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Network Characteristics

The BAM is not a fully connected network. Instead, the units are divided into two sets, or layers. The layers are generally designated as the A and B layers; the number of units in the A layer need not be the same as the number of units in the B layer. Each unit in each layer is connected to all the units in the other layer and to none of the units in the layer to which it belongs. The links are bidirectional.

The units in the network can be in one of two states, which may be denoted as on and off, and 1, or 1 and -1. If the network has NA units in the A layer and NB units in the B layer, we will denote the state of the ith unit in the A layer at time t by $\mu_i(t)$ and the state of the jth unit in the B layer at time t by $\nu_j(t)$. The weight on the link joining the ith unit in the A layer to the jth unit in the B layer is wij, where $1 \leq i \leq N_A$ and $1 \leq j \leq N_B$.It may not be the case that wij=wji; in fact, since NA need not be the same as NB, in some cases both wij and wji may not be defined.

The network has an energy function whose form is similar to that of the Hopfield network:

\begin{displaymath} E(t) = - \sum_{i=1}^{N_A} \sum_{j=1}^{N_B} w_{ij} \mu_i(t) \nu_j(t).\end{displaymath}

The figure shows a simple BAM.


 
Figure 5.23: A simple Bidirectional Associative Memory
\begin{figure} % latex2html id marker 4794 \setlength {\unitlength}{1mm} \beg... ...22){\vector(-4,1){107}} \put(23,48){\vector(4,-1){107}}\end{picture}\end{figure}

next up previous contents
Next: Network Operation Up: Bidirectional Associative Memory Previous: Introduction
Mike Alder
9/19/1997