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Concept Learning and Optimisation with Hopfield Networks

Concept Learning and Optimisation with Hopfield Networks. Kevin Swingler University of Stirling Presentation to UKCI 2011, Manchester. Hopfield Networks. Hopfield Networks. Hopfield Networks. Example – Learning Digit Images. How?. Learning w ij = w ij + u i u j Recall

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Concept Learning and Optimisation with Hopfield Networks

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  1. Concept Learning and Optimisation with Hopfield Networks Kevin Swingler University of Stirling Presentation to UKCI 2011, Manchester

  2. Hopfield Networks

  3. Hopfield Networks

  4. Hopfield Networks

  5. Example – Learning Digit Images

  6. How? • Learning wij = wij + ui uj • Recall ui = Σj≠i wij uj uj wij ui

  7. Pattern Discovery σ

  8. Learning Concepts or Optimal Patterns Concept = Symmetry σ

  9. How? • Weight update rule is adapted to: wij = wij + σui uj uj wij ui

  10. Examples Concept = Symmetry Concept = Horizontal

  11. Speed Simple Target

  12. Relation to EDA Current pattern, P = p1 ... pn f(P) = Score for pattern P EDA Probabilities, R = r1 ... rn Probability that element i=1: P(pi = 1) = ri Probability update rule: ri = ri+f(P) if pi = 1

  13. Relation to EDA Probability that element i=1: P(pi = 1) = g(W, pj≠i) Not stochastic, but marginal probabilities are not known Settling the network from a random state samples from the learned distribution without the need for joint distribution sampling explicitly.

  14. Practicalities 1 • If P is an attractor state for the network, then so is P` • Scores for target patterns need their distance metric altered accordingly • Or compare both the pattern and its inverse and score the highest =

  15. Practicalities 2 • The random patterns used during training must have elements drawn from an even distribution • Deviation from this impairs learning

  16. Uses and Benefits • In situations where there are many possible solutions, this provides a method of sampling random good solutions without the need for additional searching • Solutions tend to be close to the seeded start point, so you can use this method to find a local optimum that is close to a start point – again, without actually searching

  17. Limitations • The storage capacity of the network • The size of the search space • Can we use a sparser connected network? • Inverse patterns need care • Currently: • Only tested on binary patterns • No evolution of patterns – stimuli must all be random

  18. Thank You • kms@cs.stir.ac.uk • www.cs.stir.ac.uk/~kms

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