# Numerical simulations of the internal shock model in magnetized relativistic
jets of blazars

Jesus Rueda-Becerril and Petar Mimica and Miguel A. Aloy
Departamento de Astronomía y Astrofísica, Universidad de Valencia, E-46100
Burjassot (Valencia), Spain
E-mail<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

The internal shocks scenario in relativistic jets is used to explain the
variability of the blazar emission. Recent studies have shown that the
magnetic field significantly alters the shell collision dynamics, producing a
variety of spectral energy distributions and light-curves patterns. However,
the role played by magnetization in such emission processes is still not
entirely understood. In this work we numerically solve the magnetohydodynamic
evolution of the magnetized shells collision, and determine the influence of
the magnetization on the observed radiation. Our procedure consists in
systematically varying the shell Lorentz factor, relative velocity, and
viewing angle. The calculations needed to produce the whole broadband spectral
energy distributions and light-curves are computationally expensive, and are
achieved using a high-performance parallel code.

##  1 Introduction

Blazars are a class of radio-loud active galactic nuclei (AGNs) whose jets are
pointing near the line of sight to the observer [13], and are known for
showing the most rapid variability of all AGNs. Extensive observations
indicate that the jets of blazars are relativistic. Their most remarkable
characteristic is the presence of flares in the X- and $\gamma$-ray bands,
usually wih a duration of the order of a few hours. The internal shock (IS)
model [10], invoked to explain this variability [6, 7, 12], is an idealized
model where an intermittently working central engine ejects shells of
magnetized plasma which collide due to their velocity differences. As a
consequence internal shocks are formed, accelerating particles at the shock
fronts and producing the non-thermal, highly variable radiation.

Our long-term objective for is the study of the influence of the magnetic
field on the observed emission using numerical simulations. In [9] we studied
a large number of shell collisions with different magnetization levels. In
[11] we focused on a limited number of parameters such as the observer viewing
angle, $\theta$, the bulk Lorentz factor of the slower shell, $\Gamma_{R}$,
and the relative Lorentz factor, $\Delta g:=(\Gamma_{L}/\Gamma_{R})-1$, where
$\Gamma_{L}$ is the bulk Lorentz factor of the faster shell. In the present
work we summarize some of the results studied therein.

We describe the common numerical setup in Sec. 2. The results are shown in
Sec. 3 and discussed in Sec. 4.

##  2 Numerical Setup

A modified version of the code SPEV [8] was employed to calculate the non-
thermal emission from ISs. We assume a cylindrical shell geometry and perform
all the calculations in the rest frame of the shocked fluid (RFSF). The shell
interaction was simplified as a one-dimensional Riemann problem and focus our
resources on a more detailed treatment of the non-thermal radiation. Our
method consists of three steps that we sum up in the following paragraphs.

_Solution of the Riemann problem._ Employing an exact relativistic
magnetohydrodynamics (RMHD) Riemann solver we determine the properties of the
internal shock waves. We follow the procedure described in [9] to set-up the
shells and to extract the information needed for the steps 2 and 3.

_Non-thermal particles transport and evolution._ The particles are injected
behind the shock fronts following the prescription of [3, 5, 9]. We assume
that a fraction of the thermal electrons are accelerated into a power-law
distribution at high energies, and that their energy density is a fraction of
the internal energy density of the shocked fluid. In the RFSF the shocks are
propagating away from the initial discontinuity, injecting and leaving non-
thermal particles behind. We evolve the energy distribution of non-thermal
electrons taking into account synchrotron and inverse-Compton (IC) losses. See
[9] for more details.

_Radiative transfer._ The total emissivity at each point is assumed to be a
combination of the following emission processes: (1) synchrotron radiation,
(2) IC upscattering of an internal (SSC) and an external radiation field
(EIC).

##  3 Results

We group our models according to the initial shell magnetization,
$\sigma:=B^{2}/4\pi\rho\Gamma^{2}c^{2}$. Hereafter the subscripts $L$ and $R$
will denote left (faster) and right (slower) shells, respectively. We compute
the spectra for a typical source located at $z=0.5$. In the rest of this
section we will present some of the final SEDs resulting from our simulations.
A larger collection is shown in [11]. The SED of each model has been averaged
over the time interval $0-10^{6}\,$s.

###  3.1 Weakly-magnetized models

The SEDs computed for the models with
$\sigma_{L}=\sigma_{R}=10^{-6},\Gamma_{R}=10$, $\theta=5^{\circ}$ and varying
$\Delta g$, are shown in the upper left panel of Fig. 1. The spectra show that
with increasing $\Delta g$ the IC component also increases, up to three orders
of magnitude. In order to see the effects on each emission process, the
synchrotron, SSC and EC components for $\Delta g=0.5,2.0$ are shown as dashed,
dot-dashed and dot-dot-dashed lines, respectively. While the three spectral
components (synchrotron, SSC and EC) have approximately the same order of
magnitude for $\Delta g=0.5$, for $\Delta g=2.0$ the SSC is almost two orders
of magnitude more luminous than the other two.

###  3.2 Moderately-magnetized models

The SEDs of the family of models $\sigma_{L}=\sigma_{R}=10^{-2},\Delta g=1.0$
and $\theta=5^{\circ}$ are presented in the upper right panel of Fig. 1. As in
the previous section, SSC and EC components are shown as dashed, dot-dashed
and dot-dot-dashed lines, respectively, but now for the models with
$\Gamma_{R}=10,17,25$. The synchrotron component for $\Gamma_{R}=10$ is
$\simeq 20$ times brighter than the SSC one, in contrast to the EC which is
$100$ times dimmer. For $\Gamma_{R}=25$ the EC is of the same order of
magnitude of SSC and synchrotron. The latter two decrease one order of
magnitude between the models with $\Gamma_{R}=10$ and $\Gamma_{L}$, while the
EC grows by almost one order of magnitude. This follows from the fact that the
number of electrons and the comoving magnetic field strength decrease with the
increasing $\Gamma_{R}$ [9], which means that there are less synchrotron
photons and less electrons which can scatter them in the SSC process. We model
the Klein-Nishina cutoff as a sharp cutoff, and its effect can be seen at
$\simeq 10^{23}\,$Hz, where all the EC spectra coincide. From the inset we can
see that there is no significant change in the flux of $\gamma$-photons,
although the spectral index softens for increasing $\Gamma_{R}$.

###  3.3 Strongly-magnetized models

The third family consists of the strongly magnetized models where
$\sigma_{L}=1$ and $\sigma_{R}=0.1$. The corresponding SEDs of this series of
models (lower panel of Fig. 1 are analogous to the models of Sec. 3.2. As we
can see, for $\Gamma_{R}=10$ the synchrotron component is $\simeq 100$ times
brighter than the IC. For $\Gamma_{R}=25$ this difference decreases to one
order of magnitude. Once again, EIC component rises with rising $\Gamma_{R}$,
to the point in which it begins to be comparable to the synchrotron component,
developing an IC hump. The EIC spectra interestect in a single point due to
our treatment of the Klein-Nishina cutoff. In the inset we can see that the
flux of $\gamma$-ray photons does not change appreciably in this family of
models. Table 1 lists a number of physical parameters in the reverse shock
(RS) of the present models. We see that the electrons in the RS of the
strongly magnetized models are fast-cooling. In fact, for $\Delta g=$1.5 the
injected electron spectrum is almost mono-energetic.

Figure 1: Upper left panel: Averaged spectra resulting from collisions of weakly magnetized shells ($\sigma_{L}=\sigma_{R}=10^{-6}$). Upper right panel: Same as the upper left panel, but for moderately magnetized shells ($\sigma_{L}=\sigma_{R}=10^{-2}$) and varying $\Gamma_{R}$. Lower panel: Same as upper right panel, but for strongly magnetized shells ($\sigma_{L}=1,\sigma_{R}=0.1$). The inset in each panel shows the photon spectral slope $\Gamma_{ph}$ as a function of the photon flux $F_{ph}$ in the $\gamma$-ray band (see Sec. 3.2). Colors of the points correspond to the line colors in the main plot. For selected models, the synchrotron, SSC and EIC contributions (dashed, dot-dashed and dot-dot-dashed lines, respectively) are shown. $\Delta g$ | $\Gamma$ | $r_{r}$ | $\displaystyle{\frac{B_{r}}{1{\rm G}}}$ | $\displaystyle{\frac{Q_{r,11}}{{\rm cm}^{-3}{\rm s}^{-1}}}$ | $\displaystyle{\frac{\gamma_{1r}}{10^{2}}}$ | $\displaystyle{\frac{\gamma_{2r}}{10^{4}}}$ | $\displaystyle{\frac{t^{\prime}_{crr}}{10^{3}{\rm s}}}$ | $\displaystyle{\frac{\gamma_{cr}}{\gamma_{1r}}}$
---|---|---|---|---|---|---|---|---
$0.5$ | $12.7$ | $1.26$ | $53.51$ | $0.11$ | $0.66$ | $0.64$ | $34.6$ | $0.12$
$0.7$ | $12.8$ | $1.46$ | $54.72$ | $1.03$ | $2.29$ | $0.63$ | $34.1$ | $0.03$
$1.0$ | $13.0$ | $1.75$ | $55.84$ | $7.33$ | $7.25$ | $0.62$ | $33.6$ | $0.01$
$1.5$ | $13.2$ | $2.22$ | $56.63$ | $68.00$ | $26.38$ | $0.62$ | $32.9$ | $0.003$
$2.0$ | $13.3$ | $2.67$ | $56.82$ | $112900.75$ | $61.68$ | $0.62$ | $32.5$ | $0.001$
Table 1: Physical parameters in the RS shocked region for the family of
strongly magnetized shells with different $\Delta g$. The bulk Lorentz factor
of both shocked regions is denoted by $\Gamma$, while $r$, $B$, $Q$,
$\gamma_{1}$ and $\gamma_{2}$ denote its compression ratio, comoving magnetic
field, comoving number of electrons injected per unit volume and unit time,
and lower and upper cutoffs of the injected electrons in the RS (see Eq. 11 of
MA12). $Q_{11}=Q\times 10^{-11}$. $t^{\prime}_{cr}:=\Delta
r^{\prime}/(c|\beta^{\prime}|)$ is the shock crossing time, where $\Delta
r^{\prime}$ and $\beta^{\prime}$ are the shell width and the shock velocity in
the frame moving with the contact discontinuity separating both shocks
(section 2 of MA12).
$\gamma_{c}:=\gamma_{2}/(1+\nu_{0}\gamma_{2}t^{\prime}_{cr})$ is the cooling
Lorentz factor of an electron after a dynamical time scale (shock crossing
time). $\nu_{0}:=(4/3)c\sigma_{T}(u^{\prime}_{B}+u^{\prime}_{\rm
ext})/(m_{e}c^{2})$ is the cooling term, where $\sigma_{T}$ is the Thomson
cross section and the primed quantities are measured in the comoving frame.
When $\gamma_{c}/\gamma_{1}\gg(\ll)1$ the electrons are slow (fast) cooling.
Note that the $Q_{11}$ for $\Delta g=2.0$ is much larger than $Q_{11}$ of the
other models because $\gamma_{1}\simeq\gamma_{2}$.

###  3.4 $\gamma$-rays spectral slope

A linear least-squares algorithm is used to deduce the $\gamma$-ray spectral
slope $\Gamma_{ph}$. Due to the fact that we are not modeling the Klein-
Nishina part of the spectrum, we only performed the calculations of
$\Gamma_{ph}$ for those models that do not show a large drop-off in the photon
flux. In Fig. 2 we show $\Gamma_{ph}$ as a function of the photon flux for
energies $>0.2\,$GeV, where $F_{ph}$ is the photon flux for photon energies
$>0.1$ GeV [1]. We compare our results with sources found in 2LAC [2],
restricting the comparsion to sources with $0.4\leq z\leq 0.6$. In Fig. 2 we
see that weakly and moderately magnetized models overlap with the
observations, with more weakly than moderately magnetized models falling
within the observed part of the parameter space.

###  3.5 Compton dominance $A_{C}$

Another way to correlate magnetization with observed properties can be found
by representing the Compton dominance $A_{C}$ as a function of the ratio of
IC-to-synchrotron peak frequencies $\nu_{IC}/\nu_{syn}$. Models with
intermediate or low magnetization occupy a range of $A_{C}$ roughly compatible
with observations [4], while the strongly magnetized models tend to have
values of $A_{C}$ that are probably uncompatible with those observed in actual
sources, unless collisions in blazars happen at much larger Lorentz factors
than currently thought.

Figure 2: Left panel: Spectral slope $\Gamma_{ph}$ for the photon energies
$>200\,$MeV as a function of the photon flux for energies $>100$ MeV [1]. The
symbols joined by lines represent our numerical models, while cyan and magenta
triangles represent BL Lacs and FSRQs at redshift $z\simeq 0.5$ from 2LAC [2].
Right panel: Compton dominance $A_{C}$ as a function of the synchrotron peak
frequency $\nu_{\rm syn}$ for all the models studied in [11].

##  4 Conclusions

We have shown that the SEDs of FSRQs and BL Lacs strongly depend on the
magnetization of the emitting plasma. Our models predict a more complex
phenomenology than what is currently supported by the observational data. A
conservative conclusion is that the observations restrict the probable
magnetization of the colliding shells that take place in actual sources to, at
most, moderate values (i.e., $\sigma\lesssim 10^{-1}$), and if the
magnetization is large, with variations in magnetization between colliding
shells which are smaller than a factor $\sim 10$. We find that FSRQs have
observational properties corresponding to models with negligible or moderate
magnetic fields. BL Lacs with moderate peak synchrotron frequencies
$\nu_{syn}\lesssim 10^{16}\,$Hz and Compton dominance parameter $0.1\gtrsim
A_{C}\gtrsim 1$ display properties that can be reproduced with models with
moderate and uniform magnetization ($\sigma_{L}=\sigma_{R}=10^{-2}$). We find
that a fair fraction of the blazar sequence can be explained in terms of the
intrinsically different magnetization of the colliding shells. We observe that
the change in the photon spectral index ($\Gamma_{\rm ph}$) in the
$\gamma-$ray band can be a powerful observational proxy for the actual values
of the magnetization and of the relative Lorentz factor of the colliding
shells. Values $\Gamma_{\rm ph}\gtrsim 2.6$ result in models where the flow
magnetization is $\sigma\sim 10^{-2}$, whereas strongly magnetized shell
collisions ($\sigma>0.1$) as well as weakly magnetized models may yield
$\Gamma_{\rm ph}\lesssim 2.6$.

## Acknowledgements

We acknowledge the support from the European Research Council (grant
CAMAP-259276), and the partial support of grants AYA2013-40979-P,
CSD2007-00050 and PROMETEO-2009-103, and to the Consejo Nacional de Ciencia y
Tecnología (MEXICO) for a doctoral fellowship to J.M.R.B.

## References

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  * [3] M. Böttcher & C.D. Dermer, _Timing Signatures of the Internal-shock Model for Blazars_ , _ApJ_ 711 (445) 2010.
  * [4] J.D. Finke, _Compton Dominance and the Blazar Sequence_ , _ApJ_ 763 (134) 2013.
  * [5] M. Joshi & M. Böttcher, _Time-dependent Radiation Transfer in the Internal Shock Model Scenario for Blazar Jets_ , _ApJ_ 727 (21) 2011.
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  * [9] P. Mimica & M.A. Aloy, _Radiative signature of magnetic fields in internal shocks_ , _MNRAS_ 421 (2635) 2012\.
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# Interactive Query Clarification and Refinement via User Simulation

Pierre Erbacher  ISIR - Sorbonne UniversityParisFrance
<EMAIL_ADDRESS>,  Ludovic Denoyer  Sorbonne
UniversityParisFrance Currently working at Ubisoft  ludovic.denoyer@sorbonne-
université.fr and  Laure Soulier  ISIR - Sorbonne UniversityParisFrance
<EMAIL_ADDRESS>
###### Abstract.

When users initiate search sessions, their queries are often unclear or might
lack of context; this resulting in inefficient document ranking. Multiple
approaches have been proposed by the Information Retrieval community to add
context and retrieve documents aligned with users’ intents. While some work
focus on query disambiguation using users’ browsing history, a recent line of
work proposes to interact with users by asking clarification questions or/and
proposing clarification panels. However, these approaches count either a
limited number (i.e., 1) of interactions with user or log-based interactions.
In this paper, we propose and evaluate a fully simulated query clarification
framework allowing multi-turn interactions between IR systems and user agents.

Interactive Information Retrieval, Query Clarification, Simulation

††ccs: Information systems Users and interactive retrieval

##  1\. Introduction

Understanding information need is a long-standing issue in Information
Retrieval (IR) (Cronen-Townsend and Croft, 2002; Jansen et al., 2000;
Sanderson, 2008), often highlighted by the difficulty for users to formulate
open-ended information needs into queries. Queries are thus often under-
specified and/or ambiguous (Jansen et al., 2000). Depending on the user or the
context, the same query may refer to different intents. For instance, the
query ”Orange” may refer to several topics, including company names,
locations, songs titles, … To tackle this issue, numerous works have been
proposed. One first line of work relies on query reformulation (Amati and Van
Rijsbergen, 2002; Lavrenko and Croft, 2001; Rocchio, 1971; Zukerman and
Raskutti, 2002) where the objective is to rewrite the query. A lot of effort
has been provided by designing models based on either (pseudo-)relevance
feedback (Amati and Van Rijsbergen, 2002; Lavrenko and Croft, 2001; Rocchio,
1971) or external knowledge resources (Zukerman and Raskutti, 2002). But
recently, the advances in machine translation models and in large language
models have turned this task into a query generation task (Dalton et al.,
2020; Elgohary et al., 2019). Another category of work focuses on search/query
diversification (Agrawal et al., 2009; Cai et al., 2016; Carbonell and
Goldstein, 1998; MacAvaney et al., 2021; Nogueira et al., 2019a) to increase
the query coverage, particularly when the query is multi-faceted. While early
search result diversification work have designed or derived the Maximal Margin
Relevance (MMR) model (Carbonell and Goldstein, 1998), other techniques such
as document clustering (Agrawal et al., 2009) or document-driven voting scheme
(Dang and Croft, 2012) has been used to retrieve a diversified list of
documents. Recently, MacAvaney et al. (MacAvaney et al., 2021) have proposed
to focus on query diversification by generating queries by designing a
Distributional Causal Language Modeling. However, for all these
diversification techniques, the issued document list might include some top-
ranked documents that do not match with the user’s intent (Wang and Zhu,
2009). This highlights the need to clarify users’ queries before retrieving
documents. A last category of work aims to leverage search history to infer
user’s profile or session context, with the objective to ground the initial
query (Matthijs and Radlinski, 2011; Kong et al., 2015; Harvey et al., 2013;
Xiang et al., 2010; Bennett et al., 2012). By encoding short-term behavior or
long-term behavior as features of the ranking model, these methods manage to
retrieve more personalized documents. But, these approaches might be limited
by the user’s behavior’s variability over time (Zamani et al., 2020b). In
parallel, neural ranking models, such as (Khattab and Zaharia, 2020;
Hofstätter et al., 2021), have increased their performance due to the fine-
grained capture of queries and documents semantics. Nevertheless, the query
ambiguity is often inherent to users, increasing the need to place the user at
the center of the IR process.

A promising approach has been proposed in (Aliannejadi et al., 2019) to
clarify information needs by proactively interacting with the user. The
authors propose a conversation framework that consists in generating
clarifying questions when the query is ambiguous. Clarifying questions might
be query reformulation (e.g., ”Would you like to know how to care for your dog
during heat?” for the initial query ”dog heat” as in (Aliannejadi et al.,
2019)) or questions with possible options (e.g., ”what do you want to know
about this british mathematician? Options: movie, suicide note, quotes,
biography” for the initial query ”alan turing” as in (Zamani et al., 2020a)).
With this in mind, the classic workflow for asking clarifications is based on
three main steps (Aliannejadi et al., 2019): 1) the IR system produces a
clarifying question for the user, 2) the latter provides an answer or selects
an option, and 3) the IR system ranks documents according to the user’s
feedback. The pioneering work (Aliannejadi et al., 2019) aims at generating
clarifying questions by 1) retrieving a predefined set of questions using a
Bert-based model and 2) at each turn, selecting the best query through a
conversation history-driven model. The user’s answer corresponds to a
predefined text built using crowd-sourcing. One drawback of this approach is
that the multi-turn conversation is log-based, interactively simulated using
predefined logs of conversation history (i.e., sequence of questions/answers
obtained by HITS). This simulated conversation defined a priori without
interaction with the proposed question selection model might hinder the
evaluation performance in the sense that we are not sure about the soundness
of the conversation flow. Other work (Zamani et al., 2020a; Wu et al., 2018;
Guo et al., 2011; Santos et al., 2012; Ozertem et al., 2012) tackle this issue
by proposing generative models, that create clarification question or query
suggestions. But they do not address the multi-turn framework, stopping the
clarification process at the first interaction.

In this paper, we propose to build a fully simulated query clarification
framework allowing multi-turn interactions between IR and user agents.
Following (Aliannejadi et al., 2019), the IR agent identifies candidate
queries and ranks them in the context of the user-system interactions to
clarify the initial query issued by the user agent. We particularly target
simple information needs, multiple information needs are let for future work
since it might impact the modeling of the query ranking function. Our
framework can be seen as a basis and a proof-of-concept for future work
willing to integrate sequential models (namely reinforcement learning models)
for question clarification. It is worth noting that large language models
relying on attention mechanisms (transformers) are not yet well suited to
handle sequential interactions and long-term planning, as current models are
hardly trainable with current reinforcement learning algorithms (Chen et al.,
2020). Therefore, all agent components in our framework are based on
continuous and simple models. To validate our simulation framework, we conduct
an experimental analysis on the MS Marco dataset. We show the benefit of
multi-turn interactivity and evaluate the effectiveness of different question
selection strategies.

##  2\. Question Clarification Simulation Framework

###  2.1. Overview and Research Hypotheses

Our query clarification simulation framework is inspired from (Aliannejadi et
al., 2019), but provides the possibility of leveraging user-system agents’
interactions sequentially. More particularly, our framework is illustrated in
Figure 1 and relies on the following workflow:

  * •

A) The user issues an initial query $q_{0}$ associated to her/his information
need $i$ to the IR system.

  * •

B) The IR system generates a set $Q=\\{q_{1},q_{2},...,q_{m}\\}$ of candidate
queries which might express different query reformulations or diversified
queries to better explore the information need $i$.

  * •

C) The IR system selects $N$ queries to display to the user. To do so, we
propose to follow (Aliannejadi et al., 2019) and design a model ranking the
candidate query set $Q$ to identify the top $N$ queries.

  * •

D) The user selects one of the $N$ queries, enabling to extract positive and
negative feedback, resp. noted $(q^{+},q^{-})$.

  * •

Steps C) and D) can be repeated several times to model multi-turn
interactions. The query set ranking function (step C) integrates the user’s
sequential feedback ($q^{+},q^{-}$) to improve the query ranking along with
the interaction simulation.

  * •

E) After $T$ turns, the IR system considers the best ranked query as the
optimal query reformulation and runs a ranking model to retrieve documents.

The design of this evaluation framework is guided by some choices/research
hypothesis.
$\bullet$ First, following (Aliannejadi et al., 2019), we consider a fixed set
of candidate queries $Q=\\{q_{1},q_{2},...,q_{m}\\}$ constituting the
reformulation of the initial query $q_{0}$. All the interactions are leveraged
to improve step by step the ranking of this candidate query set so as, at the
end of the session, the final query used for retrieving documents is a good
clarification of its initial one. Obviously, this means that the set of
candidate queries includes a large variety of queries which, for some of them,
improve the search performance.
$\bullet$ Second, following (Zamani et al., 2020a), we propose to model
question clarification as a possible option between two reformulated queries.
In other words, expressed in natural language, the IR system agent would ask
the user agent the following question: ”Which reformulated query do you
prefer? A or B”. This implies that the user is willing to judge queries A or B
regarding its information need.
$\bullet$ Third, guided by the motivation to propose a framework for future
work on sequential models, we consider here that each agent component is
modeled at the embedding level. Indeed, leveraging large language models for
generating/ranking questions is very effective, but integrating them into
reinforcement learning models is still challenging (one main reason being the
computational cost). This means that we processed a priori all queries and
documents to represent them using text embeddings. This processing is done
offline, alleviating the sequential modeling of the text encoding.

In what follows, we present the different components behind the IR system and
user agents.

Figure 1. Query clarification simulation framework

###  2.2. The IR System Agent

The IR agent has three objectives in our framework: 1) generating the set of
candidate reformulated queries willing to be presented to the user, 2) ranking
this set to identify the most relevant queries according to the interaction
history, 3) ranking documents using the best-ranked query (ending the
interactive session).

#### Generation of the candidate reformulated query set.

The objective here is to instantiate various and diverse reformulation
covering a wide range of relevant topics for the initial query $q_{0}$.
Different techniques might be used, leveraging large language models (Nogueira
et al., 2019c; Raffel et al., 2020; Rao and III, 2019), query diversification
(Cai et al., 2016; MacAvaney et al., 2021; Ye et al., 2021) or query expansion
(Pal et al., 2013). We propose here to use the T5 model (Raffel et al., 2020)
which is designed to translate token sequences into other token sequences. It
has already been used for query reformulation tasks, demonstrating its ability
for our approach (Chen et al., 2020; Raffel et al., 2020; Lin et al., 2020).
On the top of that model, the generation process is driven by beam diversity
(Vijayakumar et al., 2016) which aims at generating a set $Q$ of diversified
query reformulation, $Q=\\{q_{1},q_{2},...,q_{m}\\}$.

#### Ranking of queries based on the interaction history.

The role of the selection policy is to select queries used to interact with
the user agent. Following (Aliannejadi et al., 2019) which proposes to rank
queries according to both performance criteria and the interaction context, we
use a conditional ranker (Burges et al., 2005) which computes a pairwise score
between two candidates queries given the context, namely the initial query
$q_{0}$ and the additional information provided by interaction with the user.
Let $q_{i}$ and $q_{j}$ be the candidate queries with their supervised
effectiveness scores, resp. $y_{i}$, $y_{j}$. The ranking model relies on:

(1) $P(y_{i}>y_{j}|q,q_{i},q_{j},feedback_{t-1},...,feedback_{1})$

For sake of simplicity, we assume that each query (initial or candidate) are
represented through text embeddings. In the following, $q$ refers to query
embedding and $d$ to document embedding.

In practice, the ranking model estimates a score for each query $q_{i}$ and
$q_{j}$ given all the context,
$\\{q,q_{i},q_{j},feedback_{t-1},...,feedback_{1}\\}$ and then compare these
scores to identify which one is the most relevant. $feedback_{t}$ corresponds
to selected or not selected queries (resp. $q^{+}$ and $q^{-}$) by the user
agent at interaction turn $t$. These queries are concatenated as follows:
$feedback_{t}=(q^{+},q^{-})$ and feedback overall interaction turns are
aggregated, the whole process using a Hierarchical Recurrent neural network
(RNN) to encode at the interaction level and also the sequence of
interactions. Note that queries $q^{+}$ and $q^{-}$ are encoded differently
using resp. a $cosin$ and $sin$ function. Moreover, we do not encode the
position in which each query is presented to the user agent, as this latter
does not have position bias on the clarification query selection.

#### Final ranking of documents

Documents are retrieved with the top ranked query using a Dense Retriever
model (Hofstätter et al., 2021).

###  2.3. The User Agent

After issuing the initial query $q_{0}$, the user agent interacts with the IR
system agent to refine her/his information need. With this in mind, we
hypothesize that the user is greedy toward her/his intent and fully
cooperative. Therefore, he always selects the preferred query as the most
similar to the intent. Despite being unrealistic, we ignore the click bias
problem for clarification panel presented in (Zamani et al., 2020c, b) (as
mentioned earlier). Other choices for user simulation could be done, following
(Câmara et al., 2022), but we let these variations for future work.

In practice, let $d$ be a user intent, $q_{i}$ and $q_{j}$ the clarification
queries presented to the user agent. The user agent selects the best query
(noted $q^{+}$ for highlighting positive feedback from the user) according to
a similarity metric (in our case, the dot product) between the proposed
queries $q_{i}$ and $q_{j}$ and intent $d$:

(2) $q^{+}=argmax_{q_{i}}(\langle q_{i},d\rangle)$

The non-selected query, $q^{-}$, expresses negative feedback.

##  3\. Evaluation Protocol

Evaluating our simulation framework consists in measuring the effectiveness of
the final ranking after $T$ clarification interactions. Since the user
behavior is greedy and follows a simple behavior dependent on the query
selection process, the effectiveness results mainly denote the quality of this
latter component. Other components (candidate set generation and final
document ranking) do not depend on the interaction feedback, so we mainly
focus on understanding whether the selection policy integrates users’ feedback
and takes good decisions to select the $N$ clarification questions.
For reproducibility, the code of our simulation framework and the evaluated
baselines/scenarios will be released upon acceptance.

###  3.1. Dataset

We carry out our experiments on MS Marco 2020 passages which regroups 8.8M
passages and more than 500K Query-Passage relevance pairs. Following (Nogueira
et al., 2019b), we evaluate our model on 2 sets. The small test set (43
queries) and a subset of the dev set (1000 queries sampled from 59 000). One
motivation to consider these two datasets is their difficulty level: in the
dev set, only one passage per query is labeled relevant in the ground truth,
while several passages are considered as relevant in the test set.

###  3.2. Baselines and Scenarios

To evaluate the effectiveness of our selection policy component, we compare
with:
(1) Non-interactive settings to show the gain of interacting with users. We
measure the ranking effectiveness of the user’s initial user query (noted User
Query), the Best Reformulation in the candidate query set - which can be seen
as an oracle, and the MonoT5 Documents re-ranker which acts as a strong
ranking baseline (Pradeep et al., 2021). This model is a pointwise ranking,
estimating relevance scores for query/document pairs. This model relies on a
large sequence to sequence language model pretrained on various task (Raffel
et al., 2020). Please note that using this model for the selection policy, and
therefore integrating user’s feedback, is not obvious since this is a seq2seq
pointwise model, labels associated with queries are binary (relevant or not)
and has to be grounded relative to a value. For that reason, we only consider
its non-interactive scenario.
(2) Naive interactive selection: At each step, we select the 2 top ranked
queries from the current query rank and then remove the query which has not
been selected by the user agent. The re-ranking of the candidate query set is
only carried out once, at the beginning of the session, and the size of this
list decreases with the interaction number.

To instantiate the selection policy after each interaction-driven query
ranking step (step C in Figure 1), we consider these scenarios:
(1) Interact. + Random Sampl: we sample 2 queries from the ranked candidate
query set to constitute the interaction pair.

(2) Interact. + Top 2: we select the top 2 query reformulations at each turn.

(3) Interact. + random sampl@5: we randomly select 2 queries among the top 5
query reformulations at each turn.

(4) Interact. + Kmeans selection: At each turn, queries in the candidate set
are clustered in 2 groups using Kmeans. Queries from each cluster are ranked
by the model. The best-ranked query from each cluster is then selected for
interaction with the user. The cluster of the query not selected by the user
is removed for the next turn from the set of candidate queries. This strategy
corresponds to a refinement strategy, removing a group of semantically similar
queries that have not been chosen by the user and going deeper in the other
cluster.

Figure 2. Effectiveness score of query reformulation by rank.

###  3.3. Model Implementation

All queries and passages embeddings are pre-computed using the Dense Retriever
proposed by (Hofstätter et al., 2021). Embeddings are stored and indexed using
faiss HSWN32 index (Johnson et al., 2021). The candidate query set is
generated by diversity beam with a group penalty equal to $0.6$. The size of
the candidate set is of 64. The number of queries displayed to the user agent
is set to $N=2$. For the model hyper-parameters, we use batches of size 128,
the optimizer is Adam ($\beta_{1}=0.9,\beta_{2}=0.99$) with weight decay
$(=0.01)$. We use batch normalization and dropout $(p=0.3)$ between each
layer. The learning rate is set to $1\times 10^{-4}$.

##  4\. Results

###  4.1. Preliminary Analysis

We present here a preliminary analysis to quantify the potential retrieval
performance gain of the candidate query set within the question clarification
step. To do so, we compare the performance of different query rankings: 1) the
candidate query generated by the T5 model ranked by decreasing order of
likelihood resulting from the Diversity Beam search (without application of
our ranking function); 2) the Oracle corresponding to the candidate query set
ranked in a decreasing order according to their performance according to Mean
Marginal Rank metric in the ground truth. We emphasized that this Oracle curve
shows the performance of our T5 model at generating search oriented
reformulations. 3) The MonoT5 ranking corresponding to candidate queries re-
ranked by MonoT5. Figure 2 illustrates the performance of queries depending on
their rank in the different mentioned lists. From Figure 2, we can see that
ranking queries with MonoT5 allows to improve the performance for the top $k$
queries (MonoT5 vs. Output Generator). This has a negative effect for the end
of the list, but it is not critical in our case, since we consider selection
policy regarding the top query list. Moreover, one can notice that, although
performance are increased, there is still a gap between the curve of the
MonoT5 ranked list and the Oracle curve. Our intuition is that leveraging
users’ interactions will lower this gap, which leads to the evaluation we
performed in what follows.

|  | No interaction | 1 | 2 | 3 | 4 | 5
---|---|---|---|---|---|---|---
User Query | mrr@10 | 0.4554 | - | - | - | - | -
map@10 | 0.3382 | - | - | - | - | -
Best Reformulation | mrr@10 | 0.8720 | - | - | - | - | -
map@10 | 0.5646 | - | - | - | - | -
Monot5 (query ranker) | mrr@10 | 0.4713 | - | - | - | - | -
map@10 | 0.3209 | - | - | - | - | -
Naive selection | mrr@10 | 0.2135 | 0.3270 | 0.3597 | 0.4036 | 0.4191 | 0.4271
map@10 | 0.1222 | 0.1943 | 0.2205 | 0.2553 | 0.2688 | 0.2766
Interact. + random sampl | mrr@10 | 0.4031 | 0.4786 | 0.4814 | 0.4903 | 0.4814 | 0.5019
map@10 | 0.2531 | 0.3344 | 0.3413 | 0.3529 | 0.3480 | 0.3685
Interact. + Top 2 | mrr@10 | 0.4031 | 0.4746 | 0.4693 | 0.4903 | 0.4786 | 0.5019
map@10 | 0.2531 | 0.3294 | 0.3436 | 0.3520 | 0.3471 | 0.3428
Interact. + random sampl@5 | mrr@10 | 0.4031 | 0.4734 | 0.4670 | 0.4903 | 0.4798 | 0.5019
map@10 | 0.2531 | 0.3287 | 0.3420 | 0.3517 | 0.3469 | 0.3451
Interact. + Kmean | mrr@10 | 0.4031 | 0.5232 | 0.4658 | 0.4692 | 0.4863 | 0.5515
map@10 | 0.2531 | 0.3706 | 0.3207 | 0.3402 | 0.3181 | 0.3347

Table 1. Effectiveness results on the Test set of MS Marco passage 2020 (43
queries - multiple relevant documents per query)

|  | No interaction | 1 | 2 | 3 | 4 | 5
---|---|---|---|---|---|---|---
User Query | mrr@10 | 0.2090 | - | - | - | - | -
Best Reformulation | mrr@10 | 0.4119 | - | - | - | - | -
Monot5 (query ranker) | mrr@10 | 0.1557 | - | - | - | - | -
Naive selection | mrr@10 | 0.1228 | 0.1513 | 0.1659 | 0.1767 | 0.1866 | 0.1911
Interact. + random sampl | mrr@10 | 0.1719 | 0.2012 | 0.1990 | 0.1954 | 0.2003 | 0.2016
Interact. + Top 2 | mrr@10 | 0.1719 | 0.2020 | 0.1987 | 0.1973 | 0.2017 | 0.1990
Interact. + random sampl@5 | mrr@10 | 0.1719 | 0.2020 | 0.1983 | 0.1966 | 0.2007 | 0.2008
Interact. + Kmean | mrr@10 | 0.1719 | 0.1748 | 0.1984 | 0.2016 | 0.2158 | 0.2224

Table 2. Effectiveness results on the subset of MS Marco passage 2020 dev set
(1000 queries - 1 relevant document per query)

###  4.2. Effectiveness Results

We analyze here the performance of the query ranker at different interaction
turns using mmr@10 and map@10. Tables 1 and 2 resp. show the results on the MS
Marco passage 2020 test set and dev set. From a general point of view, we can
see that performance metrics are lower for the dev set than for the test set.
This can be explained by the task difficulty, which is higher for the dev set
in which only one document per query is assessed as relevant. By comparing all
baselines and scenarios, we can outline the following trends. 1) The first
candidate query ranking within our interactive models (No interaction columns)
provides lower performance than non-interactive baselines. For instance, the
Interact. + Top2 scenario observes a decrease of 12% in terms of mrr@10 for
the test set w.r.t. the initial user query. 2) But this trend is reversed with
each interaction turn to obtain for certain scenarios performance higher than
baseline ones (see all interaction models in the test set, and the Interact +
Kmeans for the dev set). 3) The interaction model with Kmean strategy looks to
be the best selection policy for question clarification since it obtains the
highest mrr@10 for both datasets. This is somehow intuitive because this
strategy might correspond to a refinement strategy, going deeper and deeper
into clusters. This is also connected with the dataset peculiarity since MS
Marco is mainly composed mono-faceted questions in natural language.

##  5\. Conclusion and perspectives

This exploratory work focuses on sequential click-based interaction with a
user simulation for clarifying queries. We provide a simple and easily
reproducible framework simulating multi-turn interactions between a user and a
IR system agent. The advantage of our framework is the simplicity of
interaction, as there is no need for dataset of real and annotated user-system
interactions. Experiments highlight performance gain in terms of document
retrieval through the multi-turn query clarification process and provide a
comparative analysis of selection strategies. The next steps for this work
are: 1) leveraging reinforcement learning for the selection policy. 2) test
more diverse and more sophisticated user simulation, as done in (Câmara et
al., 2022) for multi-faceted information needs.

##  6\. Acknowledgments

We would like to thank the ANR JCJC project SESAMS (Projet-ANR-18-CE23-0001)
for supporting Pierre Erbacher and Laure Soulier from Sorbonne Univeristé in
this work.

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