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Abduction Using Neural Models

Abduction Using Neural Models

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Abduction Using Neural Models

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  1. Abduction Using Neural Models by Madan Bharadwaj Instructor: Dr.Avelino Gonzalez

  2. Agenda • Introduce the Concept • Why Neural Approach ? • UNIFY • Hopfield Model • Critique • Summary

  3. Abduction & NN’s • What are Neural Networks? • What is Abduction?

  4. The Analogy Figure 1: Handwritten Characters. A’s and B’s Figure 2: After training the Neural Network classifies data into classes

  5. 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

  6. Types of Abd. Problems • 4 Major Types • Open & Incompatible Classes

  7. UNIFY • NN Architecture reflects problem dynamics • Tackles all 4 classes • Architecture incrementally introduced • Simple Architecture

  8. Hypothesis Layer Observation Layer Inhibitory Weights Excitatory Weights UNIFY - Initial Model

  9. The Algorithm • Initialize cells and weights • Update cells and weights • Check Termination condition

  10. UNIFIED MODEL Intermediate Layer

  11. Modifications • Incompatibility Weights • Modified Equations

  12. Experiments • Toy Problems • Real Life Problem • Results very encouraging

  13. 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

  14. Critique • Fuzzy Framework essential for abduction • Neural Networks still abstract

  15. Future Avenues • Cancellation Class • Better designs using ART • Evolving Architectures • Other Approaches

  16. Summary • Neural Network Approach feasible • UNIFY is better • Vast scope for further research

  17. 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.

  18. A n y Q u e s t i o n s . . .