berke@zeus.cs.ucla.edu (Peter Berke) (10/27/86)
In article <1249@megaron.UUCP> wendt@megaron.UUCP writes: >Anyone interested in neural modelling should know about the Parallel >Distributed Processing pair of books from MIT Press. They're >expensive (around $60 for the pair) but very good and quite recent. > >A quote: > >Relaxation is the dominant mode of computation. Although there >is no specific piece of neuroscience which compels the view that >brain-style computation involves relaxation, all of the features >we have just discussed have led us to believe that the primary >mode of computation in the brain is best understood as a kind of >relaxation system in which the computation proceeds by iteratively >seeking to satisfy a large number of weak constraints. Thus, >rather than playing the role of wires in an electric circuit, we >see the connections as representing constraints on the co-occurrence >of pairs of units. The system should be thought of more as "settling >into a solution" than "calculating a solution". Again, this is an >important perspective change which comes out of an interaction of >our understanding of how the brain must work and what kinds of processes >seem to be required to account for desired behavior. > >(Rumelhart & Mcclelland, Chapter 4) > Isn't 'computation' a technical term? Do R&Mc prove that PDP is equivalent to computation? Would Turing agree that "settling into a solution" is computation? Some people have tried to show that symbols and symbol processing can be represented in neural nets, but I don't think anyone has proved anything about the problems they purportedly "solve," at least not to the extent that Turing did for computers in 1936, or Church in the same year for lambda calculus. Or are R&Mc using 'computing' to mean 'any sort of machination whatever'? And is that a good idea? Church's Thesis, that computing and lambda-conversion (or whatever he calls it) are both equivalent to what we might naturally consider calcuable could be extended to say that neural nets "settle" into the same solutions for the same class of problems. Or, one could maintain, as neural netters tend to implicitly, that "settling" into solutions IS what we might naturally consider calculable, rather than being merely equivalent to it. These are different options. The first adds "neural nets" to the class of formalisms which can express solutions equivalent to each other in "power," and is thus a variant on Church's thesis. The second actually refutes Church's Thesis, by saying this "settling" process is clearly defined and that it can realize a different (or non-comparable) class of problems, in which case computation would not be (provably) equivalent to it. Of course, if we could show BOTH that: (1) "settling" is equivalent to "computing" as formally defined by Turing, and (2) that "settling" IS how brains work, then we'd have a PROOF of Church's Thesis. Until that point it seems a bit misleading or misled to refer to "settling" as "computation." Peter Berke