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Wednesday 19 April 2023
QuantumML:Modelling Hidden Worlds of Information
Ghislain Fourny
Master‘s Thesis Presentation - March 29th, 2007
© Department of Computer Science | ETH Zürich
Wednesday 19 April 2023 Department of Computer Science 5
Why hidden worlds of information?
State-of-the-art search engines „merely“ look for
documents containing the words you give.
No Artificial Intelligence behind.
Though: IMDB with languages.
Wednesday 19 April 2023 Department of Computer Science 6
Why hidden worlds of information?
HausTier
MutterFenster House
Animal
MotherWindow
German world English world
Wednesday 19 April 2023 Department of Computer Science 7
Why hidden worlds of information?
HausTier
MutterFenster House
Animal
MotherWindow
German world English world
Wednesday 19 April 2023 Department of Computer Science 8
Why hidden worlds of information?
HausTier
MutterFenster House
Animal
MotherWindow
German world English world
The job of Artificial Intelligence
Research
Wednesday 19 April 2023 Department of Computer Science 9
Ontologies used in AI
Assertions: „Bordeaux“ is red wine The vintage is the year the wine was produced in
AI can infer ontologies from other ontologies
Wednesday 19 April 2023 Department of Computer Science 10
Ontologies
PinotBordeaux
MouthfeelVintage White wine
Red wine
Flavour Year
Oenologist world Not-an-expert world
Wednesday 19 April 2023 Department of Computer Science 11
Ontologies used in AI
Given a document, it is possible to make it
available in other worlds Simplify it Translate it ...
Job of the author, or of an automated AI Engine.
Wednesday 19 April 2023 Department of Computer Science 12
Ontologies used in AI
Given a document, it is possible to make it
available in other worlds Simplify it Translate it ...
Job of the author, or of an automated AI Engine.
We take this for granted
Wednesday 19 April 2023 Department of Computer Science 13
Questions that interest Information Systems people (us)
Suppose the AI work is all done.
How to describe a document available in
several worlds?
How to perform information retrieval on it?
Wednesday 19 April 2023 Department of Computer Science 14
Agenda
Introduction to QuantumML
Vector and Matrices Operations
Information Retrieval
Wednesday 19 April 2023 Department of Computer Science 15
A Document Visible in Different Worlds?
The same document is visible in three different
„worlds“: World 1: E World 2: G World 3: B
Wednesday 19 April 2023 Department of Computer Science 16
A Document Visible in Different Worlds?
Worlds as perspectives: From the right: E From the front: G From the top: B
Wednesday 19 April 2023 Department of Computer Science 17
A Document Visible in Different Worlds?
Such an object does not exist!
Are you willing to bet on this?
Wednesday 19 April 2023 Department of Computer Science 19
A Document Visible in Different Worlds?
Perspective 1
Wednesday 19 April 2023 Department of Computer Science 20
A Document Visible in Different Worlds?
Perspective 2
Perspective 1
Wednesday 19 April 2023 Department of Computer Science 21
A Document Visible in Different Worlds?
Perspective 2
Perspective 1
Perspective 3
Wednesday 19 April 2023 Department of Computer Science 22
A Document Visible in Different Worlds?
How can we encode such an object in the digital world?
A proposal:
|world1>foo<world1|
means that “foo” is visible in the world “world1”
|world2>bar<world2|
means that “bar” is visible in the world “world2”
Wednesday 19 April 2023 Department of Computer Science 23
A Document Visible in Different Worlds?
How can we encode such an object in the digital world?
A proposal:
|right>E<right|
|front>G<front|
|top>B<top|
Wednesday 19 April 2023 Department of Computer Science 24
A Document Visible in Different Worlds?
How can we encode such an object in the digital world?
A proposal:
|right>E<right|
|front>G<front|
|top>B<top|
Quantum Markup Language (QuantumML)
Wednesday 19 April 2023 Department of Computer Science 25
Another Example
World “mouse”:
Mickey likes Minnie.
World “duck”:
Donald likes Daisy.
Wednesday 19 April 2023 Department of Computer Science 26
Another Example
It could be encoded as follows:
|mouse>Mickey likes Minnie<mouse|
|duck>Donald likes Daisy<duck|
Wednesday 19 April 2023 Department of Computer Science 27
Another Example
But it is not forbidden to be clever
|mouse>Mickey<mouse|
|duck>Donald<duck|
likes
|mouse>Minnie<mouse|
|duck>Daisy<duck|
„likes“ appears in all of the worlds
Wednesday 19 April 2023 Department of Computer Science 28
Vector and Matrix Interpretation
Remember
|right>E<right|
|front>G<front|
|top>B<top|
Wednesday 19 April 2023 Department of Computer Science 29
Vector and Matrix Interpretation
Remember
|right>E<right|
|front>G<front|
|top>B<top|
Wednesday 19 April 2023 Department of Computer Science 30
Vector and Matrix Interpretation
Remember
|right>E<right|
|front>G<front|
|top>B<top|
Wednesday 19 April 2023 Department of Computer Science 31
Vector and Matrix Interpretation
Remember
|right>E<right|
|front>G<front|
|top>B<top|
Wednesday 19 April 2023 Department of Computer Science 32
Vector and Matrix Interpretation
Remember
|right>E<right|
|front>G<front|
|top>B<top|
Wednesday 19 April 2023 Department of Computer Science 33
Vector and Matrix Interpretation
Remember
|right>E<right|
|front>G<front|
|top>B<top|
Wednesday 19 April 2023 Department of Computer Science 34
Vector and Matrix Interpretation
Remember
|right>E<right|
|front>G<front|
|top>B<top|
Wednesday 19 April 2023 Department of Computer Science 35
Vector and Matrix Interpretation
Remember
|right>E<right|
|front>G<front|
|top>B<top|
Wednesday 19 April 2023 Department of Computer Science 36
Vector and Matrix Interpretation
Remember
|right>E<right|
|front>G<front|
|top>B<top|
Wednesday 19 April 2023 Department of Computer Science 37
Vector and Matrix Interpretation
Remember
|right>E<right|
|front>G<front|
|top>B<top|
Wednesday 19 April 2023 Department of Computer Science 38
Vector and Matrix Interpretation
Remember
|right>E<right|
|front>G<front|
|top>B<top|
Wednesday 19 April 2023 Department of Computer Science 39
Vector and Matrix Interpretation
Remember
|right>E<right|
|front>G<front|
|top>B<top|
An observable(Matrix Notation)
An observable(QuantumML notation)
Wednesday 19 April 2023 Department of Computer Science 40
Vector and Matrix Interpretation
Remember
|right>E<right|
|front>G<front|
|top>B<top|
It is diagonal: the basis is an eigenbasis.
An observable(QuantumML notation)
Wednesday 19 April 2023 Department of Computer Science 41
Instantiation
The user lives in a world For example, he looks from the right, or from
the top, or from the front.
Wednesday 19 April 2023 Department of Computer Science 42
Instantiation – shift
The user is in a state For example an eigenstate (a vector of the
eigenbasis (|right>, |front>, |top>)
Wednesday 19 April 2023 Department of Computer Science 43
Instantiation
The user is in an eigenstate
The observable is O
Wednesday 19 April 2023 Department of Computer Science 44
Instantiation
The user is in an eigenstate
The observable is O
What the user sees is given by:
In quantum physics, this corresponds to the result of the measure if the system is in an eigenstate.
Wednesday 19 April 2023 Department of Computer Science 45
Instantiation
The user is in an eigenstate
The observable is O
What the user sees is given by:
Two formal ways to compute it: QuantumML notation or matrix notation
Wednesday 19 April 2023 Department of Computer Science 51
Instantiation: Matrix notation
Interpretation: The user sees “E” when he/she is in eigenstate |right>
We were able to compute it
Wednesday 19 April 2023 Department of Computer Science 52
Tensor Product
We can have several “reasons” to distinguish between worlds. Right, Front, Top (3) Red Glasses, Green Glasses, Blue Glasses (3) Which gives 3x3=9 worlds!
QuantumML has the power to express this as well with tensor products.
Wednesday 19 April 2023 Department of Computer Science 53
Tensor Product
We can have several “reasons” to distinguish between worlds. Right, Front, Top (3) Red Glasses, Green Glasses, Blue Glasses (3) Which gives 3x3=9 worlds!
QuantumML has the power to express this as well with tensor products.
First „metadimension“
Wednesday 19 April 2023 Department of Computer Science 54
Tensor Product
We can have several “reasons” to distinguish between worlds. Right, Front, Top (3) Red Glasses, Green Glasses, Blue Glasses (3) Which gives 3x3=9 worlds!
QuantumML has the power to express this as well with tensor products.
Second „metadimension“
Wednesday 19 April 2023 Department of Computer Science 56
Tensor Product: yellow car example
|2,red>light red<2,red|
|2,green>dark green<2,green|
|2,blue>black<2,blue|
|1,right>door<1,right|
|1,front>window<1,front|
|1,top>roof<1,top|
Wednesday 19 April 2023 Department of Computer Science 57
Tensor Product: yellow car example
|2,red>light red<2,red|
|2,green>dark green<2,green|
|2,blue>black<2,blue|
|1,right>door<1,right|
|1,front>window<1,front|
|1,top>roof<1,top|
Wednesday 19 April 2023 Department of Computer Science 58
Our toolbox
Our QuantumML toolbox includes: An expressive language QuantumML to
describe documents visible in several worlds (observables).
Calculus with observables and user states (not necessarily eigenstates).
Wednesday 19 April 2023 Department of Computer Science 59
Our toolbox
Our QuantumML toolbox includes: An expressive language QuantumML to
describe documents visible in several worlds (observables).
Calculus with observables and user states (not necessarily eigenstates).
Information retrieval and user state estimation to enhance scoring.
Wednesday 19 April 2023 Department of Computer Science 60
Information Retrieval and User State Estimation
iU
1..
[ , ,| view ]ik
kd ik ik i nD s
,, , ,| | viewi ki k i k d i kR s D
1
1
1
iR R U
,i kk
i
R R
1
1,.
1
1
id
Q R R d
1 ,i i i iU U U h Q U
User State
Raw Search Results
Aggregation
Enhanced Results
Estimate Update
Instant State Estimate
Flip-flop(next cycle)
Information Retrieval
and ScoringUser State Estimation
Wednesday 19 April 2023 Department of Computer Science 61
Information Retrieval and User State Estimation
iU
1..
[ , ,| view ]ik
kd ik ik i nD s
,, , ,| | viewi ki k i k d i kR s D
1
1
1
iR R U
,i kk
i
R R
1
1,.
1
1
id
Q R R d
1 ,i i i iU U U h Q U
User State
Raw Search Results
Aggregation
Enhanced Results
Estimate Update
Instant State Estimate
Flip-flop(next cycle)
A weighted distribution on all of the
worlds modelling the worlds the user is assumed to
think in.
Wednesday 19 April 2023 Department of Computer Science 62
Information Retrieval and User State Estimation
A weighted distribution on all of the
worlds modelling the worlds the user is assumed to
think in.
Wednesday 19 April 2023 Department of Computer Science 63
Information Retrieval and User State Estimation
iU
1..
[ , ,| view ]ik
kd ik ik i nD s
,, , ,| | viewi ki k i k d i kR s D
1
1
1
iR R U
,i kk
i
R R
1
1,.
1
1
id
Q R R d
1 ,i i i iU U U h Q U
User State
Raw Search Results
Aggregation
Enhanced Results
Estimate Update
Instant State Estimate
Flip-flop(next cycle)
Raw Results (from
indexing table)
Wednesday 19 April 2023 Department of Computer Science 64
Information Retrieval and User State Estimation
iU
1..
[ , ,| view ]ik
kd ik ik i nD s
,, , ,| | viewi ki k i k d i kR s D
1
1
1
iR R U
,i kk
i
R R
1
1,.
1
1
id
Q R R d
1 ,i i i iU U U h Q U
User State
Raw Search Results
Aggregation
Enhanced Results
Estimate Update
Instant State Estimate
Flip-flop(next cycle)
Aggregated results („put them all in a
big document-
view matrix“)
Wednesday 19 April 2023 Department of Computer Science 65
Information Retrieval and User State Estimation
iU
1..
[ , ,| view ]ik
kd ik ik i nD s
,, , ,| | viewi ki k i k d i kR s D
1
1
1
iR R U
,i kk
i
R R
1
1,.
1
1
id
Q R R d
1 ,i i i iU U U h Q U
User State
Raw Search Results
Aggregation
Enhanced Results
Estimate Update
Instant State Estimate
Flip-flop(next cycle)
Estimated user state is
used for scoring.
Wednesday 19 April 2023 Department of Computer Science 66
Information Retrieval and User State Estimation
iU
1..
[ , ,| view ]ik
kd ik ik i nD s
,, , ,| | viewi ki k i k d i kR s D
1
1
1
iR R U
,i kk
i
R R
1
1,.
1
1
id
Q R R d
1 ,i i i iU U U h Q U
User State
Raw Search Results
Aggregation
Enhanced Results
Estimate Update
Instant State Estimate
Flip-flop(next cycle)
An instant estimate is computing
depending on the worlds in which results were found.
Wednesday 19 April 2023 Department of Computer Science 67
Information Retrieval and User State Estimation
Assumption:
If there are a lot of results in
a given world, there is a
high probability that the user
thinks in this world.
An instant estimate is computing
depending on the worlds in which results were found.
Wednesday 19 April 2023 Department of Computer Science 68
Information Retrieval and User State Estimation
iU
1..
[ , ,| view ]ik
kd ik ik i nD s
,, , ,| | viewi ki k i k d i kR s D
1
1
1
iR R U
,i kk
i
R R
1
1,.
1
1
id
Q R R d
1 ,i i i iU U U h Q U
User State
Raw Search Results
Aggregation
Enhanced Results
Estimate Update
Instant State Estimate
Flip-flop(next cycle)
The instant estimate is
used to update the estimate (using
Kalman filtering, ...)
Wednesday 19 April 2023 Department of Computer Science 69
Going further
Concatenation is not commutative
But interpreting documents as vector (with
occurences of the words) brings commutativity
The whole formalism can be reexpressed with
tensors and it works quite well.
This is already done and described in the report.
Wednesday 19 April 2023 Department of Computer Science 70
Conclusion
QuantumML is an expressive language to store
observables describing documents visible in
different worlds.
It handles „metadimensions“
Instantiation are computable.
Framework for Information Retrieval
Estimated User State used for scoring
Wednesday 19 April 2023 Department of Computer Science 71
Conclusion
We transformed an IR problem into a
mathematical problem
Optimizations of the vector, matrix and tensor
operations?