ML Anthology

Dynamics of Discrete Time, Continuous State Hopfield Networks

Pascal Koiran
NeCo 1994 pp. 459-468
doi:10.1162/NECO.1994.6.3.459 /neco/1994/koiran1994neco-dynamics/

Abstract

The dynamics of discrete time, continuous state Hopfield networks is driven by an energy function. In this paper, we use this tool to prove under mild hypotheses that any trajectory converges to a fixed point for the sequential iteration, and to a cycle of length 2 or a fixed point for the parallel iteration. Perhaps surprisingly, it seems that no rigorous proof of these results was published before.

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Cite

Text

Koiran. "Dynamics of Discrete Time, Continuous State Hopfield Networks." Neural Computation, 1994. doi:10.1162/NECO.1994.6.3.459

Markdown

[Koiran. "Dynamics of Discrete Time, Continuous State Hopfield Networks." Neural Computation, 1994.](https://mlanthology.org/neco/1994/koiran1994neco-dynamics/) doi:10.1162/NECO.1994.6.3.459

BibTeX

@article{koiran1994neco-dynamics,
  title     = {{Dynamics of Discrete Time, Continuous State Hopfield Networks}},
  author    = {Koiran, Pascal},
  journal   = {Neural Computation},
  year      = {1994},
  pages     = {459-468},
  doi       = {10.1162/NECO.1994.6.3.459},
  volume    = {6},
  url       = {https://mlanthology.org/neco/1994/koiran1994neco-dynamics/}
}