Proceedings of the Annual Meeting of the Cognitive Science Society

Synchronous firing of neural units has recently been proposed as a new way of solving the variable binding problem in connectionist networks. Firing synchrony appears to be unrelated to earlier methods of variable binding, nearly all of which can be analyzed as species of tensor product representations, where vectors representing variables and values are bound together with the outer product. In this paper, we argue that, despite appearances, firing synchrony is also a case of tensor product representation. This analysis exposes two logically independent components of the synchronous firing idea. The most obvious is the idea of using time as a resource: spatio-temporal patterns of activation are used. This, we argue, is a purely implementational issue which does not bear on the complexity issues of variable binding. In contrast, the second idea does bear on genuinely representational issues, and is the source of most of the formal properties claimed for the synchrony scheme. Rather than explicitly binding a semantic role like giver to a semantic filler like John, these two are implicitly bound—by explicitly binding each to a common formal role, via the tensor product. The analysis situates synchronous firing in a typology of alternative variable binding schemes.