## Abstract

In this paper we give under an appropriate theoretical framework a characterization about neural networks (evolving in a binary set of states) which admit an energy. We prove that a neural network, iterated sequentially, admits an energy if and only if the weight matrix verifies two conditions: the diagonal elements are non-negative and the associated incidence graph does not admit non-quasi-symmetric circuits. In this situation the dynamics are robust with respect to a class of small changes of the weight matrix. Further, for the parallel update we prove that a necessary and sufficient condition to admit an energy is that the incidence graph does not contain non-quasi-symmetric circuits.

Original language | English |
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Pages (from-to) | 327-334 |

Number of pages | 8 |

Journal | Neural Networks |

Volume | 10 |

Issue number | 2 |

DOIs | |

State | Published - Mar 1997 |

## Keywords

- Hopfield networks
- direct graphs
- energy
- parallel update
- quasi-symmetric weights
- sequential update
- symmetric weights