Abduction Using Neural Models

1 / 18

# Abduction Using Neural Models - PowerPoint PPT Presentation

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:

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## Abduction Using Neural Models

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Abduction Using Neural Models

by

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:

Handwritten Characters. A’s and B’s

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

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
• 4 Major Types
• Open & Incompatible Classes
UNIFY
• NN Architecture reflects problem dynamics
• Tackles all 4 classes
• Architecture incrementally introduced
• Simple Architecture

Hypothesis Layer

Observation Layer

Inhibitory Weights

Excitatory Weights

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

Intermediate Layer

Modifications
• Incompatibility Weights
• Modified Equations
Experiments
• Toy Problems
• Real Life Problem
• Results very encouraging
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
• Fuzzy Framework essential for abduction
• Neural Networks still abstract
Future Avenues
• Cancellation Class
• Better designs using ART
• Evolving Architectures
• Other Approaches
Summary
• Neural Network Approach feasible
• UNIFY is better
• Vast scope for further research
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.