Harmonic grammar (Legendre, et al., 1990) is a connectionist theory of linguistic on the assumption that the well-formednesswell-formed ness based of a sentence can be measured by the harmony (negative energy) of the corresponding connectionist state. Assuming a lower-level connectionist that obeys a few general connectionist principles but is otherwisenetwork we construct a higher-level network with an equivalent harmonyunspecified, function that captures the most linguistically relevant global aspects of the lower level network. In this paper, we extend the tensor product representation (Smolensky 1990) to fully recursive representations of recursively structured objects like sentences in the lower-level network.

Harmonic grammar (Legendre, et al., 1990) is a connectionist theory of linguistic well-formed ness based on the assumption that the well-formedness of a sentence can be measured by the harmony (negative energy) of the corresponding connectionist state. Assuming a lower-level connectionist network that obeys a few general connectionist principles but is otherwise unspecified, we construct a higher-level network with an equivalent harmony function that captures the most linguistically relevant global aspects of the lower level network. In this paper, we extend the tensor product representation (Smolensky 1990) to fully recursive representations of recursively structured objects like sentences in the lower-level network. We show theoretically and with an example the power of the new technique for parallel distributed structure processing.