11institutetext: Politecnico di Bari, Bari, Italy
11email<EMAIL_ADDRESS>
# FedeRank: User Controlled Feedback
with Federated Recommender Systems

Vito Walter Anelli  Yashar Deldjoo  Tommaso Di Noia  Antonio Ferrara
Corresponding author Fedelucio Narducci

###### Abstract

Recommender systems have shown to be a successful representative of how data
availability can ease our everyday digital life. However, data privacy is one
of the most prominent concerns in the digital era. After several data breaches
and privacy scandals, the users are now worried about sharing their data. In
the last decade, Federated Learning has emerged as a new privacy-preserving
distributed machine learning paradigm. It works by processing data on the user
device without collecting data in a central repository. We present FedeRank
(https://split.to/federank), a federated recommendation algorithm. The system
learns a personal factorization model onto every device. The training of the
model is a synchronous process between the central server and the federated
clients. FedeRank takes care of computing recommendations in a distributed
fashion and allows users to control the portion of data they want to share. By
comparing with state-of-the-art algorithms, extensive experiments show the
effectiveness of FedeRank in terms of recommendation accuracy, even with a
small portion of shared user data. Further analysis of the recommendation
lists’ diversity and novelty guarantees the suitability of the algorithm in
real production environments.

###### Keywords:

Recommender Systems Collaborative Filtering Federated Learning Learning to
Rank

##  1 Introduction

Recommender Systems (RSs) are well-known information-filtering systems widely
adopted for mitigating the information-overload problem. Indeed, the broad
amount of items and services has caused a cognitive impairment that takes the
name of over-choice, or choice overload. RSs have proved to be very useful in
making possible personalized access to these catalogs of items. These systems
are generally hosted on centralized servers and train their models by
exploiting massive proprietary and sensitive data. However, public awareness
related to data collection was spurred and increased. In recent years, an
increasing number of countries have introduced regulations to protect user
privacy and data security. Representative examples are the GDPR in the
European Union [15], the CCPA in California [8], and the Cybersecurity Law in
China [42]. Such policies prohibit free data circulation and force personal
data to remain isolated and fragmented.

In this context, Google has recently proposed Federated Learning (FL) as a
privacy-by-design technique which tackles data isolation while meeting the
need for big data [23, 33]. FL trains a global machine-learning model by
leveraging both users’ data and personal devices’ computing capabilities.
Unlike previous approaches, it keeps data on the devices (e.g., smartphones,
tablets, etc.) without sharing it with a central server. Today, FL is
considered the best candidate to face the data privacy, control and property
challenges posed by the data regulations.

Among the recommendation paradigms proposed in the literature, Collaborative
Filtering (CF) demonstrated a very high accuracy [32, 47]. The strength of CF
recommendation algorithms is that users who expressed similar tastes in the
past tend to agree in the future as well. One of the most prominent CF
approaches is the Latent Factor Model (LFM) [26]. LFMs uncover users and items
latent representation, whose linear interaction can explain observed feedback.

In this paper, we introduce FedeRank, a novel factorization model that
embraces the FL paradigm. A disruptive effect of employing FedeRank is that
users participating in the federation process can decide if and how they are
willing to disclose their private sensitive preferences. Indeed, FedeRank
mainly leverages non-sensitive information (e.g., items the user has not
experienced). Here, we show that even only a small amount of sensitive
information (i.e., items the user has experienced) lets FedeRank reach a
competitive accuracy. How incomplete data impacts the performance of the
system is an entirely unexplored field. Analogously, it is still to establish
the minimum amount of data necessary to build an accurate recommendation
system [46]. At the same time, preserving privacy at the cost of a worse
tailored recommendation may frustrate users and reduce the “acceptance of the
recommender system” [35]. In this work, instead of focusing on how to protect
personal information from privacy breaches (that is explored in other active
research fields), we investigate how to guarantee the users the control and
property of their data as determined by regulations. The work’s contributions
are manifold due to the number of open challenges that still exist with the FL
paradigm. To summarize, our contributions in this paper include:

  * •

the development of the first, to the best of our knowledge, federated pair-
wise recommendation system;

  * •

an analysis of the impact of client-side computation amount;

  * •

an investigation on the existing relation between incomplete data and
recommendation accuracy, and an analysis of the algorithmic bias on the final
recommendation lists, based on the data deprivation amount.

To this extent, we have carried out extensive experiments on three real-world
datasets (Amazon Digital Music, LibraryThing, and MovieLens 1M) by considering
two evaluation criteria: (a) the accuracy of recommendations measured by
exploiting precision and recall, (b) beyond-accuracy measures to evaluate the
novelty, and the diversity of recommendation lists. The experimental
evaluation shows that FedeRank provides high-quality recommendations, even
though it leaves users in control of their data.

##  2 Related Work

In the last decades, academia and industry have proposed several competitive
recommendation algorithms. Among the Collaborative Filtering algorithms, the
most representative examples are undoubtedly Nearest Neighbors systems, Latent
Factor Models, and Neural Network-based recommendation systems. The Nearest
Neighbors scheme has shown its competitiveness for decades. After them,
factorization-based recommendation emerged thanks to the disruptive idea of
Matrix Factorization (MF). Nevertheless, several generalized/specialized
variants have been proposed, such as FM [37], SVD++ [24], PITF [40], FPMC
[39]. Unfortunately, rating-prediction-oriented optimization, like SVD, has
shown its limits in the recommendation research [34]. Consequently, a new
class of Learning to Rank algorithms has been developed in the last decade,
mainly ranging from point-wise [28] to pair-wise [38], through list-wise [41]
approaches. Among pair-wise methods, BPR [38] is one of the most adopted,
thanks to its outstanding capabilities to correctly rank with an acceptable
computational complexity. Finally, in the last years, methods exploiting the
architectures of deep neural networks have established themselves in search
and recommendation research.

To make RSs work properly (easing the user decision-making process and
boosting the business), they need to collect user information related to
attributes, demands, and preferences [20], jeopardizing the user’s privacy. In
this scenario — and, more generally, in any scenario with a system learning
from sensitive data — FL was introduced for meeting privacy shortcomings by
horizontally distributing the model’s training over user devices [33]. Beyond
privacy, FL has posed several other challenges and opened new research
directions [21]. In the last years, it has extended to a more comprehensive
idea of privacy-preserving decentralized collaborative ML approaches [45],
ranging from horizontal federations, where different devices (and local
datasets) share the same feature space, to vertical federations, where devices
share training samples that differ in feature space.

Some researchers focused the attention on the decentralized and distributed
matrix-factorization approaches [12, 16]. However, in this work, we focus on
federated learning principles theoretically and practically different from
classical distributed approaches. Indeed, FL assumes the presence of a
coordinating server and the use of private and self-produced data on each
node. In general, distributed approaches do not guarantee these assumptions.
Ammad-ud-din et al. [3] propose a federated implementation of collaborative
filtering, whose security limits are analyzed in [11], which uses the SVD-MF
method for implicit feedback [19]. Here, the training is a mixture of
Alternating Least Squares (ALS) and Stochastic Gradient Descent (SGD) for
preserving users’ privacy. Nevertheless, incomprehensibly, almost no work
addressed top-N recommendation exploiting the “Learning to rank” paradigm. In
this sense, one rare example is the work by Kharitonov et al. [22], who
recently proposed to combine evolution strategy optimization with a
privatization procedure based on differential privacy. The previous work
focuses neither on search or recommendation. Perhaps, like ours, it can be
classified as a federated learning-to-rank algorithm. Finally, Yang et al.
[46] identified some recent FL challenges and open research directions.

##  3 Approach

In this section, we introduce the fundamental concepts regarding the
Collaborative Filtering recommendation using a Federated Learning scheme.
Along with the problem definition, the notation we adopt is presented.

The recommendation problem over a set of users $\mathcal{U}$ and a set of
items $\mathcal{I}$ is defined as the activity of finding for each user
$u\in\mathcal{U}$ an item $i\in\mathcal{I}$ that maximizes a utility function
$g:\mathcal{U}\times\mathcal{I}\rightarrow\mathbb{R}$ [36]. Let
$\mathbf{X}\in\mathbb{R}^{|\mathcal{U}|\times|\mathcal{I}|}$ be the user-item
matrix containing for each element $x_{ui}$ an implicit feedback (e.g.,
purchases, visits, clicks, views, check-ins) of user $u\in\mathcal{U}$ for
item $i\in\mathcal{I}$. Therefore, $\mathbf{X}$ only contains binary values,
$x_{ui}=1$ and $x_{ui}=0$ denoting whether user $u$ has consumed or not item
$i$, respectively.

The recommendation model is based on Factorization approach, originally
introduced by Matrix Factorization [27], that became popular in the last
decade thanks to its state-of-the-art recommendation accuracy [29]. This
technique aims to build a model $\Theta$ in which each user $u$ and each item
$i$ is represented by the embedding vectors $\mathbf{p}_{u}$ and
$\mathbf{q}_{i}$, respectively, in the shared latent space $\mathbb{R}^{F}$.
Let assume $\mathbf{X}$ can be factorized such that the dot product between
$\mathbf{p}_{u}$ and $\mathbf{q}_{i}$ can explain any observed user-item
interaction $x_{ui}$, and any non-observed interaction can be estimated as
$\hat{x}_{ui}(\Theta)=b_{i}(\Theta)+\mathbf{p}_{u}^{T}(\Theta)\cdot\mathbf{q}_{i}(\Theta)$
where $b_{i}$ is a term denoting the bias of the item $i$.

Among pair-wise approaches for learning-to-rank the items of a catalog,
Bayesian Personalized Ranking [38] is the most broadly adopted, thanks to its
capabilities to correctly rank with acceptable computational complexity. Given
a training set defined by $\mathcal{K}=\\{(u,i,j)\;|\;x_{ui}=1\land
x_{uj}=0\\}$, BPR minimizes the ranking loss by exploiting the criterion
$\underset{\Theta}{\max}\ G(\Theta)$, with
$G(\Theta)=\sum_{(u,i,j)\in\mathcal{K}}\ln\
\sigma(\hat{x}_{uij}(\Theta))-\lambda\lVert\Theta\rVert^{2}$, where
$\hat{x}_{uij}(\Theta)=\hat{x}_{ui}(\Theta)-\hat{x}_{uj}(\Theta)$ is a real
value modeling the relation between user $u$, item $i$ and item $j$,
$\sigma(\cdot)$ is the sigmoid function, and $\lambda$ is a model-specific
regularization parameter to prevent overfitting. Pair-wise optimization
applies to a wide range of recommendation models, including factorization.
Hereafter, we denote the model
$\Theta=\Braket{\mathbf{P},\mathbf{Q},\mathbf{b}}$, where
$\mathbf{P}\in\mathbb{R}^{|\mathcal{U}|\times F}$ is a matrix whose $u$-th row
corresponds to the vector $\mathbf{p}_{u}$, and
$\mathbf{Q}\in\mathbb{R}^{|\mathcal{I}|\times F}$ is a matrix in which the
$i$-th row corresponds to the vector $\mathbf{q}_{i}$. Finally,
$\mathbf{b}\in\mathbb{R}^{|\mathcal{I}|}$ is a vector whose $i$-th element
corresponds to the value $b_{i}$.

###  3.1 FedeRank

FedeRank redesigns the original factorization approach for a federated
setting. Indeed, the initial factorization model and its variants use a
single, centralized model, which does not guarantee users to control their
data. FedeRank splits the pair-wise learning model $\Theta$ among a central
server $S$ and a federation of users $\mathcal{U}$. Federated learning aims to
optimize a global loss function by using data distributed among a federation
of users’ devices. The rationale is that the server no longer collects private
users’ data. Rather, it aggregates the results of some steps of local
optimizations performed by clients, preserving privacy, ownership, and
locality of users’ data [6]. Formally, let $\Theta$ be the machine learning
model parameters, and $G(\Theta)$ be a loss function to minimize. In Federated
learning, the users $\mathcal{U}$ of a federation collaborate to minimize $G$
(under the coordination of a central server $S$) without sharing or exchanging
their raw data. From an algorithmic point of view, $S$ shares $\Theta$ with
the federation of devices. Then, the optimization problem of minimizing $G$ is
locally solved. Since each user participates to the federation with her
personal data and with her personal client device, we will interchangeably use
the terms “client”, “user”, and “device”.

To set up the framework, we consider the central server $S$ holding a model
$\Theta_{S}=\Braket{\mathbf{Q},\mathbf{b}}$, where
$\mathbf{Q}\in\mathbb{R}^{|\mathcal{I}|\times F}$ is a matrix in which $i$-th
row represents the embedding $\mathbf{q}_{i}$ for item $i$ in the catalog,
while the element $b_{i}$ of $\mathbf{b}\in\mathbb{R}^{|\mathcal{I}|}$ is the
bias of item $i$. That is, the information on $S$ only characterizes the items
of the catalog. On the other hand, each user $u\in\mathcal{U}$ holds a local
model $\Theta_{u}=\Braket{\mathbf{p}_{u}}$, where
$\mathbf{p}_{u}\in\mathbb{R}^{F}$ corresponds to the representation of user
$u$ in the latent space of dimensionality $F$. Each user holds a private
interaction dataset $\mathbf{x}_{u}\in\mathbb{R}^{|\mathcal{I}|}$, which —
compared to a centralized recommender system — corresponds to the
$\mathbf{X}$’s $u$-th row. The user $u$ leverages her private dataset
$\mathbf{x}_{u}$ to build the local training set
$\mathcal{K}_{u}=\\{(u,i,j)\;|\;x_{ui}=1\land x_{uj}=0\\}$. Finally, the
overall number of interactions in the system can be obtained by exploiting the
local datasets. Let us define it as
$X^{+}=\sum_{u\in\mathcal{U}}|\\{x_{ui}|x_{ui}=1\\}|$.

The training procedure iterates for $E$ epochs, in each of which rpe rounds of
communication between the server and the devices are performed. A round of
communication envisages a Distribution to Devices $\rightarrow$ Federated
Optimization $\rightarrow$ Transmission to Server $\rightarrow$ Global
Aggregation sequence. The notation $\\{\cdot\\}_{S}^{t}$ denotes an object
computed by the server $S$ at round $t$, while $\\{\cdot\\}_{u}^{t}$ indicates
an object computed by a specific client $u$ at round $t$.

(1) Distribution to Devices. Let $\\{\mathcal{U}^{-}\\}_{S}^{t}$ be a subset
of $\mathcal{U}$ with cardinality $m$, containing $m$ clients
$u\in\mathcal{U}$. The set $\\{\mathcal{U}^{-}\\}_{S}^{t}$ can be either
defined by $S$, or the result of a request for availability sent by $S$ to
clients in $\mathcal{U}$. Each client $u\in\\{\mathcal{U}^{-}\\}_{S}^{t}$
receives from $S$ the latest snapshot of $\\{\Theta_{S}\\}_{S}^{t-1}$.

(2) Federated Optimization. Each user $u\in\\{\mathcal{U}^{-}\\}_{S}^{t}$
generates the set $\\{\mathcal{K}_{u}^{-}\\}_{u}^{t}$ containing $T$ random
triples $(u,i,j)$ from $\mathcal{K}_{u}$. It is worth underlining that Rendle
[38] suggests, for a centralized scenario, to train the recommendation model
by randomly choosing the training triples from $\mathcal{K}$, to avoid data is
traversed item-wise or user-wise, since this may lead to slow convergence.
Conversely, in a federated approach, we require to train the model user-wise.
Indeed, the learning is separately performed on each device ($u$), that only
knows the data in $\mathcal{K}_{u}$. Thanks to the user-wise traversing,
FedeRank can decide who controls (the designer or the user) the number of
triples $T$ in the training set $\\{\mathcal{K}_{u}^{-}\\}_{u}^{t}$, to tune
the degree of local computation. With the local training set, the user $u$ can
compute her contribution to the overall optimization of $\Theta_{S}$ with the
following update:

$\\{\Delta\Theta_{S}\\}_{u}^{t}=\\{\Delta\Braket{\mathbf{Q},\mathbf{b}}\\}_{u}^{t}\mathrel{\mathop{:}}=\sum_{(u,i,j)\in\\{\mathcal{K}_{u}^{-}\\}_{u}^{t}}\frac{\partial}{\partial\Theta_{S}}\ln\
\sigma(\hat{x}_{uij}(\\{\Theta_{S}\\}_{S}^{t-1};\\{\Theta_{u}\\}_{u}^{t-1})),$
(1)

plus a regularization term. At the same time, the client $u$ updates its local
model $\Theta_{u}$, and incorporates it in the current model by using:

$\\{\Delta\Theta_{u}\\}_{u}^{t}=\\{\Delta\Braket{\mathbf{p}_{u}}\\}_{u}^{t}\mathrel{\mathop{:}}=\sum_{(u,i,j)\in\\{\mathcal{K}_{u}^{-}\\}_{u}^{t}}\frac{\partial}{\partial\Theta_{u}}\ln\
\sigma(\hat{x}_{uij}(\\{\Theta_{S}\\}_{S}^{t-1};\\{\Theta_{u}\\}_{u}^{t-1})),$
(2)

plus a regularization term. The partial derivatives in Eq. 1 and 2 are
straightforward, and can be easily computed by following the scheme proposed
by Rendle et al. [38]. At the end of the federated computation, given a shared
learning rate $\alpha$, each client can update its local model $\Theta_{u}$ —
containing the user profile — by aggregating the computed update:

$\\{\Theta_{u}\\}_{u}^{t}\mathrel{\mathop{:}}=\\{\Theta_{u}\\}_{u}^{t-1}+\alpha\\{\Delta\Theta_{u}\\}_{u}^{t}.$
(3)

(3) Transmission to Server. In a purely distributed architecture, each user in
$\mathcal{U}^{-}$ returns to $S$ the computed update. Here, instead of sending
$\\{\Delta\Theta_{S}\\}_{u}^{t}$, each user transmits a modified version
$\\{\Delta\Theta_{S}^{\Phi}\\}_{u}^{t}$. To introduce this aspect of FedeRank,
let us define
$\mathcal{F}=\\{i,\,\forall(u,i,j)\in\\{\mathcal{K}_{u}^{-}\\}_{u}^{t}\\}$,
and a randomized object $\Phi=\Braket{\mathbf{Q}^{\Phi},\mathbf{b}^{\Phi}}$,
with $\mathbf{Q}^{\Phi}\in\mathbb{R}^{|\mathcal{I}|\times F}$, and
$\mathbf{b}^{\Phi}\in\mathbb{R}^{|\mathcal{I}|}$. Each row
$\mathbf{q}_{i}^{\Phi}$ of $\mathbf{Q}^{\Phi}$ and each element $b_{i}^{\Phi}$
of $\mathbf{b}^{\Phi}$ assume their value according to the probabilities:

$\begin{gathered}P(\mathbf{q}_{i}^{\Phi}=\mathbf{1},b_{i}^{\Phi}=1\mid
i\in\mathcal{F})=\pi,\quad
P(\mathbf{q}_{i}^{\Phi}=\mathbf{0},b_{i}^{\Phi}=0\mid
i\in\mathcal{F})=1-\pi,\\\
P(\mathbf{q}_{i}^{\Phi}=\mathbf{1},b_{i}^{\Phi}=1\mid
i\notin\mathcal{F})=1\end{gathered}$ (4)

Based on $\\{\mathbf{Q}^{\Phi}\\}_{u}^{t}$ and
$\\{\mathbf{b}^{\Phi}\\}_{u}^{t}$, $\Delta\Theta_{S}^{\Phi}$ can be computed
as it follows:

$\\{\Delta\Theta_{S}^{\Phi}\\}_{u}^{t}=\\{\Delta\Theta_{S}\\}_{u}^{t}\odot\\{\Phi\\}_{u}^{t}\mathrel{\mathop{:}}=\Braket{\\{\Delta\mathbf{Q}\\}_{u}^{t}\odot\\{\mathbf{Q}^{\Phi}\\}_{u}^{t},\\{\Delta\mathbf{b}\\}_{u}^{t}\odot\\{\mathbf{b}^{\Phi}\\}_{u}^{t}},$
(5)

where the operator $\odot$ denotes the Hadamard product. This transformation
is motivated by a possible privacy issue. The update $\Delta\mathbf{Q}$
computed in Eq. 1 by user $u$ is a matrix whose rows are non-zero in
correspondence of the items $i$ and $j$ of all the triples
$(u,i,j)\in\mathcal{K}_{u}^{-}$ [38]. An analogous behavior can be observed
for the elements of $\Delta\mathbf{b}$. Focusing on the non-zero elements, we
observe that, for each triple $(u,i,j)\in\mathcal{K}_{u}^{-}$, the updates
$\\{\Delta\mathbf{q}_{i}\\}_{u}^{t}$ and $\\{\Delta\mathbf{q}_{j}\\}_{u}^{t}$,
as well as $\\{\Delta b_{i}\\}_{u}^{t}$ and $\\{\Delta b_{j}\\}_{u}^{t}$, show
the same absolute value with opposite sign [38]. In fact, this makes
completely distinguishable for the server the consumed and the non-consumed
items of user $u$, allowing $S$ to reconstruct $\mathcal{K}_{u}^{-}$, thus
raising a privacy issue. Since our primary goal is to put users in control of
their data, we leave users the possibility to choose a fraction $\pi$ of
positive item updates to send. The remaining positive item updates (a fraction
$1-\pi$) are masked by setting them to zero, by means of the transformation in
Eq. 5. Conversely, the negative updates are always sent to $S$, since their
corresponding rows are always multiplied by a $\mathbf{1}$ vector. Indeed,
these updates are related to non-consumed items, which are indistinguishably
negative or missing values, assumed to be non-sensitive data.

(4) Global Aggregation. Once $S$ has received
$\\{\Delta\Theta_{S}^{\Phi}\\}_{u}^{t}$ from all clients
$u\in\mathcal{U}^{-}$, it aggregates the received updates in $\mathbf{Q}$ and
$\mathbf{b}$ to build the new global model, with $\alpha$ being the learning
rate:

$\\{\Theta_{S}\\}_{S}^{t}\mathrel{\mathop{:}}=\\{\Theta_{S}\\}_{S}^{t-1}+\alpha\sum_{u\in\mathcal{U}^{-}}\\{\Delta\Theta_{S}^{\Phi}\\}_{u}^{t}.$
(6)

Although Federated Learning was conceived as a privacy-by-design paradigm for
distributed machine learning, it still does not provide formal privacy
guarantees. Malicious actors might acquire different information. They may be
able to analyze remote devices or communication flows in the network or infer
users’ private data by inspecting updates received on the server [21].
Possible solutions include the encryption of data on local devices, the
network traffic, or the adoption of secure multi-party computation [7].
Moreover, local differential privacy can guarantee that even if an adversary
can inspect the communication between a user and the central server, she can
learn only limited information [13, 14, 43]. To date, FedeRank explicitly
provides the needed APIs to work, out of the box, with encryption
communication libraries, thus providing state-of-the-art privacy guarantees.
We have chosen this solution since discussing privacy and security
implications in FL is beyond our scope. In this way, the system designer can
choose the privacy solution while disregarding the underlying machine learning
model. Moreover, FedeRank can also be easily adapted to guarantee local
differential privacy. Indeed, it is not due to chance the choice of putting
the user in control of $\Phi$. Suppose the $\Phi$ object also considers
sending fake information. In that case, FedeRank becomes utterly compliant
with the randomized response technique, which guarantees differential privacy
[44].

##  4 Experiments

Datasets. We have investigated the performance of FedeRank considering three
well-known datasets: Amazon Digital Music [31], LibraryThing [48], and
MovieLens 1M [18]. The former includes the users’ satisfaction feedback for a
catalog of music tracks available with Amazon Digital Music service. It
contains 1,835 users and 41,488 tracks, with 75,932 ratings ranging from $1$
to $5$. LibraryThing collects the users’ ratings on a book catalog. It
captures the interactions of 7,279 users on 37,232 books. It provides more
than two million ratings with 749,401 unique ratings in a range from $1$ to
$10$. The latter is MovieLens 1M dataset, which collects users’ ratings in the
movie domain: it contains 1,000,209 ratings ranging from $1$ to $5$, 6,040
users, and 3,706 items. We have filtered out users with less than $20$ ratings
(considering them as cold-users). Table 1 shows the characteristics of the
resulting datasets adopted in the experiments.

Table 1: Characteristics of the datasets used in the offline experiments: $\left|\mathcal{U}\right|$ is the number of users, $\left|\mathcal{I}\right|$ the number of items, $X^{+}$ the amount of positive feedback. Dataset | $\left|\mathcal{U}\right|$ | $\left|\mathcal{I}\right|$ | $X^{+}$ | $\frac{X^{+}}{\left|\mathcal{U}\right|}$ | $\frac{X^{+}}{\left|\mathcal{I}\right|}$ | $\frac{X^{+}}{\left|\mathcal{I}\right|\cdot\left|\mathcal{U}\right|}\%$
---|---|---|---|---|---|---
Amazon DM | 1,835 | 41,488 | 75,932 | 41.38 | 1.83 | 0.000997%
LibraryThing | 7,279 | 37,232 | 749,401 | 102.95 | 20.13 | 0.002765%
MovieLens 1M | 6,040 | 3,706 | 1,000,209 | 165.60 | 269.89 | 0.044684%

Baseline Algorithms. We compared FedeRank with representative centralized
algorithms to position its performance with respect to the state-of-the-art
techniques: VAE [30], a non-linear probabilistic model taking advantage of
Bayesian inference to estimate the model parameters; User-kNN and Item-kNN
[25], two neighbor-based CF algorithms, that exploit cosine similarity to
compute similarity between users or items; BPR-MF [38], the centralized
vanilla BPR-MF implementation; and FCF [3], the only federated recommendation
approach, to date, based on MF111Since no source code is available, we
reimplemented it in the reader’s interest.. We have evaluated FedeRank
considering $|\mathcal{U}^{-}|=1$. That is, in each round of communication we
involve only a single client to avoid noisy results. We thereby guarantee the
sequential training, needed to compare against centralized pir-wise
techniques. We have investigated with two different FedeRank settings. In the
first setting, we have set $T=1$, i.e., each client extracts solely one triple
$(u,i,j)$ from its dataset when asked for training the model; with this
special condition, we test whether FedeRank is effectively comparable to BPR.
Moreover, to make the comparison completely fair, we extract triples as
proposed by Rendle et al. [38]. The second setting follows a real Federated
scenario where the client local computation is not limited to a single triple.
Specifically, the number $T$ of triples extracted by each client is set to
$\frac{X^{+}}{|\mathcal{U}|}$.

Reproducibility and Evaluation Metrics. To train FedeRank, we have adopted a
realistic temporal hold-out $80$-$20$ splitting for training set and test set
[17]. We have further split the training set adopting a temporal hold-out
strategy on a user basis to pick the last 20% of interactions as a validation
set. Hence, we have explored a grid in the range $\\{0.005,\dots,0.5\\}$.
Then, to ensure a fair comparison, we have used the same learning rate to
train FedeRank. We have set up the remaining parameters as follows: the user-
and positive item-regularization parameter is set to $1/20$ of the learning
rate; conversely, the negative item-regularization parameter is set to $1/200$
of the learning rate as suggested by Anelli et al. [4]. Moreover, for each
setting, we have selected the best model in the first 20 epochs. Finally, the
number of latent factors is equal to $20$. This value reflects a trade-off
between latent factors’ expressiveness and memory space limits (given by a
realistic Federated Learning environment). We have measured the recommendation
accuracy by exploiting: Precision ($P@N$) (the proportion of relevant items in
the recommendation list), and Recall ($R@N$), that measures the relevant
suggested items. Regarding diversity, we have adopted Item Coverage ($IC$) and
Gini Index ($G$). The former provides the overall number of diverse
recommended items, and it highlights the degree of personalization expressed
by the model [1]. The latter measures how unequally an RS provides users with
different items [10], being higher values corresponding to more tailored
lists.

###  4.1 Performance of Federated Learning to Rank

Table 2: Recommendation performance for baselines and FedeRank on the three
datasets. For each value of $T$, the experiment with the best $\pi$ is shown.

Amazon Digital Music LibraryThing MovieLens 1M P@10 R@10 IC@10 G@10 P@10 R@10
IC@10 G@10 P@10 R@10 IC@10 G@10 Random 0.00005 0.00005 14186 0.28069 0.00054
0.00028 31918 0.60964 0.00871 0.00283 3666 0.85426 Most Popular 0.00469
0.00603 24 0.00023 0.05013 0.03044 36 0.00031 0.10224 0.03924 118 0.00569
User-kNN 0.01940 0.02757 4809 0.04115 0.14193 0.10115 3833 0.01485 0.12613
0.06701 737 0.04636 Item-kNN 0.02147 0.03171 4516 0.03801 0.20214 0.14778
12737 0.09979 0.08873 0.05475 2134 0.19292 VAE 0.01580 0.02289 3919 0.04179
0.10834 0.07711 7800 0.04638 0.11735 0.06192 1476 0.09259 BPR-MF 0.00921
0.01298 739 0.00415 0.07009 0.04303 3082 0.01359 0.11911 0.05817 1444 0.08508
FCF 0.00839 0.01222 2655 0.01861 0.10760 0.04392 829 0.01305 0.10760 0.04392
829 0.01305 FedeRank $T=1$ 0.00610 0.00889 349 0.00136 0.06309 0.03738 1650
0.00512 0.11805 0.05902 1041 0.06608 $T=X^{+}/|\mathcal{U}|$ 0.01422 0.02060
2586 0.02153 0.08512 0.05627 5404 0.02784 0.11599 0.05571 1326 0.02513

We begin our experimental evaluation by investigating the efficacy of
FedeRank, and we assess whether its performance is comparable to baseline
algorithms. Table 2 depicts the results in terms of accuracy and diversity.
The Table is visually split into two parts. The algorithms in the bottom part
(BPR-MF, FCF, and the two settings of FedeRank) are the factorization-based
models. The upper part provides the positioning of FedeRank to the other
state-of-the-art approaches. Focusing on the factorization-based methods, we
can note that BPR-MF outperforms FedeRank for $T=1$, but it remains at about
67% and 88% of the centralized algorithm for Amazon Digital Music and
LibraryThing, respectively. However, the realistic Federated setting is with
$T=X^{+}/|\mathcal{U}|$. Here, FedeRank consistently improves the
recommendation performance with respect to BPR-MF and FCF, over the three
datasets. Actually, for Amazon Digital Music and LibraryThing FedeRank
improves accuracy metrics of about 50% and 25% with respect to BPR-MF. The
achievement can be explained as an advantage brought by the increased local
computation. It is worth noticing that these results partially contradict
Rendle et al. [38] since they hypothesize that traversing user-wise the
training triples would worsen the recommendation performance. The same
accuracy improvements are not visible in MovieLens 1M, where we witness
results comparable or worse than BPR-MF, probably due to the overfitting
caused by the very high ratio between ratings and items. FedeRank with
increased computation still results robust with respect to the $IC$ metric,
since, in general, it outperforms or remains comparable to FCF and BPR-MF.

###  4.2 Analysis of Positive Feedback Transmission Ratio

$0$$0.5$$1$$0.000$$0.005$$0.010$$0.015$$\pi$P@10

$0$$0.5$$1$$0.000$$0.020$$0.040$$0.060$$0.080$$\pi$P@10

$0$$0.5$$1$$0.100$$0.110$$0.120$$\pi$P@10

$0$$0.5$$1$$0$$2{,}000$$4{,}000$$\pi$IC@10 (a) Amazon Digital Music

$0$$0.5$$1$$2{,}000$$4{,}000$$6{,}000$$\pi$IC@10 (b) LibraryThing

$0$$0.5$$1$$500$$1{,}000$$\pi$IC@10 (c) MovieLens 1M

Figure 1: F1 performance at different values of $\pi$ in the range $[0.1,1]$.
Dark blue is $T=1$, light blue is $T=X^{+}/|\mathcal{U}|$.

We have extensively analyzed the behavior of FedeRank when tuning $\pi$ for
sending progressive fractions of positive feedback in $[0.0,\dots,1.0]$ with
step $0.1$. We believe that the most important dimensions for this analysis
are accuracy (Precision), and aggregate diversity (Item Coverage). Figure 1
reports the results for the two experimented settings. Even here, Amazon
Digital Music and LibraryThing show similar trends. The accuracy of the
recommendation progressively increases reaching the maximum with fractions
$0.8$ and $0.5$, respectively, for $T=1$, and with fractions $0.9$ and $1.0$
for $T=X^{+}/|\mathcal{U}|$. First, this suggests that, at the beginning of
the training, some positive feedback is needed for establishing the value of
an item. Notwithstanding, even with $\pi=0.1$ (i.e., sharing just 10% of
private information), we witness a jump in recommendation accuracy (one order
of magnitude), reaching up to 92% of the best accuracy. We should also observe
another significant behavior. With a fraction of $0.0$, we observe a high
value of IC, with poor recommendation accuracy. It suggests that the system
could not capture population preferences, and it behaves similarly to Random.
However, even with a small fraction of positive feedback like $0.1$, we
observe a significant decrease in diversity metrics. The system learns which
items are popular and starts suggesting them. Moreover, if we observe large
fractions, we may notice that diversity increases as we feed the system with
more information. For MovieLens 1M, it is worth noticing that FedeRank shows
accuracy performance extremely close to the best value by sharing only $10\%$
of positive interactions. This behavior may be due to several reasons.
Firstly, MovieLens 1M is a relatively dense dataset in the recommendation
scenario (it has a sparsity of $0.955$). Secondly, it shows a very high user-
item ratio [2] (i.e., $1.63$) compared to Amazon Digital Music ($0.04$), and
LibraryThing ($0.20$), and it shows high values for the average number of
ratings per user ($132.87$), and ratings per item ($216,56$). All these clues
suggest that the system learns how to rank items even without the need for the
totality of ratings. If we focus on diversity metrics, $IC$ and Gini, we may
notice that diversity is progressively increasing from fraction $0.1$ to
$1.0$. It suggests that the system recommends a small number of popular items
with a fraction of $0.1$, while it provides more diversified recommendation
lists considering larger portions of positive user feedback. At this stage of
the analysis, we can draw an interesting consideration: in general, the
highest accuracy values do not correspond to the fraction of $1.0$.
Specifically, the experiments show that, initially, the recommender struggles
to suggest relevant items without positive feedback (fraction $0.0$). However,
with a small injection of feedback, the system starts to work well.
Nonetheless, in Amazon Digital Music and LibraryThing, if we increase the
fraction, we witness an increase concerning accuracy only until a certain
value of $\pi$. Although this consideration, we observe an increase in
diversity metrics when we continue to increase the value of $\pi$. Since it
has a small or even detrimental impact on accuracy, those items might be
unpopular items erroneously suggested to users.

Figure 2: Normalized number of item updates during the training: the 1,000
most updated items for different values of $\pi$ (from $\pi=0.0$ in red to
$\pi=1.0$ in blue).

Figure 3: Normalized number of recommendations for each item (colored curves
from $\pi=0.0$ in red to $\pi=1.0$ in blue) vs. normalized amount of positive
feedback per item (black dashed curve). The 250 most popular items are shown.

###  4.3 Study on FedeRank algorithmic bias

In this section, we study how incomplete transmission of user feedback affects
the item popularity in the recommendations and during the learning process. It
is essential to discover whether the exploitation of a FL approach influences
the algorithmic bias, determining popular items to be over-represented [5, 9].
We have re-trained FedeRank with all the previously considered $\pi$. For each
experiment, we analyzed the data flow between the clients and the server.
Afterward, we have extracted the number of updates for each item. Figure 2
illustrates the occurrences for the $1,000$ most updated items. In the Figure,
the curve colors denote the different $\pi$, while the values represent the
update frequency during the training process for each item on the horizontal
axis. Analogously, we considered the final top-10 recommendation list of each
user. Following the same strategy, we analyzed the occurrences of the items in
the recommendation. Then, we ordered items from the most to the least
recommended, and we plotted the occurrences of the first 250 in Figure 3. To
compare the different datasets, we have normalized the values considering the
overall dataset occurrences. Figure 2 shows that data disclosure, i.e., the
value of $\pi$, highly influences the information exchanged during the
training process. Additionally, the update frequency curve exhibits a constant
behavior for all the datasets, when $\pi=0.0$. This trend suggests that items
are randomly updated without taking into account any information about item
popularity. This behavior explains the high IC entirely observed in Figure 1
for $\pi=0.0$. The curve for $\pi=0.1$ shows that the exchanged data is enough
to provide the system with information about item popularity. The curves
suggest that the information on item popularity is being injected into the
system. By increasing the value of $\pi$, the trend becomes more evident. Due
to the original rating distribution, the system initially exchanges more
information about the very popular items. To analyze the algorithmic bias, we
can observe Figure 3, where the colored curves represent the frequency of item
recommendation on the horizontal axis, and the black dashed curve the amount
of positive feedback for that item in the dataset. Remarkably, item popularity
in recommendation lists does not vary as we may expect based on the previous
analysis. The setting $\pi=0.0$ is an exception, as extensively explained
before. Since in Amazon Digital Music and LibraryThing the updates sent by the
clients are randomly selected among the negative items, FedeRank acts like a
Random recommender. The system cannot catch popularity information and it
struggles to make the right items popular. Finally, we can focus on the curves
for $\pi>0$. It is noteworthy that the $\pi$ curves behave similarly, and they
propose the same proportion of popular items. The curves show the model
absorbs the initial variation in exchanged item distribution, unveiling an
unknown aspect of factorization models.

##  5 Conclusion and Future Work

In this paper, we have tackled the problem of putting users in control of
their private data for a recommendation scenario. Witnessing the growing
concern about privacy, users might want to exploit their sensitive data and
share only a small fraction of it. In such a context, classic CF approaches
are no more feasible. To overcome these problems, we have proposed FedeRank, a
novel recommendation framework that respects the FL paradigm. With FedeRank,
private user feedback remains on user devices unless they decide to share it.
Nevertheless, FedeRank ensures high-quality recommendations despite the
constrained setting. We have extensively studied the performance of FedeRank
by comparing it with other state-of-the-art methods. We have then analyzed the
impact of progressive reduction of user feedback and studied the effects on
the diversity of the recommendation results. Finally, we have investigated
whether the federated algorithm imposes an algorithmic bias to the recommended
lists. The study paves the way for further research directions. On the one
hand, the results’ analysis suggests that centralized recommender systems are
not performing at their best. Feeding recommender systems with all the
available feedback, without any filtering, may lead to a performance
worsening. On the other hand, the competitive results of FedeRank suggest that
the FL-based algorithms show a recommendation quality that makes them suitable
to be adopted on a massive scale.

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# Boosting the public engagement with astronomy through arts

Valentin D. Ivanov  European Southern Observatory, Karl-Schwarzschild-Str. 2,
85748 Garching bei München, Germany<EMAIL_ADDRESS>
(2021-07-02)

###### Abstract

Arts are a seamless way to introduce the general public to both basic and more
sophisticated astronomical concepts. The visual richness of astronomy makes it
attractive and easily incorporated in painting and literature. Astronomy is
the only science with a muse – Urania – implying that, at least in the eyes of
the ancients, it was an art itself. I review some less well known
representation of astronomical concepts in literature with potential
application in education.

##  1 Motivation

The most ancient art is discovered on the walls of caves and usually depicts
everyday scenes – somewhat direct studies of the human condition in the
immediate environments of its creators. The existence of such artistic
examples is evidence that even in those much more difficult times than today,
the humans have found resources to investigate the surrounding world,
themselves and their place in that world via artistic tools. It is also a
testament of the motivational power of art, needed to ensure those resources
were allocated in epochs that we would call times of extreme scarcity.

I set here a modest goal – to use this power of art for educational purposes,
taking advantage that it appeals to human emotions. The emotions are a key to
long term memory [54]. Furthermore, they provoke and feed human curiosity,
posing with the same intensity the questions on different scales: what lies
behind the neighboring hill and what lies behind the neighboring galaxy. Art
equally provokes human imagination and charges the investigative spirit – two
necessary tools for addressing these questions.

Many educators have invoked art before in teaching to bring in convenient
examples and colorful illustrations of material that otherwise may seem to
students unappealing and challenging at the same time. Michael Brotherton from
the University of Wyoming in Laramie went even further and organized a series
of Launch Pad111 https://www.launchpadworkshop.org/ workshops to teach some
basic astronomical concepts to interested writers.

Here I consider a few less well known literary works with potential
application in astronomical education. They are dominated by the genre of hard
science fiction, which by construction is “science heavy”. Hopefully, they
will be added to the astronomical teaching practices and will help both
teachers and students. This summary is aimed at educators.

##  2 Primers

###  2.1 Architecture of planetary systems in the novel The Photon Starship

The discovery of the first hot jupiter 51 Peg b [39] was a surprise for the
astronomical community because our expectations for exoplanetary systems were
based on the Solar system and it lacks an analogue of giant gas planets that
move around their host stars on orbits tighter than that of Mercury. Later we
discovered that the Solar system does not have representatives of another
class of planets either – the so-called super-Earths or mini-Neptunes,
reported by [2] and [12], among others.

The system of 51 Peg posed a difficult question how giant gas planets can
exist so close to their star. Such planets could not have formed in situ
because of the tidal forces. This leaves the orbital migration as a likely
explanation [30]. It should be noted that the widely accepted Nice model of
the Solar system evolution does include planetary migration (for a general
description of the Nice model see [41]).

Exotic exoplanets are well covered in fiction. Probably, the most
scientifically accurate and useful is the anthology A Kepler’s Dozen (2009),
edited by S. Howell and D. Summers. It contains 13 stories, taking place on
planets, discovered by the Kepler space telescope. However, the concept of an
evolving planetary system is less well covered.

A surprising example with a potential educational application was penned by
Dr. Dimitar Peev (1919-1966), a science fiction writer and avid promoter of
science from Bulgaria. His degree was in Law, but for the entire duration of
his multi-decade career he worked as a science journalist, founding and
contributing to the development of the two best known popular science
publications in his native country – the magazine Kosmos and the newspaper
Orbita.

Peev described in his novel The Photon Starship (1964; Fig. 1, left column) a
crewed sub-light speed flight to our nearest neighbor in the constellation of
Centaurus. The book follows the life of Aster, a kid born on the ship, who has
never seen Earth. The story line includes the usual well-known surprises –
“meteor attack, radiation attack, malfunctioning robotic kitchen”.

Figure 1: Covers of the novel The Photon Starship and a collection Prisoners
of an Asteroid that includes Infra Draconis (top, left and right) and
portraits of their authors Dr. Dimitar Peev and Georgi Gurevich (bottom, left
and right).

In the contest of this analysis, the most important element of the novel is
the discovery that the expedition makes upon arrival: Proxima is surrounded by
a ultra-rich system of more than hundred planets with sizes between those of
Mercury and Neptune.

Here we should remind ourselves that Proxima, in addition to being the closest
star to the Sun (at just over 4 light years), is the third component in a
stellar system where the primary itself is a close stellar binary, known as
Alpha Cen A and B. This is relevant for the analysis carried out by the
fictional astronomers in the book. They find that the bodies orbiting Proxima
fall into two distinct classes:

(i) “Native” planets, with orbits nearly aligned into a single plane, similar
to the planets in the Solar system. The scientists in the book speculate that
these have been formed in the protoplanetary disk that once have surrounded
Proxima itself, much like the planet of our system have formed in the
protoplanetary Solar disk.

(ii) Accreated planets on highly elliptical orbits, with random orbital
inclinations. These planets are likely descendants of captured planetesimals
that have been ejected from the neighboring Alpha Cen A and B early in the
history of that system. The stability of this system is not discussed.

The book offers background material for explaining a number of astronomical
concepts. The stellar multiplicity and the various mechanisms of binary
formation are perhaps the most obvious ones. A suitable topic for discussion
in class is the validity of the fictional hypothesis, explaining the existence
of the accreted part of the Proxima’s planetary system: is it realistic in the
light of the more recent – with respect to the publication year of the novel –
discovery that the chemical composition of Alpha Cen A and B is different than
that of Proxima? This was found during detailed abundance analysis of the
three stars: [Fe/H]=0.22$\pm$0.10 to 0.26$\pm$0.08 [23] for Alpha Cen A and B,
and [Fe/H]=$-$0.07$\pm$0.14 [45] to 0.05$\pm$0.20 [24] for Proxima (the
statistical significance of that difference is yet another topic for
discussion that I will only point at here). This implies that while the
central pair has formed together, while Proxima is a later acquisition, most
likely being accreted during a stellar flyby. The time of this flyby is
unknown, but the probability that it might have happened early enough while
the central binary still had multiple planetesimals is low, just because this
is a short period – of up to a few tens of millions of years [25, 29] – with
respect to the billion year age of the two main stars in the system. Dynamic
studies of the Alpha Cen system also favor different origin of its components
[15].

Stellar flybys like the one during which Proxima joined the Alpha Cen system
are extremely rare on human lifetimes, but common by astronomical standards.
Our Solar system underwent one only about 70 thousands of years ago [37, 6,
22], but the passing star had only $\sim$15 % of the Solar mass (Proxima is
comparable – 12 % of the Solar mass). Such events rise the question of the
fragility of the planetary systems [47]. They are difficult to detect, because
the encounters are statistically likely to involve the most common type of
stars in the Milky way – low-mass, cool and intrinsically faint objects – the
reason why Proxima itself was discovered only in 1915 by Robert Innes [18, 19]
when astronomical photography became a common tool, making it possible to
carry out studies of proper motions of thousands of stars. The work of Innes
was an early but important precursor of moderns space missions like HIPPARCOS
[46] and Gaia [16] that draw detailed maps of the Milky Way and its nearest
neighboring galaxies.

One can use the novel as a topic starter for a discussion on exoplanetary
systems’ architecture as well. If we set aside the Solar system (keeping in
mind the argument about the status of Pluto222 A non-fictional account of the
Pluto debate can be found in How I Killed Pluto and Why It Had It Coming, by
Michael E. Brown, 2010. and about the hypothetical Planet IX – see [3, 8]),
then the richest planetary system we know of is Kepler-90, with eight planets
[53]. Incidentally, Kepler-90 is a G type solar analog, but the majority of
richest planetary systems are found around M stars, just like Proxima. An
example of that is the seven-planet TRAPPIST-1 [17]. This apparent preference
for late type host stars reflects the observational fact that low mass stars
tend to be orbited by more, but lower mass planets, in comparison with Solar
type stars [14], although some planets may have evaded detection [7]. Indeed,
[5] noticed some time ago that hot Jupiters are rarely found around cool low-
mass stars. Later on this was explained with the limitations of the planet
formation in the protoplanetary disks – it is easy to understand this
intuitively: the lower the stellar mass, the lower the mass of the
protoplanetary disk, the lower the mass of the planets that can form inside
them. The effect is boosted by an additional bias that the lower mass planets
are easier to discover around lower mass stars, than around higher mass stars
[40, 44].

It is unlikely that Dimitar Peev predicted by a stroke of genius the fine
details of the planetary formation in the vicinity of M stars. Still, the
agreement between the properties of his fictional planetary system and the
real planetary systems of M stars is not entirely a chance coincidence,
because in an attempt to make the his fictional world as realistic as
possible, he based the reality of the novel on first physical principles. A
number of important phenomena were taken into account: the scattering of
protoplanets by the two close-in companions, the conservation of momentum that
would preserve the orientation of planetary orbits in the plane of the
protoplanetary disk. There are some inconsistencies or rather improbable
elements, but they could only be recognized based on information that was not
available at the time when the book was written.

###  2.2 Pre-discovery brown dwarfs in the novella Infra Draconis

The novella Infra Draconis was first serialized in a popular science magazine
Knowledge – power in late-1958. It was written by Georgi Gurevich (1917-1998;
Fig. 1, right column) – a Soviet and Russian science fiction writer.
Interestingly, this novella has appeared in English twice, in collections of
science fiction stories by Soviet writers: A Visitor from Outer Space (1961,
Foreign Language Press, Moskow) and Soviet Science Fiction (1962, Collier, New
York). The latter has an introduction by Isaac Asimov. Before becoming a full-
time writer Gurevich had a successful career as a construction engineer. He
also published many popular science articles in newspapers and magazines –
which seems to be a common pattern among the writers who produced works
suitable for educational purposes.

The story follows a space flight to an ultra-cool object, called infra,
located in the Draco constellation. We learn that in the fictional world these
are recently discovered objects, too small to sustain fusion in their cores.
The infras are analogues of the real-world brown dwarfs (BDs).

Hypothetical dark substellar objects floating freely in space and not massive
enough to sustain hydrogen fusion were first considered in the scientific
literature only five years after the publication of Infra Draconis by [28] who
named them black dwarfs. They still burn Lithium, though, unlike planets –
their even lower mass “cousins”. The name was later replaced with “brown
dwarf”, as a truer description of their colors, as suggested by Jill Tarter,
better known for her SETI work. The first BD was observed in 1988 – it is a
companion to the white dwarf GD165, but it was not recognized that it belongs
to the class for a decade [38]. Modern theoretical models suggest these
objects span a range between $\sim$12 and $\sim$60 MJup [1, 42].

It is too late to ask the late Georgi Gurevich how he came up with the idea
for sub-stellar objects. In a similar situation, Frederick Pohl was asked how
he came up with the idea that a super-massive object resides at the center of
every galaxy – a statement made by one of the characters in his novella “The
Gold at the Starbow’s End” (1972). Apparently, he read it in a popular science
journal and with some speculation this hypothesis – at the time – can be
traced to works by Salpeter and Zeldovich published at around the same time
[50, 59]

The closest infra in the fictional world of Gurevich is only seven light days
away – a much smaller distance than to the nearest star Alpha Cen (discussed
in the previous section). This is also the most interesting infra, because its
surface temperature is 10 C – about the average winter day-time temperature on
the Bulgarian Black Sea coast (at about 42 deg north of the equator). This
puts Infra Draconis at the temperature range allowing existence of liquid
water. Unlike Earth, with its significant diurnal-nocturnal (day-to-night)
temperature variations, the infras have constant surface temperatures, because
they are heated internally. Their energy source is contraction – for the same
reason Jupiter emits more energy than the amount it receives from the Sun.

The kosmonavts from the novella spend fourteen years to reach their target,
but in the middle of the journey they discover that the Earth-side
observations were wrong – Infra Draconis is binary object. The two components
have surface temperatures of $-$6 C and 24 C. The original planning sends the
expedition to the cooler object – a giant methane and ammonia gas ball,
similar to Jupiter in our Solar system. However, the warmer one turns out to
be a liquid water world. The expedition’s leader makes the ultimate sacrifice,
descending below the surface (captains going on away missions is not a
tradition limited to Starfleet), only to discover in his last moments a
thriving technological extraterrestrial civilization (ETC) at the bottom of
the alien ocean.

In the real world the nearest binary BD we know of is Luh-16 (a.k.a. WISE
J104915.57$-$531906.1), located at about 2 pc from the Sun [33], but the
effective temperatures of both its components place them well above the liquid
water regimen. Much closer analog of the fictional Infra Draconis is the BD
WISE J085510.83$-$071442.5 (often abbreviated to W0855) – as far as we know, a
single object – with an effective temperature $\sim$250 K (close to $-$20 C)
at a distance of 2.2 pc from the Sun [34, 4]. It is probably 3–10 times more
massive than Jupiter and its age range is poorly constrained – it may lay
anywhere between 1 and 10 Gyr.

Why were these nearby objects discovered only recently? In fact, Luh-16 was
detected in a number of surveys going as far back as the 1970-90s [36], but
its high proper motion (8.1$\pm$0.1 arcsec yr-1) and the crowded region of the
sky it resided in prevented astronomers from recognizing that these detections
belong to the same object. The non-detection of W0855 is due to its intrinsic
faintness [4, 26, 35, 58].

Life on planets around BDs was considered by [31] (in fact, the first directly
imaged planet orbits a brown dwarf [10, 11]. They concluded that only more
massive BDs (M$\geq$30 MJup) are likely to sustain planets with habitable
conditions on sufficiently long time scales. Surprisingly, the idea of
Gurevich that life may thrive inside the atmospheres of a BD has also been
studied by [57] and [32]. They argue that there are a few tens of W0855like
objects within ten parsecs from the Sun, and that the habitable volume in them
may be hundred times larger than on Earth-like planets.

In the context of this summary the novella Infra Draconis is suitable to
introduce the ultra-cool sub-stellar mass objects, to underline their high
spatial density, and the possibility that they may harbor life – either on
planets or within their own atmospheres. The latter topic may be particularly
appealing to the public: recent data suggests that our Solar system may harbor
up to ten subsurface oceans, compared with only one planet with a habitable
surface – Earth. If the subsurface oceans are viable habitable zones, this may
increase the habitable space of a planetary system by an order of magnitude.

###  2.3 Astronomical methods and social environment in the astronomical
community in the novel Stars and Waves

The novel Stars and Waves333 https://www.starsandwaves.net/ was written by the
well-known astronomer Roberto Maiolino from University of Cambridge. He is
specializing in extragalactic studies and observational cosmology. This book
is different from previous examples. First, because it is a work of a
professional astronomer who knows the research process and astronomical
environment inside out. Second, because it is marketed as a thriller.

Stars and Waves offers information about various aspects of exoplanet research
and paints a realistic and detailed view of the life in the astronomical
community at a page-turning pace. An important disclaimer: in the real world
the astronomers’ lives do not lead to untimely ends as a result of fierce
competition to publish, and generally, the life in academia is not amply
sprinkled with violence, as the readers may be led to believe – these are only
plot drivers and concessions to the genre. The book can be used as educational
tool, but for more mature audience.

The novel often detours into the history of astronomy – the work of Newton,
Galileo and others are prominently featured in an inspirational manner. Some
relevant past and present-day technologies are also explained, so the novel
can provide background for a discussion how fast the technological progress
enables the astronomical progress.

The central scientific question in Stars and Waves – not revealed at the
beginning – is of finding life elsewhere in the Universe. The answer had been
pursued in two ways. The typical programs to search for advanced technological
extraterrestrial intelligence (SETI) usually rely on various leaked emission –
for example, radio from communications or heat from massive computation or
from Dyson spheres [49, 48, 56]. We argued in [20] that advanced technological
ETCs are likely to reduce such losses, rendering these strategies inefficient.
This leaves us with the options of communicating either with advanced ETCs
that are willing to set up beacons intentionally aimed at and optimized for
“younger” cousins like us, or with nearby (in both space and development)
peer-level ETCs that allow significant radio or thermal leaks.

The second path to search for life in the Universe is to look for traces of
the natural products of this life – the so-called biosignatures [43, 52]. An
excellent introductory reading material can be found at the NASA Astrobiology
page444 https://astrobiology.nasa.gov/education/alp/what-is-a-biosignature/.
The Oxygen and Ozone are the most informative biosignatures. Strictly
speaking, water is not a biosignature, but it is an important solvent and its
presence is considered critical for life as we know it. The Carbon dioxide and
Methane are other potential indicators of life, although some geological
sources can contribute to their content in the atmospheres of exoplanets [13,
51].

Stars and Waves presents to the reader an intriguing combination of bio- and
technosignature based ETC searches.

On more technical level, Maiolino introduces the transmission spectroscopy as
a main exoplanet characterization tool – in the real world this is a commonly
used technique that brought up the first direct detections of exoatmospheres
[9, 55]. This method can be traced further back to the Russian scientist
Mikhail Lomonosov (1711-1765) who discovered the atmosphere of Venus during a
transit of that planet across the Sun in 1761. [27] summarizes the present-day
status of the transmission spectroscopy.

The novel is written in what almost qualifies for a semi-documentary style,
the action takes place on existing (and exotic) astronomical locations and it
draws quite realistic picture of every-day’s life of researchers and
astronomical institutions. Some concessions to action have been made, though:
most large, modern observatories maintain stringent account for every second
of observing time, or every obtained image or a spectrum, especially if they
are funded by public money. Unsanctioned target changes at such observatories
are hardly ever possible. Finally, the book spectacularly succeeds conveying
the competitive academic atmosphere.

Stars and Waves can be used to stimulate discussion and interest towards a
number of subjects, ranging from astronomical instrumentation, including
spectroscopy; concepts why a certain site is suitable or not for observations,
including dryness and light pollution. A rarely touched upon topic is how
actually the work at observatories is organized and the novel invites a
comparison with the Commencement address that the famous astronomer Edward
Pickering (1846-1919) gave at Case School of Applied Science in Cleveland on
May 27, 1909. He outlined his uniquely insightful view of astronomical
institutions of the future, and they look surprisingly similar to the modern
observatories that Maiolino describes.

##  3 Summary

I describe a few literary works that can be useful for astronomical education.
They help to introduce many basic concepts, including binary stars, planet
formation, brown dwarfs. The big question about the search for other life in
the Universe is also covered.

This material can be used in different manners – as introductory points, as
basis for class discussion, or as cases to be troubleshooted by the students –
and for students at different level, from high school to amateur astronomers
[21] and even graduate level students who can exercise debugging some of the
false concepts and conclusions that were present in these works.

A number of novels and stories that can be useful to educators were omitted.
Among them are the anthologies Diamond in the Sky (2008) and Science Fiction
by Scientists (2017; both edited by M. Brotherton), the novel Les Robinsons du
Cosmos ((The Robinsons of the Cosmos; 1955) by the French SciFi writer Francis
Carsac (1919-1981), the upcoming astrobiological anthology Life Beyond Us
(2022, Eds. S. Forest, L. K. Law, J. Nováková), and in particular the
excellent non-fiction teaching manual Exploring Science Through Science
Fiction (2013) by B. B. Luokkala.

Finally, this paper offers an eclectic mix of references, ranging from
fiction, to popular articles and research works to help educators in finding
sources that match the level of their audience.

## Acknowledgements

This is an extended write up of a poster presented at the European
Astronomical Society (EAS) Annual Meeting held on line, Jun 28 – Jul 2, 2021,
Special Session SS6 (Jul 2, 2021): Diversity and Inclusion Day. I thank the
organizers for giving me the opportunity to demonstrate the power of art as an
educational tool.

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