Technical Report Number
We give algorithms to convert any network of binary threshold units (that does not oscillate) into an equivalent network with symmetric weight matrix (like Hopfield networks [Hopfield 82] or Boltzmann machines [Hinton, Sejnowski 88]). The motivation for the transformation is dual: a) to demonstrate the expressive power of symmetric networks; i.e. binary threshold networks (that do not oscillate) are subsumed in the energy minimization paradigm; 2) to use network modules (developed for the spreading activation paradigm for example), within the energy minimization paradigm. Thus optimization [Tank, Hopfield 88] and approximation of hard problems can be combined with efficient modules, that solve tractable sub-problems; 3)to unify a large class of networks under one paradigm. For acyclic networks we give an algorithm that generates an equivalent symmetric network that is of the same size and performs as efficiently as the original network. For the conversion of recurrent networks, we introduce several techniques; however, the generated networks may be larger (in size) then the original.
Pinkas, Gadi, "Converting Binary Thresholds Networks into Equivalent Symmetric Networks" Report Number: WUCS-91-31 (1991). All Computer Science and Engineering Research.