Harmony Networks Do Not Work

Harmony networks have been proposed as a means by which connectionist models can perform symbolic computation. Indeed, proponents claim that a harmony network can be built that constructs parse trees for strings in a context free language. This paper shows that harmony networks do not work in the following sense: they construct many outputs that are not valid parse trees. In order to show that the notion of systematicity is compatible with connectionism, Paul Smolensky, Geraldine Legendre and Yoshiro Miyata (Smolensky, Legendre, and Miyata 1992; Smolen sky 1993; Smolen sky, Legendre, and Miyata 1994) proposed a mechanism, "Harmony Theory," by which connectionist models purportedly perform structure sensitive operations without implementing classical algorithms. Harmony theory describes a "harmony network" which, in the course of reaching a stable equilibrium, apparently computes parse trees that are valid according to the rules of a particular context-free grammar.