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Original Article

Statistical mechanics as the underlying theory of ‘elastic’ and ‘neural’ optimisations

Pages 89-103 | Received 06 Jul 1989, Published online: 04 Aug 2009

References

  • Hopfield, J J. Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. USA 1982; 79: 2554–8Neurons with graded response have collective computational properties like those of two-state neurons. Proc. Natl. Acad. Sci. USA. 1984. 81. 3088–92Learning algorithms and probability distributions in feed-forward and feed-back networks. Proc. Natl. Acad. Sci. USA. 1987. 84. 8429–33. Peretto, P. Collective properties of neural networks: a statistical physics approach. Biol. Cybern.. 1984. 50. 51–62. Amit, D J, Gutfreund, H, Sompolinsky, HSpin-glass models of neural networks. Phys. Rev.. 1985. A 32. 1007
  • Hopfield J J, Tank D W. Neural computation of decisions in optimisation problems. Biol. Cybern. 1985; 52: 141–52
  • Lawler E L, Lenstra J K, Rinnooy Kan A H G, Shmoys D B. Travelling Salesman Problem, E L Lawler, J K Lenstra, A H G Rinnooy Kan, D B Shmoys. Wiley, New York 1984, Garey M R and Johnson D S 1987 Computers and Intractability (San Francisco: Freeman)Johnston D 1987 More approaches to the travelling salesman guide Nature 330 525
  • Hopfield J J, Tank D W. Simple ‘neural’ optimisation networks: an A/D converter, signal decision circuit, and a linear programming circuit. IEEE Trans. Circuits Syst. 1986; CS-33: 533, For some applications in early vision see, for example:Koch C, Marroquin J and Yuille A, 1986, Analogue ‘neural’ networks in early vision Proc. Natl. Acad. Sci. USA, 83 4263–7Grzywacz N M and Yuille A 1988 Massively parallel implementations of theories for apparent motion Spatial Vision 3 15–44For other applications see, for example:Anderson D (ed) 1987 Neural Information Processing Systems (New York: American Institute of Physics)
  • Fox G, Furmanski W. The physical structure of concurrent problems and concurrent computers. Phil. Trans. R. Soc. 1988; A 326: 411–44, 1987 Report CalTech C3P-493, California Institute of Technology;1988 The Third Conference on Hypercube Concurrent Computers and Applications, vol 1 ed G C Fox pp 241–78, 285–305 (New York: ACM Press)Fox G, Furmanski W, Ho A, Koller J, Simic P and Wong I 1989 Neural networks and dynamic complex systems Report CalTech C3P-695 (presented at SCS Eastern Conference, Florida, 1989)
  • Wilson G V, Pawley G S. On the stability of the travelling salesman problem algorithm of Hopfield and Tank. Biol. Cybern. 1988; 58: 63–70
  • Hinton G E, Sejnowski T J (1983) Optimal perceptual inference. Proc. IEEE Comp. Soc. Conf. on Computer Vision and Pattern Recognition, Washington, DC, June, 1983. IEEE, Piscataway, NJ, 448–53, Bertero M, Poggio T and Torre V 1988 Ill-posed problems in early vision Proc. IEEE, August 1988, August 1988 ed H Li and J R Kender (Piscataway, NJ IEEE)Terzopoulos D 1984 Multi-Resolution Image Processing and Analysis ed A Rosenfeld (Berlin: Springer)
  • Mead C. Analogue VLSI and Neural Systems. Addison-Wesley, Reading, MA 1988
  • Rumelhart D, Hinton G, Williams R. Learning internal representations by error propagation. Parallel Distributed Processing. MIT, Cambridge, MA 1986; 1, Foundations Le Cun Y 19895 A learning procedure for asymmetric threshold network Proc. Cognitiva 85 599–604
  • Minski M, Papert S. Perceptrons. MIT, Cambridge, MA 1988, (expanded edition)
  • Durbin R, Willshaw D. An analogue approach to the travelling salesman problem using an elastic net method. Nature 1987; 326: 689–91
  • Willshaw D J, von der Malsburg Ch. A marker induction mechanism for the establishment of ordered neural mappings: its application to the retinotectal problem. Phil. Trans. R. Soc. 1979; B 287: 203–43
  • Gaze, R M. The Formation of Nerve Connections. AcademicNew York1970. Kirkpatrick, S, Gelatt, C D, Vecchi, M P. The Molecular Basis of Neural Development, G M Edelman, Gall, W E, Cowan, W M. WileyNew York1986; 389–428
  • Kirkpatrick S, Gelatt C D, Vecchi M P. Optimization by simulated annealing. Science 1983; 220: 671
  • Simic P D. Preprint. CalTech. 1989
  • This particular form of the second term in equation (25) was suggested by A Yuille; see the comment in [11]
  • Peterson C, Anderson J. A mean field theory learning algorithm for neural networks. Complex Systems 1987; 1: 995–1019
  • Simic P. CalTech. 1989, Preprint
  • Li, H, Kender, J R. Proc. IEEE, August 1988. IEEEPiscataway, NJ1988. Yuille, A. Energy functions for early vision and analog networks. A I MemoMIT. 987, For a recent survey see papers and references in:
  • Blake A, Zisserman A. Visual Reconstruction. MIT Press, Cambridge, MA 1987
  • Simic P D. Preprint. CalTech. 1989

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