4. Case Study- Suspension Bridge
Higher Level Abstraction
To find out if they are strong enough to bear the required loads with
an acceptable level of movement,
typically as a function of different patterns of traffic flow,
wind conditions, and
tidal forces.
Lower Level Abstraction
It is used to check the materials used for it and the interdependency
the concrete foundations,
the suspension cables,
the cable anchors,
the road surface, and
the traffic that uses it
5. Abstraction in Cognitive System
Deciding on the best level of abstraction is not always straightforward. Other types of
system — biological ones.
For biological systems level of abstraction is very person to person and there is some
disagreement in the scientific community.
Two approaches are followed for abstracting a cognitive system
Marrs Model
Scott Kelso’s Model
6. Three Level of Abstraction
Also known as Levels of Understanding
developed by David Marr for human visual
system.
At the level of the computational theory, you
need to answer questions such as
Goal of computation
Why is it appropriate?
How to implement it through logic and
strategy?
The Second level Represents
How the computation theory need to be applied?
Representation of input and output
Required algorithm to input transform input to output
7. Three Level of Abstraction
At the level of the Hardware Implementation
following things are asked:
How to build the physical system?
How the representation and algorithms
physically realized?
8. How to see three level of Abstraction?
According to Marr these levels are loosely
coupled – think about only one level rather
concentrating on lower level.
The first level represents the problem through
some mathematical formalism and then
moving on to representations and algorithms
once the model is complete.
The algorithm and representation levels are more accessible, it is the computational or
theoretical level that is critically important from an information processing
perspective.
The states that the problem can and should first be modelled at the abstract level of the
computational theory without strong reference to the lower and less abstract levels
9. Conclusion of Marrs Model
Many people believe that cognitive systems — both biological and artificial — are
effectively information processors, Marr’s hierarchy of abstraction is very useful.
According to Marr
“Trying to understand perception by studying only neurons is
like trying to understand bird flight by studying only feathers: it
just cannot be done. In order to understand bird flight, we have to
understand aerodynamics; only then do the structure of feathers
and the different shapes of birds’ wings make sense”
First decouple the different levels of abstraction and begin your analysis at the
highest level and avoid the implementation issues until the computational or
theoretical model is complete
10. Scott Kelso’s Model
He think that the physical implementation has a direct role to play in understanding the
computational theory
He takes the example of non-linear dynamical types
of systems that he believes may provide the true
basis for cognition and brain dynamics.
All the level of abstraction should developed
distinctly but at the same time.
Boundary – determines the goal of the system
Collective Variables - characterizes the behavior of
the system.
Components - related to the Physical System
11. Scott Kelso’s Model
The specification of these three levels of model
abstraction are tightly coupled and mutually
dependent.
The environment constraints decides the behavior
of the system and do the feasible study.
At the same time properties of physical system may
simplify the necessary behavior.
According to Rolf Pfeifer the properties of the physical shape or the forced needed
for required movements may actually simplify the computational problem.
The realization of the system and its particular shape or morphology cannot be
ignored and should not be abstracted away when modelling the system.
12. Relation between system realization and modelling
The specification of these three levels of model
abstraction are tightly coupled and mutually
dependent.
The environment constraints decides the behavior
of the system and do the feasible study.
At the same time properties of physical system may
simplify the necessary behavior.
If we look carefully, we see a circularity, with
everything depending on something else. It’s not
easy to see how you break into the modelling circle.
13. Modified Marr’s Model
Consider these questions:
a) Is there a computational
theory for learning?
b) Are there algorithms for
learning?
c) Are there mechanisms in
the neuroanatomy for
learning?
Answer is yes. I think it might
be more useful to think of
learning as having a
computational, algorithmic
and mechanisms level.
