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node-version: '12' | ||
check-latest: true | ||
- run: | | ||
git clone -b pipeline-new https://github.com/virtual-labs/ph3-lab-mgmt | ||
git clone --depth 1 https://github.com/virtual-labs/ph3-lab-mgmt | ||
cd ph3-lab-mgmt | ||
npm install | ||
node exp.js | ||
npm run build-exp | ||
cd ../ | ||
git config --local user.email "[email protected]" | ||
git config --local user.name "vleadadmin" | ||
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{ | ||
"unit-type": "lu", | ||
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### Aim of the experiment | ||
The objective of this experiment is to demonstrate different annealing strategies in the solutions to optimization problems using a Hopfield model. This is illustrated using the weighted matching problem as a case study. | ||
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The optimization is guided by the activation dynamics of a Hopfield network. The activation dynamics is guided by the energy surface defined by the activation states of the units in the Hopfield network. The three relaxation strategies studied are: | ||
(a) Deterministic relaxation | ||
(b) Stochastic relaxation | ||
(c) Mean-field approximation |
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1. What is a local minima problem in optimization ? | ||
2. How is mean-field annealing applied in the solution of optimization problems? | ||
3. Discuss the solution to the Traveling salesman problem using deterministic relaxation and stochastic relaxation. | ||
**Hint**: Refer [Yegnanarayana, 1999, pg. 299] and [Wilson and Pawley, 1988] | ||
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## Experiment name | ||
## Deterministic, Stochastic and Mean-field Annealing of Hopfield Models |
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- Deterministic relaxation can get stuck in local minima depending on the starting point. | ||
- Stochastic relaxation uses simulated annealing at different temperatures with probablistic update, which can help the network get out of the local minima, to settle for a deeper minima. | ||
- Stochastic relaxation can take time to reach equilibrium. | ||
- Mean-field annealing is used to speed up the process. | ||
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### Procedure | ||
- Go through the example presented, so as to understand the operation being done in the experiment to optimize the weighted matching problem. | ||
- Select the type of relaxation. | ||
- Select a graph type with given number of nodes along with the location of the nodes in a 2-D plane. | ||
- Click on 'Init' to initialize the graph. | ||
- After observing the set of points generated and the equations used to optimize the weighted graph, click on 'Anneal' to start annealing the network. | ||
- Go through the output of the problem and the output states of nodes after each update. | ||
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### Link your references in here | ||
- B. Yegnanarayana, Artificial Neural Networks, New Delhi, India : Prentice-Hall of India, p. 293, 1999. | ||
- C. Peterson and B. Soderberg, "Neural optimization", in The Handbook of Brain Theory and Neural Networks (M.A. Arbib, ed.), Cambridge, MA: MIT Press, pp. 617-621, 1995. | ||
- J.A. Hertz, A. Krogh, and R.G. Palmer, Introduction to the Theory of Neural Computation, New York: Addison-Wesley, 1991. | ||
- B. Muller and J. Reinhardt, Neural Networks: An Introduction, Physics of Neural Networks, New York: Springer-Verlag, 1991. | ||
- A.L. Yuille, "Constrained optimization and the elastic net", in The Handbook of Brain Theory and Neural Networks (M.A. Arbib, ed.), Cambridge, MA. MIT Press, pp. 250-255, 1995. | ||
- S. Geman and D. Geman, "Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images", IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, pp. 721-741, 1984. | ||
- N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, and E. Teller, "Equation of state calculations by fast computing machines", J. Chem. Phy., vol. 21, no. 6, pp. 1087-1092, 1953. | ||
- C. Peterson and J.R. Anderson, "A mean field theory learning algorithm for neural networks", Complex Systems, .vol. 1, pp. 995-1019, 1987. | ||
- R.J. Glauber, "Time-dependent statistics of the Ising model", J. Math. Phys., vol. 4, pp. 294-307, 1963. | ||
- S. Haykin, Neural Networks: A Comprehensive Foundation, New York: Macmillan College Publishing Company Inc., 1994. | ||
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