Are multilayer feedforward networks effectively Turing Machines?

SummaryCan connectionist networks implement any symbolic computation? This would be the case if networks have effective Turing machine power. It has been claimed that a recent mathematical result of Hornik, Stinchcombe, and White on the generative power of multilayer feedforward networks has that implication. The present paper considers whether this claim is correct. It is shown that finite approximation measures, as used in Hornik et al.'s proof, are not adequate for capturing the infinite recursiveness of recursive functions. The result is therefore irrelevant to the issue at hand.