# Ex2Vec: Characterizing Users and Items from the Mere Exposure Effect

Bruno Sguerra  Deezer ResearchFrance ,  Viet-Anh Tran  Deezer ResearchFrance
and  Romain Hennequin  Deezer ResearchFrance

(2023)

###### Abstract.

The traditional recommendation framework seeks to connect user and content, by
finding the best match possible based on users past interaction. However, a
good content recommendation is not necessarily similar to what the user has
chosen in the past. As humans, users naturally evolve, learn, forget, get
bored, they change their perspective of the world and in consequence, of the
recommendable content. One well known mechanism that affects user interest is
the Mere Exposure Effect: when repeatedly exposed to stimuli, users’ interest
tends to rise with the initial exposures, reaching a peak, and gradually
decreasing thereafter, resulting in an inverted-U shape. Since previous
research has shown that the magnitude of the effect depends on a number of
interesting factors such as stimulus complexity and familiarity, leveraging
this effect is a way to not only improve repeated recommendation but to gain a
more in-depth understanding of both users and stimuli. In this work we present
(Mere) Exposure2Vec (Ex2Vec) our model that leverages the Mere Exposure Effect
in repeat consumption to derive user and item characterization and track user
interest evolution. We validate our model through predicting future music
consumption based on repetition and discuss its implications for
recommendation scenarios where repetition is common.

††journalyear: 2023††copyright: acmlicensed††conference: Seventeenth ACM
Conference on Recommender Systems; September 18–22, 2023; Singapore,
Singapore††booktitle: Seventeenth ACM Conference on Recommender Systems
(RecSys ’23), September 18–22, 2023, Singapore, Singapore††price: 15.00††doi:
10.1145/3604915.3608856††isbn: 979-8-4007-0241-9/23/09††ccs: Information
systems Recommender systems††ccs: Applied computing Psychology

##  1\. Introduction

“No man ever steps in the same river twice, for it is not the same river and
he is not the same man” is a quote credited to Heraclitus, the pre-Socratic
Greek philosopher, six hundred years before Christ. Heraclitus’ celebrated
phrase illustrates his view of an ever dynamic world and individual, both in a
perpetual state of change. Heraclitus understood something that is often
overlooked in recommender systems literature, i.e., the past rarely repeats
itself. The traditional recommendation framework seeks to connect user and
content, by finding the best match possible based on users past interaction
(Koren et al., 2009; Rendle, 2021). However, a good content recommendation is
not necessarily similar to what the user has chosen in the past. One
limitation of basing future interaction on what happened in the past is that
it ignores the fact that both sides of the problems are dynamic. As humans,
users naturally evolve, learn, forget, get bored, they change their
perspective of the world and in consequence, of the recommendable content. The
development of effective recommender systems, therefore, requires researchers
and practitioners to account for this dynamism.

The last years have witnessed an increase in the number of works that attempt
to embed recommender systems with psychology-derived knowledge on human
behavior (Lex et al., 2021; Curmei et al., 2022; Sguerra et al., 2022; Reiter-
Haas et al., 2021). There is an extensive body of psychological research
concerned with different effects that affect users and their preferences when
dealing with content consumption (Curmei et al., 2022). One example of a well
studied effect that has implications for recommender systems is the Mere
Exposure Effect (MEE). The effect states that the mere exposure of an
individual to a stimulus is enough to result in the development of a positive
attitude towards the stimulus (Zajonc, 1968). Therefore, the MEE should play a
significant role in shaping the evolution of a user’s interest in various feed
recommendation scenarios where repeated consumption is prevalent, such as
music streaming.

In this article we present Ex2Vec, our model that leverages repeat consumption
to learn joint user and item representations. Based on the finding that the
magnitude of MEE depends on both user and stimuli (Bornstein, 1989; Sguerra et
al., 2022), Ex2Vec learns to predict the user’s interest evolution from
repeated exposure by characterizing both user and item. We believe that the
representation learned by Ex2Vec can not only improve recommendation where
repeated consumption is common, but more importantly, provide researchers with
new information about users and stimuli, such as perceived familiarity,
complexity and more.

To summarize, our paper includes three major contributions: (1) an analysis
conducted to confirm the existence of the Mere Exposure in music streaming
consumption; (2) Ex2Vec, a model that allows for both user and item
characterization and the prediction of repetitive consumption behavior; (3)
the publication of the collected data to the research community.

##  2\. Related Work

Mere exposure effect. The MEE is a long known effect in psychology which
states that the “mere” exposure of an individual to a given stimulus is enough
to increase both recognition and affect (read liking or pleasantness) towards
said stimulus (Zajonc, 1968). In (Bornstein, 1989; Montoya et al., 2017) the
reader will find a comprehensive meta-analysis on over forty years of
controlled experiments involving it. The effect is robust and consistent
across different types of stimuli, including images, words, simple sounds, and
music. (Zajonc, 2001; Bornstein, 1989). Previous research has identified
several factors that can affect the strength of the MEE, such as a person’s
personality, age, the order and length of presentation, and stimulus
complexity (Bornstein, 1989). While exposure to stimuli results in increased
affect, the effect is not monotonic and eventually reaches a maximum point,
after which further repetitions can lead to satiation. The resulting behavior
is described by an inverted-U shaped curve, a pattern rather consistent across
different domains (Montoya et al., 2017). Among the many models attempting to
explain the effect (Bornstein, 1989), we call attention to Berlyne’s two
factor model (Berlyne, 1970). Where the effect is described as the interaction
of two-factors: (1) a rising habituation factor over exposures coupled with
(2) a tedious factor. The habituation factor occurs during the initial
repeated exposures, as the individual becomes accustomed to the stimuli. This
familiarity allows previously imperceptible details or aspects of the stimuli
to become accessible to the individual, until eventual satiation or boredom
sets in. Bornstein described boredom as a limiting factor of the MEE
(Bornstein, 1989) and is a common aspect of repeat consumption in many
domains, where users lose interest after over-consuming an item (Benson et
al., 2016; Kapoor et al., 2015; Anderson et al., 2014). Not only restricted to
the MEE, Berlyne provides a more general theory for aesthetic preference
(Berlyne, 1960), where preference follows an inverted-U shape over a number of
collative variables, such as complexity, novelty, familiarity, among others. A
theory that has been tested extensively and is rather consistent (Chmiel and
Schubert, 2017).

There are many interesting aspects of the MEE for recommender systems. Curmei
et al., in (Curmei et al., 2022), describe how the MEE, among other known
psychological effects, can create feedback loops changing users’ interest.
They formulate the mere exposure effect by linearly modifying the user
preference vector towards the interacted item. In consequence, when a user
interacts with a given content, the vector representing their taste is moved
towards the content to represent that “whenever users are exposed to content,
this makes them like this content more”. This has obvious limitations, for
instance, the fact that someone is discovering a new interest does not mean
they stopped liking their previous preferences: one can like both The Beatles
and The Rolling Stones. Moreover, this simple linear model does not account
for the saturation of the effect and its characteristic inverted-U shape. In
(Sguerra et al., 2022) we analyzed the actual consumption patterns of newly
released music on Deezer, a music streaming service. We show that, for users
listening repeatedly to newly released songs, the interest curve follows an
inverted-U shape over exposures, characteristic of the MEE.

Psychology-informed recommender systems. In recent years, there has been a
growing interest in incorporating psychological knowledge into recommender
systems, moving away from purely algorithmic models and towards greater
interpretability. In their recent survey (Lex et al., 2021), Lex et al.
present efforts made along three axes: (1) cognition, (2) personality and (3)
affect. In this section we revise the literature of the first category as it
is the most relevant to our research. Cognitive-inspired recommender systems
exploit mental processes of memory, attention and learning for modeling user
behavior and adapting feedback to improve recommendation. Considering memory,
in (Reiter-Haas et al., 2021), authors introduce a time-based exponential
decay factor to weight explicit feedback and improve the accuracy to the
collaborative filtering framework. The premise being that users’ taste
evolution can be modeled as a type of information forgetting, with their time
decay factor inspired by Ebbinghaus’ forgetting curve (Ebbinghaus, 1913). The
same curve is used in (Hu and Ogihara, 2011) to model a “freshness” factor of
a listened song, in order to modulate recommendations and avoid overexposure.
One of the most popular models of human cognition employed in recommender
system’s literature is Anderson’s cognitive architecture ATC-R (Anderson,
2009). This fixed architecture has been used to model a multitude of cognitive
tasks and simulate human cognitive performance. Authors in (Reiter-Haas et
al., 2021; Kowald et al., 2020, 2017) employ a specific module of ACT-R, the
declarative one, to model either the reuse of hashtags on twitter or the
relistening of music. ACT-R’s declarative module represents a “window to the
past” where learned information or facts can be accessed and serves to model
human memory processes. Since it accounts for both frequency and recency, it
has been quite successful in modeling repeat consumption as in the work cited
above.

The literature discussed describes various efforts to incorporate knowledge of
human cognitive processes and limitations into recommender systems. While
psychology offers a wealth of information on the MEE, little research has been
conducted on using this knowledge to enhance recommender systems. In the
upcoming sessions, we aim to fill this gap by exploring its potential.

##  3\. The Mere Exposure Effect in Music Consumption

Among the many application domains where recommender systems are used, we
posit that music streaming is one where the MEE is more easily observed and
perhaps useful to account for. First, the engagement of listening to a music
track is quite light when compared to watching movies or buying products, both
in terms of time and money, increasing the overall number of user interactions
(Schedl, 2019). Additionally, repetition is a rather common phenomenon in
music consumption, allowing for tracking the evolution of interest based on
exposure or repetition (Sguerra et al., 2022), while for other domains such as
books and movies, repetition behavior emerges at a higher level of abstraction
(Kapoor et al., 2015). Also, the number of items in commercial music catalogs
has a magnitude of tens of millions of tracks that is quite diverse in terms
of popularity, language and others, that can be easily controlled for
exposure. Lastly, music itself is a complex stimuli that has been studied in a
large body of literature of the MEE (Chmiel and Schubert, 2017; Szpunar et
al., 2004). For these reasons, in this article we focus on the domain of music
consumption in streaming platforms.

In previous work we focused on newly released albums to study the MEE in music
consumption (Sguerra et al., 2022). We show that for the new albums, the
listening probability follows an inverted-U shape over exposures, while for
classic rock music, the probability of listening decreases monotonically with
exposures. Accordingly, accounting for newly released songs reduces the
chances of the music being known by the users and that the rise of interest
corresponds to a form of “learning” as users get habituated to the song.
Therefore we also focus our research on newly released music tracks. In the
next section we outline some characteristics of the MEE.

###  3.1. Data

The present study utilizes song listening histories obtained from Deezer, a
well-established music streaming platform. We isolated the listening history,
from August to December 2022, related to the tracks released during the month
of August 2022. We filter out tracks that were not listened to by at least 20
different users and users that did not listen to at least 20 different tracks.
To increase the likelihood of the user’s interest evolution having finished
its course, we remove from the data the entire user-item consumption sequences
that appear after 80% of the considered time window. Every row of the
resulting dataset contains an user identifier, an item identifier, a timestamp
and the user listening time.

###  3.2. Empirical Observation of the MEE

In this section we check to see if the MEE is observable in the data. For
accessing the evolution of interest over exposures, the number of exposures is
of most importance. Here we consider only consumption sequences with 5 or more
exposures. To obtain a more representative view of the different behaviors
related to the number of exposures, we sampled the data based on the total
size of the consumption sequence. We filtered out the entire user-item
consumption sequences with more than 50 exposures (less than 0.05 of the data)
and discretized the dataset into 4 classes with the same repetition interval
based on the total number of repetitions of a pair user-item: (i) LowRep, the
lowest total number of repetitions from 5.0 to 16.0, with $|U|=29.6$k distinct
users and $|I|=9.2$k distinct tracks; (ii) ModRep, number of repetitions from
17.0 to 27.0, $|U|=26$k and $|I|=7.6$k; (iii) HighRep, high number of
repetitions from 28.0 to 38.0, $|U|=22.5$k and $|I|=6.9$k and (iv) VHRep, the
highest total number of repetitions, from 39 to 50, $|U|=19.8$k distinct users
and $|I|=6.5$k distinct items. The resulting dataset comprehends the
consumption history of $|U|=52$k and $|I|=13.7$k and contains about 4.7M
lines. Figure 1 depicts the fraction of the tracks that were listened to at a
given exposition $j$. Here we consider that the user listened to an item,
$L=1$, if the user listens to more than 80% of the duration of the track and
$L=0$ otherwise. At first exposure, all classes had a similar listening ratio
($\approx 0.62$), subsequently evolving differently. If this fraction is taken
as a proxy for the user’s interest, the maximal attained value increases with
the total number of exposures, later on decreasing at a similar ratio. All
classes (with the exception of LowRep where interest decreases with exposures)
exhibited an inverted-U shape, which is a characteristic of the MEE.

Figure 1. The fraction of listening events per exposure for each class of
repetition.

Although the fraction of listening events can be used as a proxy of interest,
it ignores the frequency of consumption. As previously discussed, presentation
sequence is one of the modulating factors of the effect (Bornstein, 1989) . In
order to account for the presentation sequence frequency, we employ the
popular ATC-R’s declarative module. Part of the declarative module is the
base-level activation that accounts for repetition, frequency and recency and
is given by: $B_{i}(t)=\ln\sum_{j=1}^{n}\mathbbm{1}_{t>t_{j}}(t-t_{j})^{-d}$,
where $n$ is the number of access to a given information $i$ (in our case, the
number of past consumption of song $i$), $t_{j}$ is the time of the $j$-th
access to that information (in our case, time of the $j$-th consumption of
song $i$), $\mathbbm{1}_{t>t_{j}}$ is the indicator function that is $1$ when
$t>t_{j}$ and $0$ otherwise, and $d$ is a decay parameter ($d>0$). We compute
the base-level activation for the consumption sequences in our dataset (only
considering a repetition when $L=1$) as it provides a more accurate
representation of interest: if users are interested in a song, not only they
will repeat it more, but with increased frequency. Here we make a distinction
between exposure and repetition, where repetitions are exposures where the
user actually consumed the item, or in this case, when $L=1$. Following
ACT-R’s community we set $d=0.5$, which is a value that has surfaced as the
default setting for this parameter (Anderson, 2009). Figure 2 depicts on the
left side, the evolution of the median time gap in hours between repetitions
at a given exposure (note that the time gap at repetition $j$ is given by
$gap_{j}=timestamp_{j}-timestamp_{j-1}$) and on the right the evolution of the
median base-level activation value per exposure (note that in the figure, we
only present the values after the first consumption). We consider the most
popular repetitions for each class: LowRep (5), ModRep (17), HighRep (28), and
VHRep (39). The left side of Figure 2 shows periods of relatively stable
interest (except for the LowRep class) before slowly growing, indicating
satiation. The observed behavior for the base-level activation is also
consistent with the MEE theory, where users tend to consume a song more
frequently after initial exposure then slowly losing interest.

Figure 2. Left: Median time gap between listening events with 0.95 confidence
interval over the number of exposures for each class of repetitive behavior.
Right: The median value of the base-level activation with 0.95 confidence
interval over the number of exposures for each class.

##  4\. (Mere) Exposure 2 Vec

The last section was concerned with observing the MEE in consumption of newly
released songs. In this section, we define the Ex2Vec model and describe how
it is able to characterize both users and items based on the dynamics of the
MEE as well as track users’ interest evolution over repetitions. Subsection
4.1 reviews the concepts behind Ex2Vec and Subsection 4.2 describes it.

###  4.1. MEE Dynamics

Berlyne’s theory of aesthetic preference posits that preferences follow an
inverted-U shape as a function of collative variables, such as uncertainty,
familiarity, and novelty (Berlyne, 1960, 1970; Chmiel and Schubert, 2017).
Accordingly, interest for a stimulus is expected to start low, increase with
familiarity, reach a peak, and then decrease, as observed in Section 3.2.
Uncertainty has also been related to musical pleasure as part of the enjoyment
derives from being able to anticipate some aspects of the song while still
being surprised by others (Cheung et al., 2019; Gold et al., 2019). However,
too little or too much uncertainty can reduce the pleasure of the experience.
Repeating the same song therefore would increase familiarity, and eventually
decrease uncertainty, resulting in the inverted-U shape. We relate this
increase of familiarity and decrease of uncertainty as a learning process and
to model this mechanism we employ ACT-R’s declarative module.

Originally, ACT-R’s declarative module was proposed to model the dynamics of
human memory. The base-level activation, presented above, is part of a series
of activation energies that modulate how easily and readily an information is
retrievable in memory. In ACT-R, the probability of a memory $i$ being
retrieved is given by $P_{i}=\sigma(\frac{A_{i}-\tau}{s})$, where
$\sigma(x)=1/(1+e^{-x})$ is the sigmoid function; $\tau$ is the activation
threshold (below which the odds of the information being retrieved are low);
$s$ is a smoothness parameter; and $A_{i}$ is the activation energy of
information $i$, given by: $A_{i}=\sum_{j\in C}W_{j}S_{ji}+B_{i}$, where
$B_{i}$ is the same base-level activation already presented, and the other
component represents a sort of similarity of information $i$ with the
previously stored knowledge (for more details we recommend (Anderson, 2009)).
The intuition being that memory recall depends on two factors, (1) repetition
and (2) past knowledge. However, with time, memories tend to degrade given the
decay factor $d$. This activation energy $A_{i}$ provides us with a proxy of
how well encoded in memory a given piece of information is (or in our case a
given song) and how easily a given piece of information can be accessed or
recalled. It is worth noting that not only liking, but also memory and
recognition, have been studied as a function of exposure and may be
interconnected (Szpunar et al., 2004).

Following Berlyne’s theory of aesthetic pleasure, interest should then follow
an inverted-U shaped pattern along the evolution of $A_{i}$, if the $A_{i}$ is
too small, the stimuli might be too uncertain/complex to the user, with
repetition, as the user gains a better understanding of the song, interest
might develop until overexposure where it falls back again. These are the two
mechanisms modeled by Ex2Vec that are formalized in the next section.

###  4.2. Ex2Vec Definition

Much as traditional collaborative filtering techniques such as Matrix
Factorization, Ex2Vec projects users and items into a latent space. Users are
described by an embedding vector noted $\mathbf{u}$ and items by an embedding
vector $\mathbf{v}$, both with the same number of latent dimensions $D$. We
assume the distance $d(\mathbf{u},\mathbf{v})$ to behave as a number of
collative variables such as perceived uncertainty/complexity etc. As the user
repeats a song, we linearly modify this distance similarly to (Curmei et al.,
2022). However, instead of moving the user embedding towards the item at every
new interaction, Ex2Vec modulates only the relative distance between
$\mathbf{u}$ in respect to item $i$. This approach better reflects a user’s
tastes, as discovering new items does not necessarily mean losing interest in
previous preferences. When $d(\mathbf{u},\mathbf{v})$ diminishes it indicates
that the user has gained a better understanding of the item, representing a
form of learning. Since humans forget with time, Ex2Vec accounts for a time-
decay factor based on ACT-R’s declarative module. If the discovery of new
items is seen as a form of learning, it is natural to base the learning
evolution in the dynamics of human memory provided by the declarative module.
At time $t$ for item $i$, the distance $d_{u,i}(t)$ is given by:

(1)
$d_{u,i}(t)=max(d(\mathbf{u},\mathbf{v})-\lambda_{u}\sum_{j=1}^{n}\mathbbm{1}_{t>t_{j}}(t-t_{j}+c)^{-d},0),$

where $n$ is the number of past consumption of item $i$, $t_{j}$ stands for
the time of past consumption $j$ of item $i$ ($t_{j}<t$); $d$ is the decay
parameter similar to ACT-R’s declarative module and $\lambda_{u}$ ¿ 0 is the
step size, regulating how much to change the distance. We make the
$\lambda_{u}$ a summation of a global $\lambda$ and a user specific bias:
$\lambda_{u}=\lambda+\lambda_{u}^{b}$. Note that we removed the $\ln$
transformation from ACT-R’s base-level to ensure the minimum value to subtract
from the distance to be zero and we added a cutoff term $c>0$ to keep the
change in distance bounded when $t-t_{j}$ is too small. Moreover, we take the
maximum value between 0 and the modified distance in order to, at the very
limit, have the distance $d_{u,i}=0$. Ex2Vec models the MEE as a form of
learning. The base distance $d(\mathbf{u},\mathbf{v})$, similar to $A_{i}$
from ACT-R’s declarative module, models the user’s base familiarity/knowledge
with a given item. The more the user repeats a given song, the smaller
$d_{u,i}(t)$ will be. With time, without new repetitions, $d_{u,i}(t)$ will
return to the base distance $d(\mathbf{u},\mathbf{v})$, indicating the
forgetting of the item. The base activation, given by the term
$\sum_{j=1}^{n}\mathbbm{1}_{t>t_{j}}(t-t_{j}+c)^{-d}$ modulates the distance
evolution.

In order to account for the inverted-U shape characteristic of the MEE,
instead of simply using the distance $d_{u,i}(t)$ as a proxy for the user’s
interest, we introduce a quadratic term for the user’s interest in an item at
time $t$:

(2) $I(\mathbf{v},\mathbf{u},t)=\alpha d_{u,i}(t)+\beta
d_{u,i}(t)^{2}+\gamma+b,$

Where $\alpha$, $\beta$ and $\gamma$, are global parameters of the quadratic
function and $b$ is the sum of a user and item bias. The main functioning of
Ex2Vec, inspired by the dynamics of the mere exposure effect, are described by
equation 1 and equation 2.

##  5\. Learning User and Item characterization from MEE

In order to learn the user and item characterizations from data, we take
inspiration from NeuMF (He et al., 2017). Much as in NeuMF, as input values we
have a binarized sparse identity vector for users and items followed by a
fully connected embedding layer, that projects both binary vectors into the
dense ones $\mathbf{u}$ and $\mathbf{v}$ with dimension $D$. From the
embedding vectors we compute the base distance $d(\mathbf{u},\mathbf{v})$ (we
used the Euclidean distance as it provides the best performance), modulating
it in accord to the factor
$\lambda_{u}(\sum_{j=1}^{n}\mathbbm{1}_{t>t_{j}}(t-t_{j}+c)^{-d})$ of equation
1 obtaining the final distance $d_{u,i}(t)$. Lastly we apply the quadratic
function of equation 2 to the computed distance obtaining the user interest
that is used as input of a sigmoid function obtaining the final predicted
score $y^{\prime}_{u,i}$ constricted to a range of $[0,1]$. Since we are
modeling the listening behavior of users, i.e., if a user listens to a song or
not, we train our model with both instances when $L=1$ or $L=0$. Much as in
(He et al., 2017) we use the log loss for training with a $L2$ regularization
term. We employ the Adam algorithm (Kingma and Ba, 2014), jointly learning
both the user item representations and the parameters: $c$, $\lambda$,
$\lambda_{b}^{u}$, $b$ and $\alpha$, $\beta$ and $\gamma$ of the quadratic
function. We fix the decay parameter to $-0.5$ according to ACT-R’s
literature.

###  5.1. Evaluation

Since Ex2Vec predicts interest evolution with repetitions. We evaluate Ex2Vec
performance in predicting the consumption sequences i.e., if a user at a given
exposure is going to listen to a given song ($L=1$) or not ($L=0$). This is a
task consistent with the real case scenario of creating playlists for music
discovery or of new released tracks. In the real case scenario, by predicting
the interest of users over time, given the number of past consumption, songs
can be added or removed dynamically to these playlists, removing songs that
were already overexposed or keeping items whose interest peak takes longer to
attain. We train Ex2Vec on the same listening histories presented in Section
3.1. To ensure that every user and song have enough interactions to be
properly characterized, such as in (Sun et al., 2020), we implement a
$k^{item}$ and $k^{user}$ pre-processing step. This step consists in
recursively filtering the data until all users have interacted with at least
$k^{item}$ items and every item was consumed by at least $k^{user}$ users. We
empirically decided on $k^{item}=k^{user}=30$, which results in a dataset of
about 1.5M interactions, $|U|=3.6$k and $|I|=878$. For the validation and test
set, we randomly selected four items for each user in the dataset and entirely
removed from the training set any instances of the user being exposed to these
items. While the items themselves are still included in the training set, any
interaction of a user with their sampled items were removed to prevent them
from influencing the training process. Two items per user of the removed
instances are used as validation set and the other two as test set. We
implement Ex2Vec with pytorch and make both the code and data available
online111https://github.com/deezer/ex2vec.

We compared our model with four baselines for predicting repeated behavior:
(1) $SLRC$, a sequential recommendation model that learns item-specific
temporal patterns of re-consumption (with the base intensity given by Bayesian
Personalized Ranking)(Wang et al., 2019). (2) $BL$, which uses ACT-R’s base-
level activation as a proxy for interest. (3) $BL_{fit}$, which utilizes the
base-level activation with a fitted decay parameter, as demonstrated in
(Kowald et al., 2017) to be effective in predicting relistening events. (4)
$Prev$ simply assumes that a user will relisten at the next exposure if they
have listened to it in the previous exposure. Although simple, with this
baseline, we intend to shift the inverted-U shape by a single exposure. For
predicting the relistening of a song, for Ex2Vec, $SLRC$, $BL$, and
$BL_{fit}$, we discretized two classes: $L=1$ or $L=0$ based on: the interest
(for Ex2Vec), the intensity for $SLRC$, and the two base-level values. The
discretization threshold was defined as the value that maximizes the balanced
accuracy on the validation set. Both Ex2Vec and $SLRC$ were set with the same
embedding dimension ($D=64$) and optimized on the validation set with learning
rate values in {5e-5, 0.0002, 0.00075, 0.001} for 100 epochs. For Ex2Vec we
initialized the parameters as following: $\alpha=1.0$, $\beta=-0.0065$,
$\gamma=0.5$, $\sigma=1.0$, $c=3.0$, the user and item embeddings where
initialized from $\mathcal{N}(0,1)$. Ex2Vec shows an overall better
performance as shown in Table 1.

Model | Balanced Accuracy (in %) | Weighted F1-score (in %)
---|---|---
$Ex2Vec$ | 64.27 $\pm$ 0.4 | 64.3 $\pm$ 0.38
$SLRC$ | 58.16 $\pm$0.16 | 58.15 $\pm$0.17
$BL$ | 57.81 $\pm$0.28 | 58.13 $\pm$ 0.31
$BL_{fit}$ | 57.48 $\pm$ 0.35 | 57.9 $\pm$ 0.42
$Prev$ | 59.88 $\pm$ 0.32 | 59.83 $\pm$ 0.32

Table 1. Experimental results. Scores averages computed on five splits of the
test set.

###  5.2. Further Analysis

Figure 3. Above left: the interest over the computed $d_{u,i}(t)$ distance
with no base-level activation; above right: the first and second dimensions of
the item embeddings with the corresponding predicted interest with no base-
level activation; below left: the predicted interest given the distance with a
higher base-level activation value; below right: the first and second
dimensions of the item embeddings with the higher base-level computed
interest.

However, more than the predictive performance of Ex2Vec, the main interest
comes from the user/item representations learned. Instead of moving users and
items closer in space to reflect interest, as traditional collaborative
filtering techniques, Ex2Vec will position them based on repetitive behavior
and the quadratic interest function. Therefore, items too close to a user have
low predicted interest, as for items too far from the user, according to the
inverted-U shape. For illustration, on top of Figure 3 depict, on the left,
the predicted interest given the computed $d_{u,i}(t)$ distance between the
items and a sampled user with no base-level activation, i.e. before any
repetition. On the top right the first and second dimensions of the learned
item embeddings are depicted with the corresponding predicted interest. Much
as Berlyne’s collative variables, interest is following an inverted-U shape
along the distance: items that are closer and furthest from the user have
smaller predicted interest. The items with the optimal predicted interest are
thus found in a ring-like shape around a user reference. When the user starts
consuming these items the distance user-item diminishes according to the base-
level activation. The bottom of Figure 3 depicts the same items as above but
with the interest computed with more frequent or recent repetition (base-level
activation = 11.12). The more a user listens to the songs, the smaller the
distance and the interest therefore either decreases or increases accordingly
to the inverted-U shape based on the relative position of user and item.
Therefore, the distances in the embedding space serve as a proxy of how much
repetition a user needs in order to either start to like a new song or start
to lose interest in another. This allows for recommendation to be made by
balancing items that have high predicted interest, stop recommending items
that are saturated or even repeatedly recommending novel items that are
further away and take more consumption for the user to start liking them.
Balancing these cases might be a way to ease the cognitive charge of
discovering different content and avoid boredom in feed-like applications for
instance.

##  6\. Conclusion and Future Directions

We introduce Ex2Vec, a model for leveraging repeated exposure to characterize
users and items. We demonstrate that Ex2Vec has a dual capability, allowing
for both user and item characterization and prediction of relistening
behavior. We posit that Ex2Vec enables new recommendation paradigms by
tracking the user’s interest and balancing recommendation at different levels
of familiarity, promoting learning and habituation while preventing boredom.
Furthermore, as Ex2Vec positions users and items based on the evolution of
user interest through repetition, it is likely to reflect some of Berlyne’s
collative variables, such as uncertainty and familiarity, among others. We
believe that Ex2Vec serves as an example of how leveraging psychological
research allows not only for the improvement of recommender systems, but to
help leveraging the rich human behavior data available to understand users and
stimuli better.

One limitation of Ex2Vec is its treatment of relative distances between users
and items, which results in changes of interest only related to the interacted
item. To address this, future enhancements should explore modeling the
relational dynamics among items, accounting for the effects of listening to
closely related items on users’ learning and forgetting processes.
Additionally, fluctuations in users’ attention, context, and intention, which
often lead to significant changes in preferences and learning abilities,
should also be accounted for in the future. Finally, future work should
investigate the relationship between the learned embeddings and Berlyne’s
collative variables in more depth. If this relationship holds, Ex2Vec could
become a valuable tool for inferring stimuli characteristics, such as relative
familiarity and complexity, as well as user-specific traits, such as
personality and knowledge.

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  *[Ex2Vec]: (Mere) Exposure2Vec
  *[MEE]: Mere Exposure Effect


[a,b]M. Khurana

# Prospects of detecting gamma-ray signal of dark matter interaction with the
MACE telescope

A. Pathania  K. K. Singh  C. Borwankar  P. K. Netrakanti  K. K. Yadav

###### Abstract

The MACE (Major Atmospheric Cherenkov Experiment) telescope has started its
regular gamma-ray observations at Hanle in India. Located at an altitude of
$\sim$ 4.3 km above sea level and equipped with a 21 m diameter large quasi-
parabolic reflector, it has the capability to explore the gamma-ray sky in the
energy range above 20 GeV with very high sensitivity. In this work, we present
the results from the feasibility studies for searching high-energy gamma-ray
signals from dark matter interaction in potential astrophysical environments.
We study the impact of MACE response function and other instrumental
characteristics to probe the velocity average interaction cross-section
($<\sigma v>$) of the weakly interacting massive particles (WIMPs), expected
from the thermal dark matter freeze-out during the decoupling era. We consider
the presence of dark matter in the form of pure WIMPs in the mass range 200
GeV - 10 TeV to produce distinctive gamma-ray spectra through its self-
annihilation into standard model particles using the Pythia simulation
package. The convolution of gamma-ray spectra corresponding to different
standard model channels with the MACE response function is used to estimate
the upper limit on $<\sigma v>$ for 100 hours of expected MACE observation of
Segue1 (a dwarf spheroidal galaxy) which is a potential site of dark matter.

##  1 Introduction

In modern cosmology, the concept of dark matter (DM) in Universe plays a
dominant role to explain a wide range of astrophysical observations such as
fluctuations in the cosmic microwave background radiation, baryon acoustic
oscillations, flattening of galaxy rotation curves, gravitational lensing,
large scale structure formations and their evolutions etc [1]. The ordinary or
baryonic matter contributes $\sim$ 4$\%$ of the total energy budget of
Universe while DM contributes $\sim$ 26$\%$ and remaining 70$\%$ is
contributed by the dark energy. In spite of large DM abundance in galaxies and
cluster of galaxies in the present Universe, its nature and particle origin,
such as the mass and coupling to the standard model (SM) particles, remain the
biggest mysteries of modern astro-particle physics and cosmology. In the
widely accepted standard model of cosmology, a potential DM candidate is
assumed to be neutral, long-lived, cold matter [2]. After decades of
theoretical and experimental research on DM, it is generally believed that any
theoretical description of DM should include a production mechanism which
predicts its relic abundance of $\Omega_{DM}\approx 0.25$. Many theories,
based on super-symmetric extensions of the SM of particle physics, predict
weakly interacting massive particles (WIMPs) as natural potential candidates
for cold dark matter in the mass range 10 GeV -10 TeV. An appealing frame-work
for the genesis of WIMPs is thermal freeze-out from the primordial plasma of
SM particles in the early Universe [3]. Initially, WIMPs were in chemical and
thermal equilibrium with the hot soup of SM particles produced after the big-
bang and subsequently freezed-out of the thermal equilibrium as the
interaction rate became smaller than the expansion rate of Universe. After
this freeze-out, the density of WIMPs remains constant. The expected value of
velocity weighted average annihilation cross section ($<\sigma v>$) of WIMPs
with mass of the electro-weak scale is $\approx~{}3\times
10^{-26}cm^{3}s^{-1}$ [4]. Experimental searches of WIMPs approach the
sensitivity to probe annihilation cross-section of this order to match the
observed energy density of the cold dark matter.

Direct and collider experiments for WIMP detection have not yielded any
acceptable statistically significant signal so far. In recent years, indirect
methods, related to the detection of signal from products of WIMP annihilation
in the plausible astrophysical sites, have seen increasing interest. The
products of WIMP annihilation can come from the hadronization or decay of
primary SM particles such as quark-antiquark, boson and lepton through a given
channel with its own branching ratio [5]. The main type of products are
neutrinos, positrons, anti-protons and gamma-rays. In this contribution, we
present the feasibility study of search for gamma-ray signal of WIMP
annihilation from the dwarf spheroidal galaxy Segue1 using the newly
commissioned Major Atmospheric Cherenkov Experiment (MACE) telescope in India.
This galaxy, located at a distance of $\sim$ 23 kpc from Earth, is considered
to be one of the prominent DM sites with a mass-to-luminosity (M/L) ratio of
$\approx$ 3400 $(M_{\odot}/L_{\odot})$, where $M_{\odot}$ and $L_{\odot}$ are
the mass and luminosity of Sun respectively.

##  2 MACE Telescope

MACE is a newly commissioned imaging atmospheric Cherenkov telescope (IACT) at
Hanle, Ladakh in India [6]. A picture of the telescope captured during night
is shown in Figure 1. Located at an altitude of $\sim$ 4.3 km above sea level,
MACE is the highest existing IACT in the world. The geographical location of
the MACE telescope appropriately fills the longitudinal gap among the leading
current and future IACTs around the globe [7, 8]. Equipped with a 21 m
diameter large light collector, it has capability of detecting very high
energy gamma-ray photons in the energy range above 20 GeV with very high point
source sensitivity. The compact imaging camera at the focal plane comprises
1088-photomultipliers with a pixel resolution of 0.125∘ and provides a total
field of view of $\sim~{}4.36^{\circ}~{}\times~{}4.03^{\circ}$. The important
salient features of MACE are summarized in Table 1. These features place the
MACE telescope as the second largest stand alone IACT after LST-1 in the
northern hemisphere. It is a prime case for the installation of low threshold
energy stereoscopic IACT systems at high altitude in future.

Figure 1: The MACE Telescope at Hanle, Ladakh in India.

Altitude | 4.3 km (asl)
---|---
Location | Hanle, India
| (32.8 ∘ N, 78.9 ∘ E)
Diameter | 21m
Field of View | 4.36 ${}^{\circ}\times 4.03^{\circ}$
Energy Range | Above 20 GeV
Energy Resolution | 20 $\%$ at 1 TeV
Pixel Resolution | 0.125 ∘
Sensitivity | 2.7 $\%$ Crab Flux
| in 50 hrs

Table 1: Salient features of the MACE telescope.

##  3 $\gamma-$ ray signal from WIMP annihilation

WIMPs in dense astrophysical environments would annihilate into a pair of SM
particles and produce gamma-rays in final state from their hadronization,
radiation and decay [9]. These high energy photons can be eventually detected
by the space- and ground-based telescopes ( e.g. MACE) provided the mass of
WIMPs ($m_{\chi}$) is high enough to obtain the most robust and stringent
constraints on WIMP annihilation into a variety of final states and therefore
probing the parameter space of WIMPs as dark matter candidate. The gamma-ray
continuum in astrophysical systems can be produced by the WIMP annihilation
into any SM particle pair ($\chi+\chi\rightarrow SM+\bar{SM}$) with gamma-ray
photons being either radiated off or emanating from the decay of a particle
that has arisen either directly from a primary decay product or as a result of
its hadronization. The photon energy ranges from $E_{max}\sim m_{\chi}$ to all
the way down. The expected signal from the Majorana WIMP annihilation is
characterized by a specific spatial shape and specific energy spectrum. The
differential flux of gamma-ray photons lying within a solid angle
$\Delta\Omega$ is expresses as [10]

$\frac{dN}{dE}=\frac{<\sigma v>}{8\pi
m_{\chi}^{2}}\sum_{f}b_{f}\frac{dN_{\gamma}^{f}}{dE}\times J(\Delta\Omega)$
(1)

where $\frac{dN_{\gamma}^{f}}{dE}$ is the differential photon spectrum per
WIMP annihilation event in the channel $`f^{\prime}$ with its corresponding
branching ratio $b_{f}$. The first term in the right hand side of Equation 1
accounts for the particle physics contributions and is therefore referred to
as the _particle physics factor_. It controls the shape of gamma-ray spectrum
and carries the physics involved in WIMP interactions. The second term
$J(\Delta\Omega)$ is known as the _Astrophysical-J factor_. It is defined as

$J(\Delta\Omega)=\iiint\limits_{l.o.s}\rho^{2}(r)dld\Omega$ (2)

where $\rho(r)$ represents the density profile of WIMPs in a given
astrophysical environment. J-factor is a measure of DM density square
integrated over the line-of-sight (l.o.s) $l$ and solid angle $\Delta\Omega$.
The density of DM is assumed to spherically symmetric and depends only the
radial distance $r$ from the center. The value of J-factor, a measure of total
DM content, plays an important role in source selection as it decides overall
strength of the signal.

##  4 Results and Discussion

Dwarf spheroidal galaxies, less massive than Milky-Way, are considered as
potential targets for unambiguous detection of dark matter signal since they
have negligible astrophysical gamma-ray background. This is because neither
known gamma-ray sources such as supernova remnants/pulsar wind nebula nor
gases acting as targets for cosmic rays are observed in spheroidal galaxies.
Being small in size at distant locations, these galaxies appear as point
sources for ground-based gamma-ray telescopes like MACE and therefore the
instrumental background is also negligible. Motivated by these
characteristics, we have considered Segue1 as a test case for MACE in the
present study.

Figure 2: Differential photon spectrum per WIMP annihilation in
$b\bar{b}$-channel for different values of $m_{\chi}$.

We have used Pythia numerical package [11] to estimate
$\frac{dN_{\gamma}^{f}}{dE}$ by considering the Majorana nature of WIMPs and
assuming that the WIMP pair annihilation proceeds into a single channel alone
with 100$\%$ probability. Based on the theoretical motivations available in
literature, we have considered $b\bar{b},\tau^{+}\tau^{-},Z\bar{Z},h\bar{h}$ &
$W^{+}W^{-}$ as the single channel dominance for WIMP annihilation. A
representative $\frac{dN_{\gamma}^{f}}{dE}$ for $b\bar{b}$ channel
corresponding to different masses of WIMP is presented in Figure 2.

Detailed physics involved in these interactions are either derived from theory
or based on phenmological models with parameters derived from Large Hadron
Collider data with strong nuclear forces governed by Quantum Chromodynamics.
For estimation of J-factor, we consider the widely used dark matter density
profile given by Navarro-Frenk-White (NFW) as [12]

$\rho(r)=\frac{\rho_{s}}{\left(\frac{r}{r_{s}}\right)\left(1+\frac{r}{r_{s}}\right)^{2}}$
(3)

where $\rho_{s}$ and $r_{s}$ are defined as scale density and scale radius
respectively. For Segue1, $\rho_{s}=21.005GeV/cm^{3}$ and $r_{s}=0.1461kpc$.
Since the J-factor is calculated within an angular region of radius equal to
the point spread function (PSF) of a given telescope, it is evident from
Figure 3 that majority of dark matter in Segue1 is contained within the MACE-
PSF of $\approx 0.125^{\circ}$ for the scale radius of $r_{s}=0.36^{\circ}$.
Therefore, the value of J-factor for MACE is estimated to be
$J_{MACE}=3.05\times 10^{19}GeV^{2}/cm^{5}$.

Figure 3: Fraction of total J-factor enclosed as a function of angular extent
($\theta$) of the Segue1 galaxy.

The integral gamma-ray rate from the Segue1 galaxy can be calculated by
convoluting Equation 1 with the MACE response function $A_{eff}(E)$ and is
given by

$R_{\gamma}~{}=~{}\int_{20GeV}\frac{dN}{dE}A_{eff}(E)dE$ (4)

The estimated integral gamma-ray photon rates as a function of WIMP mass
($m_{\chi}$) in the MACE energy range above 20 GeV for different channels of
WIMP annihilation for $<\sigma v>\approx~{}3\times 10^{-26}cm^{3}s^{-1}$ are
reported in Figure 4.

Figure 4: Integral photon rate for different channels in MACE energy range as
function of WIMP mass.

However, the value of expected integral gamma-ray rate ($R_{\gamma}^{*}$) from
any weak source for 3$\sigma$ detection in a given observation ($T_{obs}$) can
be obtained using the Li-Ma formula [13] and is given as

$R_{\gamma}^{*}=\frac{9+\sqrt{81+72R_{CR}T}}{2T}$ (5)

where $R_{CR}$ is the measured cosmic ray background rate by any ground-based
telescope. Therefore, this is translated into an upper limit on $<\sigma v>$
for WIMP annihilation into a given channel. From Equations 1 & 4, the derived
upper limit on $<\sigma v>$ at 3$\sigma$ confidence level can be expressed as

$<\sigma v>=3\times
10^{-26}\times\left(\frac{R_{\gamma}^{*}}{R_{\gamma}}\right)~{}~{}~{}~{}\rm
cm^{3}~{}s^{-1}$ (6)

Expected results for $T_{obs}=$ 100 Hours using MACE observations of Segue1
galaxy at 3$\sigma$ confidence level are depicted in Figure 5. We observe that
the value of $<\sigma v>$ can be constrained to an upper limit of $\sim$
6.44$\times 10^{-24}~{}cm^{3}~{}s^{-1}$ at 3$\sigma$ confidence level for the
WIMP annihilation of masses $m_{\chi}=$ 300 GeV through $\tau^{+}\tau^{-}$
channel. The corresponding upper limit on the relic density parameter of WIMPs
can be estimated using the relation

$\Omega_{WIMP}=\frac{6.0\times 10^{-27}\rm cm^{3}~{}s^{-1}}{<\sigma v>}$ (7)

The value of $\Omega_{WIMP}\approx$ 0.06 is referred to as _WIMP miracle_.
Therefore, in order to arrive the so called WIMP miracle, the $<\sigma v>$
value should be obtained of the order of $10^{-25}\rm cm^{3}~{}s^{-1}$ from
any observational approach. Long-term observations of Segue1 for about 160
Hours with the stereoscopic MAGIC telescope have placed stringent upper limit
of $1.4\times 10^{-23}\rm cm^{3}~{}s^{-1}$ (95$\%$ confidence level) on
$<\sigma v>$ at $m_{\chi}=$ 700 GeV under the frame-work of brane-world theory
[14]. In this model of dark matter, the characteristics of the proposed
massive brane fluctuations or branons match with those of the WIMPs [15].

Figure 5: Constraints on $<\sigma v>$ as a function of WIMP mass.

##  5 Conclusions

Ground-based IACTs with extraordinary point source sensitivity are deemed to
be an ideal instrument for searching weak gamma-ray signals produced from the
WIMP annihilation in the dwarf spheroidal galaxies. In this study, we find
that the recently commissioned MACE telescope can be effectively used to
constrain the parameter space of WIMPs in the mass range 200 GeV - 10 TeV. The
feasibility study suggest that 100 Hours of dedicated observation of the
Segue1 galaxy with MACE would be able to constrain $<\sigma v>$ value close to
the order of $10^{-24}cm^{3}s^{-1}$ at 3$\sigma$ confidence level for WIMP
annihilation of mass $\sim$ 300 GeV into $\tau^{+}\tau^{-}$. However, results
corresponding to other decay channels such as $b\bar{b},Z\bar{Z},h\bar{h}$ &
$W^{+}W^{-}$ can constrain the $<\sigma v>$ value up to the order of
$10^{-23}cm^{3}s^{-1}$.

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