Abstract
This paper shows a new type Hopfield multivalued recurrent neural model (MREM) and some of its learning capabilities. So, the network can be used as an associative memory (multivalued counterpart of Hopfield network). Moreover, when only two states ({-1, 1} or {0, 1}) are allowed, the network coincides with the bipolar or binary Hopfield discrete models.
Although there exist some other multivalued type Hopfield models, this model uses, in a more proper way, the multivalued information contained in a multivalued neuron. It is possible because we have considered that the interaction between neurons is expressed by a general real function between their outputs, whereas most of others models use the product function that produces only two possible values with a drastic lost of the multivalued information.
The introduction of this function of the outputs of neurons (that we are naming function of similarity as it measures the similarity between the outputs of neurons) allows to represent more properly the interaction between two similar, but different, neuron outputs (for example: waves, colors, etc.) than a binary (or previous multivalued models) do.
In this paper, a method to load a set of patterns into the network has been studied. That method generalizes the Hopfield's one when multivalued neurons are been considered.
Finally, it is shown that by using an augmented network and loading augmented patterns we can avoid the storage of spurious patterns into the network, as the well-known effect of loading the opposite pattern into the Hopfield's network. For this new storage technics has been obtained an expression that allows to set bounds to the capacity of the network.
It must be considered that multivalued patterns contains much more information than bipolar ones. So, for similar capacity value a multivalued network must be preferred to another one whose neuron outputs can take only two values.
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