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Abduction Using Neural Models by Madan Bharadwaj Instructor: Dr.Avelino Gonzalez Agenda Introduce the Concept Why Neural Approach ? UNIFY Hopfield Model Critique Summary Abduction & NN’s What are Neural Networks? What is Abduction? The Analogy Figure 1:

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abduction using neural models

Abduction Using Neural Models

by

Madan Bharadwaj

Instructor:

Dr.Avelino Gonzalez

agenda
Agenda
  • Introduce the Concept
  • Why Neural Approach ?
  • UNIFY
  • Hopfield Model
  • Critique
  • Summary
abduction nn s
Abduction & NN’s
  • What are Neural Networks?
  • What is Abduction?
the analogy
The Analogy

Figure 1:

Handwritten Characters. A’s and B’s

Figure 2: After training the Neural Network classifies data into classes

major references
Major References
  • “A Unified Model for Abduction-Based Reasoning” by Ayeb et al
  • “A Neural Architecture for a Class of Abduction Problems” by Goel et al
types of abd problems
Types of Abd. Problems
  • 4 Major Types
  • Open & Incompatible Classes
unify
UNIFY
  • NN Architecture reflects problem dynamics
  • Tackles all 4 classes
  • Architecture incrementally introduced
  • Simple Architecture
unify initial model

Hypothesis Layer

Observation Layer

Inhibitory Weights

Excitatory Weights

UNIFY - Initial Model
the algorithm
The Algorithm
  • Initialize cells and weights
  • Update cells and weights
  • Check Termination condition
unified model
UNIFIED MODEL

Intermediate Layer

modifications
Modifications
  • Incompatibility Weights
  • Modified Equations
experiments
Experiments
  • Toy Problems
  • Real Life Problem
  • Results very encouraging
hopfield model
Hopfield Model
  • Energy Function approach
  • Only linear and monotonic classes
  • Partition data into sub domains
  • Map sub domains
  • Minimize Energy Function
  • ART Model also proposed
critique
Critique
  • Fuzzy Framework essential for abduction
  • Neural Networks still abstract
future avenues
Future Avenues
  • Cancellation Class
  • Better designs using ART
  • Evolving Architectures
  • Other Approaches
summary
Summary
  • Neural Network Approach feasible
  • UNIFY is better
  • Vast scope for further research
references
References

[1].       B.Ayeb, S.Wang and J.Ge, “A Unified Model for Abduction-Based Reasoning” IEEE Transaction on Systems, Man and Cybernetics – Part A: Systems and Humans, Vol 28, No. 4, July 1998

[2].       A.K. Goel and J. Ramanujam, “A Neural Architecture for a Class of Abduction Problems”, IEEE Transaction on Systems, Man and Cybernetics – Part B – Cybernetics, Vol. 26, No. 6, December 1996

[3].       _____, “A Connectionist Model for Diagnostic Problem Solving: Part II”, IEEE Transaction on Systems, Man and Cybernetics., Vol19, pp. 285-289, 1989

[4].       A. Goel, J. Ramanujam and P. Sadayappan, “Towards a ‘neural’ architecture of abductive reasoning”, in Proc. 2nd Int. Conf. Neural Networks, 1988, pp. I-681-I-688.

[5].       D.Poole, A. Mackworth and R.Goebel, “Computational Intelligence: A Logical Approach”, pp 319-343, Oxford University Press, 1998.

[6].       C. Christodoulou and M. Georgiopoulos, “Applications of Neural Networks in Electromagnetics”, Boston: Artech House, 2001.

[7].       Castro, J.L.; Mantas, C.J.; Benitez, J.M., “Interpretation of artificial neural networks by means of fuzzy rules”, IEEE Transactions on Neural Networks, Volume: 13 Issue: 1, Jan. 2002. Page(s): 101 –116

[8].       T. Bylander, D. Allemang, M. C. Tanner, and J. R. Josephon, “The computational complexity of abduction,” Artif. Intell., vol. 49, pp. 25–60, 1991.