The roles of stability and symmetry in the dynamics of neural networks

The authors study the retrieval phase of spin-glass-like neural networks. Considering that the dynamics should depend only on gauge-invariant quantities, they propose that two such parameters, characterising the symmetry of the neural net's connections and the stabilities of the patterns, are responsible for most of the dynamical effects. This is supported by a numerical study of the shape of the basins of attraction for a one-pattern neural network model. The effects of stability and symmetry on the short-time dynamics of this model are studied analytically, and the full dynamics for vanishing symmetry is shown to be exactly solvable.

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