Saturday, 29 August 2015 QuantumML: Modelling Hidden Worlds of Information Ghislain Fourny Master‘s Thesis Presentation - March 29 th, 2007 © Department.

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 2

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.



HausTier

MutterFenster House

Animal

MotherWindow

German world English world



HausTier

MutterFenster House

Animal

MotherWindow




HausTier

MutterFenster House

Animal

MotherWindow


The job of Artificial Intelligence

Research


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


Ontologies

PinotBordeaux

MouthfeelVintage White wine

Red wine

Flavour Year

Oenologist world Not-an-expert world



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.



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


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?


Agenda

Introduction to QuantumML

Vector and Matrices Operations

Information Retrieval


A Document Visible in Different Worlds?

The same document is visible in three different

„worlds“: World 1: E World 2: G World 3: B



Worlds as perspectives: From the right: E From the front: G From the top: B



Such an object does not exist!

Are you willing to bet on this?





Perspective 1



Perspective 2

Perspective 1



Perspective 2

Perspective 1

Perspective 3



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”




A proposal:

|right>E<right|

|front>G<front|

|top>B<top|




A proposal:

|right>E<right|

|front>G<front|

|top>B<top|

Quantum Markup Language (QuantumML)


Another Example

World “mouse”:

Mickey likes Minnie.

World “duck”:

Donald likes Daisy.


Another Example

It could be encoded as follows:

|mouse>Mickey likes Minnie<mouse|

|duck>Donald likes Daisy<duck|


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


Vector and Matrix Interpretation

Remember

|right>E<right|

|front>G<front|

|top>B<top|



Remember

|right>E<right|

|front>G<front|

|top>B<top|



Remember

|right>E<right|

|front>G<front|

|top>B<top|



Remember

|right>E<right|

|front>G<front|

|top>B<top|



Remember

|right>E<right|

|front>G<front|

|top>B<top|



Remember

|right>E<right|

|front>G<front|

|top>B<top|



Remember

|right>E<right|

|front>G<front|

|top>B<top|



Remember

|right>E<right|

|front>G<front|

|top>B<top|



Remember

|right>E<right|

|front>G<front|

|top>B<top|



Remember

|right>E<right|

|front>G<front|

|top>B<top|



Remember

|right>E<right|

|front>G<front|

|top>B<top|



Remember

|right>E<right|

|front>G<front|

|top>B<top|

An observable(Matrix Notation)

An observable(QuantumML notation)



Remember

|right>E<right|

|front>G<front|

|top>B<top|

It is diagonal: the basis is an eigenbasis.

An observable(QuantumML notation)


Instantiation

The user lives in a world For example, he looks from the right, or from

the top, or from the front.


Instantiation – shift

The user is in a state For example an eigenstate (a vector of the

eigenbasis (|right>, |front>, |top>)


Instantiation

The user is in an eigenstate

The observable is O


Instantiation


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.


Instantiation


The observable is O

What the user sees is given by:

Two formal ways to compute it: QuantumML notation or matrix notation


Instantiation: Matrix notation











Interpretation: The user sees “E” when he/she is in eigenstate |right>

We were able to compute it


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.


Tensor Product



First „metadimension“


Tensor Product



Second „metadimension“


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|



|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|


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).


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.


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



iU

1..

[ , ,| view ]ik

kd ik ik i nD s


1

1

1

iR R U

,i kk

i

R R

1

1,.

1

1

id

Q R R d


User State

Raw Search Results

Aggregation

Enhanced Results

Estimate Update



A weighted distribution on all of the

worlds modelling the worlds the user is assumed to

think in.



A weighted distribution on all of the

worlds modelling the worlds the user is assumed to

think in.



iU

1..

[ , ,| view ]ik

kd ik ik i nD s


1

1

1

iR R U

,i kk

i

R R

1

1,.

1

1

id

Q R R d


User State

Raw Search Results

Aggregation

Enhanced Results

Estimate Update



Raw Results (from

indexing table)



iU

1..

[ , ,| view ]ik

kd ik ik i nD s


1

1

1

iR R U

,i kk

i

R R

1

1,.

1

1

id

Q R R d


User State

Raw Search Results

Aggregation

Enhanced Results

Estimate Update



Aggregated results („put them all in a

big document-

view matrix“)



iU

1..

[ , ,| view ]ik

kd ik ik i nD s


1

1

1

iR R U

,i kk

i

R R

1

1,.

1

1

id

Q R R d


User State

Raw Search Results

Aggregation

Enhanced Results

Estimate Update



Estimated user state is

used for scoring.



iU

1..

[ , ,| view ]ik

kd ik ik i nD s


1

1

1

iR R U

,i kk

i

R R

1

1,.

1

1

id

Q R R d


User State

Raw Search Results

Aggregation

Enhanced Results

Estimate Update



An instant estimate is computing

depending on the worlds in which results were found.



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.



iU

1..

[ , ,| view ]ik

kd ik ik i nD s


1

1

1

iR R U

,i kk

i

R R

1

1,.

1

1

id

Q R R d


User State

Raw Search Results

Aggregation

Enhanced Results

Estimate Update



The instant estimate is

used to update the estimate (using

Kalman filtering, ...)


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.


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


Conclusion

We transformed an IR problem into a

mathematical problem

Optimizations of the vector, matrix and tensor

operations?


Thank you for your attention!

Questions?

Saturday, 29 August 2015 QuantumML: Modelling Hidden Worlds of Information Ghislain Fourny Master‘s Thesis Presentation - March 29 th, 2007 © Department.

Documents

expert world slide

different worlds

b slide

e world

g world

document visible

document available

information systems