$a_{\mathbf{a}}^{(1)}(\gamma_{\mathbf{a}}^{(1)})^{2}+2a_{\mathbf{a}}^{(0)}\gamma_{\mathbf{a}}^{(1)}\gamma_{\mathbf{a}}^{(2)}=2\left(a_{\mathbf{a}}^{(1)}\gamma_{\mathbf{a}}^{(1)}+a_{\mathbf{a}}^{(0)}\gamma_{\mathbf{a}}^{(2)}\right)\left(\gamma_{\mathbf{a}}^{(1)}\right)-\left(a_{\mathbf{a}}^{(1)}\right)\left(\gamma_{\mathbf{a}}^{(1)}\right)^{2}\;,$
(D.6)

and get

$\begin{split}{}&a_{\mathbf{a}}^{(1)}(\gamma_{\mathbf{a}}^{(1)})^{2}+2a_{\mathbf{a}}^{(0)}\gamma_{\mathbf{a}}^{(1)}\gamma_{\mathbf{a}}^{(2)}\\\
=&-(1+(-1)^{\ell})(\mathtt{f}_{s})_{\mathbf{a}}\
\frac{\Gamma(\ell+3)^{2}}{\Gamma(2\ell+5)}\frac{16\left(5\ell^{2}+25\ell+24\right)}{3\ell(\ell+1)^{2}(\ell+4)^{2}(\ell+5)}\\\
&+(\mathtt{e}_{s_{1}}+(-1)^{\ell}\mathtt{e}_{s_{2}})_{\mathbf{a}}\
\frac{\Gamma(\ell+3)^{2}}{\Gamma(2\ell+5)}\left[-\frac{32\left(2\ell^{3}+23\ell^{2}+65\ell+32\right)}{\ell(\ell+1)^{3}(\ell+4)^{3}(\ell+5)}\right.\\\
&\qquad\quad+\left.\frac{8\left(12\psi^{(0)}(\ell+3)-12\psi^{(0)}(2\ell+5)+19\right)}{3(\ell+1)^{2}(\ell+4)^{2}}\right]\;.\end{split}$
(D.7)

Note this result should only be trusted down to $\ell=2$. This is because it
uses the one-loop data. The presence of the contact counterterm at one loop
spoils the analyticity in spin at $\ell=0$.

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