Triggered by van Rijsbergen's seminal work about the geometry of information retrieval, a recent development is the utilisation of the theory of quantum mechanics and quantum probabilities as an expressive integrated framework to capture a user's context and interaction with the system. In our talk, we will briefly introduce some fundamentals and early works behind information retrieval inspired by quantum theory. We will discuss how information needs and relevance can be expressed in our interactive framework, neatly combining geometry and (quantum) probability theory. We will then outline how quantum probabilities and Hilbert spaces can be utilised to express concepts of information foraging theory as an example of modelling user interaction.

1. Interactive Information Retrieval inspired by
Quantum Theory
Ingo Frommholz1
Haiming Liu2
Amit Kumar Jaiswal2
1
University of Wolverhampton
ifrommholz@acm.org
2
University of Bedfordshire
haiming.liu@beds.ac.uk
amit.jaiswal@study.beds.ac.uk
Refinitiv Labs London
January 14, 2021

2. Outline
Quantum-inspired Information Retrieval
Information Foraging Theory
Information Foraging and Quantum Probabilities

3. A Challenge

4. Quantum-inspired Information Retrieval

5. IR Models and Principles
Geometry, Probability and Logics [van Rijsbergen, 2004]
LUP
pDatalog
VSM LSI
LM
PRP
BM25
iPRP Boolean

6. IR Models and Principles
Geometry, Probability and Logics [van Rijsbergen, 2004]
LUP
pDatalog
VSM LSI
LM
PRP
BM25
iPRP Boolean
QM

7. IR Models and Principles
Geometry, Probability and Logics [van Rijsbergen, 2004]
LUP
pDatalog
VSM LSI
LM
PRP
BM25
iPRP Boolean
QMqPRP
QIA

8. A Language for IR
The geometry and mathematics behind quantum mechanics can
be seen as a ’language’ for expressing the different IR models
[van Rijsbergen, 2004].
Combination of geometry, probability and logics
Leading to non-classical probability theory and logics
Potential unified framework for IR models
Applications in areas outside physics emerging
Quantum Interaction symposia

9. IR as Quantum System?
An Analogy
Quantum System IR System
Particles, physical properties in
Hilbert spaces
Documents, relevance, informa-
tion needs in Hilbert Spaces
System state uncertain Information need (IN) uncertain
Observation changes system
state
Observed user interaction
changes system state
Observations interfere (Heisen-
berg)
Document relevance interferes
Combination of systems Combination of IN facets,
polyrepresentation, multimodal-
ity

10. Qubits and Quantum Systems
|0
|1
|ϕ
Qubit: basic unit of quantum information and
computing
A simple quantum system represented in a
Hilbert space
Two possible states: |0 and |1
(|. Dirac notation of vectors)
Qubits can be in state other than |0 and |1 (a
linear combination called superposition)
|ϕ = α|0 +β|1
with α,β ∈ C and |α|2
+|β|2
= 1
Then:
Pr(0| |ϕ ) = |α|2
(squared length of projection)

11. Quantum-inspired Information Access
Information Need Space [Piwowarski et al., 2010]
R
p1
p2
p4
p3
p5
System uncertain about user’s IN
Expressed by an ensemble S of possible
IN vectors :
S = {(p1,|ϕ1 ),...,(pn,|ϕn )}
Document relevance R richly described
as subspace (R is projector)
Probability of relevance:
Pr(R|d,S) = ∑
i
pi ·Pr(R|d,ϕi )
=||R|ϕ ||2
= tr(ρR)
with density matrix ρ = ∑i pi |ϕi ϕi |

12. User Interaction and Feedback
R∗
|ϕ1
|ϕ2
|ϕ5
|ϕ3
Outcome of feedback: Query,
relevant document, ...
Expressed as subspace
Project IN vectors onto
document subspace

13. User Interaction and Feedback
R∗
|ϕ1
|ϕ2
|ϕ4
|ϕ3
|ϕ5
Outcome of feedback: Query,
relevant document, ...
Expressed as subspace
Project IN vectors onto
document subspace
Document now gets
probability 1
System’s uncertainty
decreases
Also reflects changes in
information needs

14. Problems to Solve
How does our information need space look like?
How to build document subspaces R for relevance?
How to build ensemble S for information needs (in our case from
queries)?

15. Textual Representation
IN Space / Documents
|crash (Term)
|car (Term)
|jupiter (Term)
|jupiter crash
|car crash
R∗
topic
|ϕ
IN space based on term
space
IN vectors made of document
fragments
Weighting scheme (e.g., tf,
tf-idf,...)
Document is relevant to all
INs found in its fragments
Document subspace R
spanned by IN vectors
No length normalisation
necessary

16. Single-Term Query
Take all fragments vectors (IN
vectors) containing term t
This makes up ensemble St

17. Multi-Term Query
Mixture
Mixture of all combinations of
term fragments
The more term fragments are
contained, the more relevant
the document
S(M) = ∑n
i=1 wi Sti
wi is term weight

18. Multi-Term Query
Mixture of Superposition
Superpose all combinations
(e.g. 1√
2
(|ϕ +|ψ ))
The more fragment
superpositions are contained,
the more relevant a document
is
Indication that it works well
with multi-term concepts (e.g.
“digital libraries”)

19. Multi-Term Query
Tensor product
Assumption: each term
covers an IN aspect
Tensor product of all fragment
vectors combination of IN
aspects
The more tensor products are
satisfied, the more relevant is
the document
S(T) = i Sti
R(T) = i R
Pr(R(T)|d,S(T)) =
∏i Pr(R|d,Sti
)

20. What can it bring to IR?
Evaluation with several TREC collections
[Piwowarski et al., 2010]
Tensor representation of query could compete with BM25
We don’t lose retrieval effectiveness in an ad hoc scenario (but
gain expressiveness)
TREC-1 TREC-2 TREC-3 TREC-5 TREC-6 TREC-7 TREC-8 RB-2004
BM25 0.230 0.209 0.282 0.148 0.224 0.182 0.236 0.242
TF-IDF 0.084†
0.041†
0.056†
0.035†
0.088†
0.056†
0.082†
0.074†
M 0.205†
0.184†
0.226†
0.115†
0.173†
0.142†
0.165†
0.180†
MS 0.209†
0.167†
0.206†
0.112⇤
0.157†
0.117†
0.159†
0.165†
T1 0.232 0.195†
0.281 0.148 0.214 0.182 0.234 0.240
T2 0.222 0.200 0.259†
0.139 0.216 0.179 0.212†
0.228†
Table 1: This table reports mean average precision (MAP). The first line shows the test collection. The second and third lines
show the MAP value for BM25 and TF-IDF, respectively. For the query construction, M stands for mixture, MS for mixture
of superpositions, T1 and T2 for tensor product. For completeness, significance of the di↵erence with BM25 is shown for the
0.05 level (⇤
) and the 0.01 level (†
).
the span of the window (5). We can first observe that in all

21. Modelling Example: Author Space
Each author is a dimension
Non-orthogonal vectors:
authors not mutually exclusive
(conditional probability)
Angle between vectors
reflects the degree of
dependency (90◦ =
orthogonal = upright =
disjoint)
Example: Jones and Smith
(somehow) related, Smith and
Miller not

22. Modelling Example: Author Space
Document by Smith and Miller
User seeks for documents by
Jones
Document retrieved due to
relationship between Jones
and Smith

23. Modelling Example: Author/Topic Space
Combined author/topic space
Authors may be related only
w.r.t. a specific topic
Ex.: A user interested in
Smith’ documents about
logics may be interested in
Jones’ documents about
logics, but not in Jones’
documents about interactive
IR
Author represented as a
subspace
|SmithLogics
|JonesLogics
|JonesIIR

24. Modelling Example: Rating Space
Example: rating scale
good/bad/average – each is a
dimension
“Average” rated book
represented by 2-dimensional
subspace
User wants books which are
rated good
⇒ not relevant (|good
orthogonal)
Rrating
|good
|average
|bad

25. Polyrepresentation/Multiple Evidence
[Frommholz et al., 2010]
Content Author
Ratings
Comments
Polyrepresentation space as tensor product of single spaces
Probability that document is in total cognitive overlap:
Prpolyrep = Prcontent ×Prratings ×Prauthor ×Prcomments
User interaction may lead us into an entangled state (so far
unexplored relationship between polyrepresentation and
entanglement)

26. System Architecture
R∗
R∗
Quantum engine
Frontend / UI
User interaction
Subspace representation
State change
New state fed back
to frontend

27. QIA Extensions
Polyrepresentation [Frommholz et al., 2010]
Queries in sessions [Frommholz et al., 2011]
Use geometry and projections to determine type of and handle
follow-up query (generalisation, information need drift,
specialisation)
Summarisation [Piwowarski et al., 2012]
QIA interpretation of LSA-based methods
Query algebra for the QIA framework [Caputo et al., 2011]
Multimodal Query Auto Completion [Jaiswal et al., 2020b]

28. QIA Conclusion
QIA framework
User’s IN as ensemble of vectors
Documents as subspaces
User interaction and feedback
Term space, query construction
Can compete in an ad hoc scenario
Different representations
QIA extensions
Term space representation also applied in Quantum Language
Models (e.g., [Zhang et al., 2019])

29. Information Foraging Theory

30. Information Foraging Theory (IFT)
Optimal Foraging Theory aims to understand the rules that shape
the foraging behaviour of animals [Pirolli and Card, 1999].
[Pirolli, 2007] suggests how human seek information is like how
wild animals seek food
Information scent model
Information patch model
Information diet model

31. Information Scent Model
Describes how foragers follow information cues to find patches
with relevant information.
Aims to explain how people identify the value of information
based on cues.

32. Information Patch Model
Describes how foragers move between and within patches.
Predicts the amount of time a forager would/should spend within
a patch.

33. Information Diet Model
Describes how foragers decide which information to
use/consume
If a forager is too generalized, then they will waste too much
time on handling unprofitable information.
If a forager is too specialized, then they may waste too much
time searching for profitable information.

34. Application of IFT
Understanding user search behaviours and
preferences [Liu et al., 2010, Loumakis et al., 2011,
Azzopardi, 2014, Wittek et al., 2016, Ong et al., 2017,
Azzopardi et al., 2018, Niu and Fan, 2019, Shi et al., 2020,
Drias and Pasi, 2020, Jaiswal et al., 2019a, Jaiswal et al., 2019b,
Jaiswal et al., 2020b]
Improving effectiveness of the search
models [Azzopardi, 2014, Azzopardi et al., 2018,
Niu and Fan, 2019, Jaiswal et al., 2019a, Jaiswal et al., 2019b,
Jaiswal et al., 2020b]
Modelling and profiling Users [Liu et al., 2010]

35. Information Foraging and Quantum
Probabilities

36. Information Foraging Theory

37. Information Patch

38. Information Scent

39. IFT for Interactive IR
[Jaiswal et al., 2019a, Jaiswal et al., 2019c]
Information Foraging Theory (IFT) [Pirolli and Card, 1999] to
describe information retrieval behaviour which includes:
Information seeking: to locate interesting items.
Seeking strategies: to drive the users’ attention over a specific
item.
Behavioural effects: The influence on the selection of interesting
items.
Figure: The schematic architecture of Personalized Image RecSys

40. Personalised Content-based Image Recommendation
Interface
Image (I) = {Ipi,1
,Ipi,2
,...,Ipi,n
}

41. Image Query-auto Completion
[Jaiswal et al., 2020b]
qa∗ = argmax
q
P(q|qp,I) = argmax
{t1t2...tn}
P(t1t2...tn|qp,I)
Loss function = −∑
k
yk log( ˆqpk )+(1 −yk )log(1 − ˆqpk )

42. Intuitive Description using IFT
Probabilistic Patch Selection

43. How IFT Benefits an Interactive Framework?
IFT meets Reinforcement Learning (RL) [Jaiswal et al., 2020a]
To guide the searcher (or forager) during the information seeking
process (especially information exploration) by means of
Reinforced Foraging mechanism.
Reinforced Foraging: Reinforcement learning helps us devise
the Information Foraging strategy to follow the feat of information
seeking.
Assumption: We consider uncertainty in IS to be a problem that
is closely related to information need.
Representation of user actions (i.e. queries as information need)
follows the quantum probabilistic
constructs [Van Rijsbergen, 2004].
Theoretical framework that describes guided information
seeking powered by quantum-parameterised reinforced foraging.

44. Trivia
Why RL?
There is no supervision, only a reward signal.
Feedback is delayed, not instantaneous.
Agent’s actions effect subsequent data it receives.
Central idea of RL:
Interacts with the environment.
Learns from experience.
The target is to get the maximum expected cumulative rewards.
Central idea of Information Foraging theory (IFT):
Searches via information patches and constantly makes decision
among it.
Learns from enrichment.
The target is to get as much relevant information in as little time
as possible.

45. RL with IFT: Reinforced Foraging
Hypothesis: Information seeker as Forager [Wittek et al., 2016]
as RL agent.
Seeker adopts foraging behaviour (explore as well as exploit).
Reinforcement learning process enhanced by such type of
information seekers - so called, an adaptive RL agent.
IFT can resolve RL limitation of delayed reward i.e. "why every
step of seeker is important".
Foraging behaviour can enhance "experience" in reinforcement
learning mechanism.

46. Quantum Probability
Classical Probability
Given complete information,
there’s no residual
uncertainty; all probabilities
are then 0 or 1
Finite events - discrete and
mutually-exclusive
Quantum Probability
In every state, even if pure,
there are hypotheses whose
probabilities are neither 0 nor
1
Events defined in a complex
continuous vector space
(Hilbert Space) can be
represented as an arbitrary
vector

47. Constructs of quantum-inspired RL framework
Agent In our framework, the agent is a forager (information
seeker).
Action The agent executes query (as action |at , receives
states (|st ) and a scalar reward (Rei,ai
).
Environment Receives agent action (query) and emits
observation (|st+1 ) with corresponding reward.
State In our case, a state can be seen as the product of the
probability amplitudes of global-local projection (word
meanings) for all words of a query.
State Transition We use a feedback mechanism to compute the
transition among the states.
Policy We use stochastic policy network, so called Actor-Critic
reinforcement learning method.
Reward The success value of an agent’s action (|qi )

48. Quantum-inspired Reinforcement Learning Framework

49. Conclusion
Presented Quantum Information Access model based on Hilbert
spaces
Introduced Information Foraging Theory
Application of IFT in IR tasks – query auto-completion for image
search and recommendation
Formalised reinforcement learning with IFT in a quantum
framework

50. Thanks for your attention!
Questions?

51. Bibliography I
Azzopardi, L. (2014).
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Azzopardi, L., Thomas, P., and Craswell, N. (2018).
Measuring the utility of search engine result pages: an information
foraging based measure.
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A Query Algebra for Quantum Information Retrieval.
In Proceedings of the 2nd Italian Information Retrieval Workshop
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52. Bibliography II
Drias, Y. and Pasi, G. (2020).
Credible information foraging on social media.
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Frommholz, I., Larsen, B., Piwowarski, B., Lalmas, M., Ingwersen,
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(2011).
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53. Bibliography III
6611 of Lecture Notes in Computer Science, pages 751–754.
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Effects of foraging in personalized content-based image
recommendation.
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Jaiswal, A. K., Liu, H., and Frommholz, I. (2019c).
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content-based image recommendation.
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54. Bibliography IV
Jaiswal, A. K., Liu, H., and Frommholz, I. (2020a).
Reinforcement learning-driven information seeking: A quantum
probabilistic approach.
arXiv preprint arXiv:2008.02372.
Jaiswal, A. K., Liu, H., and Frommholz, I. (2020b).
Utilising Information Foraging Theory for User Interaction with
Image Query Auto-Completion.
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(ECIR 2020). Springer.
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Applying information foraging theory to understand user
interaction with content-based image retrieval.
In Proceedings of the third symposium on Information interaction
in context, pages 135–144.

55. Bibliography V
Loumakis, F., Stumpf, S., and Grayson, D. (2011).
This image smells good: effects of image information scent in
search engine results pages.
In Proceedings of the 20th ACM international conference on
Information and knowledge management, pages 475–484.
Niu, X. and Fan, X. (2019).
Deep learning of human information foraging behavior with a
search engine.
In Proceedings of the 2019 ACM SIGIR International Conference
on Theory of Information Retrieval, pages 185–192.
Ong, K., Järvelin, K., Sanderson, M., and Scholer, F. (2017).
Using information scent to understand mobile and desktop web
search behavior.
In Proceedings of the 40th International ACM SIGIR Conference
on Research and Development in Information Retrieval, pages
295–304.

56. Bibliography VI
Pirolli, P. (2007).
Information foraging theory: Adaptive interaction with information.
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Information foraging.
Psychological review, 106(4):643.
Piwowarski, B., Amini, M.-R., and Lalmas, M. (2012).
On using a Quantum Physics formalism for Multi-document
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(2010).
What can Quantum Theory Bring to Information Retrieval?
In Proc. 19th International Conference on Information and
Knowledge Management, pages 59–68.

57. Bibliography VII
Shi, X., Zheng, X., and Yang, F. (2020).
Exploring payment behavior for live courses in social q&a
communities: An information foraging perspective.
Information Processing & Management, 57(4):102241.
Van Rijsbergen, C. J. (2004).
The geometry of information retrieval.
Cambridge University Press.
van Rijsbergen, C. J. (2004).
The Geometry of Information Retrieval.
Cambridge University Press, New York, NY, USA.
Wittek, P., Liu, Y.-H., Darányi, S., Gedeon, T., and Lim, I. S.
(2016).
Risk and ambiguity in information seeking: Eye gaze patterns
reveal contextual behavior in dealing with uncertainty.
Frontiers in psychology, 7:1790.

58. Bibliography VIII
Zhang, L., Zhang, P., Ma, X., Gu, S., Su, Z., and Song, D. (2019).
A Generalized Language Model in Tensor Space.
Proceedings of the AAAI Conference on Artificial Intelligence,
33:7450–7458.

59. Reinforcement Learning Setup