Re: Dynamic evaluation of layered networks

*To*: mathgroup at smc.vnet.net*Subject*: [mg109439] Re: Dynamic evaluation of layered networks*From*: "OmniaOpera" <OmniaOpera at _deletethistext_googlemail.com>*Date*: Tue, 27 Apr 2010 04:06:33 -0400 (EDT)*References*: <hqmok8$4ch$1@smc.vnet.net>

Thank you for your responses. I'll gather my response(s) together here: I already use things like SparseArray, Dot (and lots more besides) and I do a complete reevaluation every time something changes. I can get a big gain from using Mathematica's sparse linear algebra, but there is a lot more reevaluation going on than is actually necessary. The general computational architecture that I envisage is lots (eventually, lots might be LOTS) of simple interconnected processors updating themselves. A neural network package might seem to be the way to go, but I really need the general capabilities of Mathematica. Maybe I will eventually farm out (e.g. MathLink to C) code that is hostile to efficient implementation in Mathematica. What I want to do would be logically equivalent to a dynamic presentation, and small examples could actually be dynamic presentations. I want to produce an output which depends on an arbitrary set of user definable/changeable quantities, which could be network inputs, network layer-to-layer mappings, etc. However, I wondered whether I could finesse the recalculation problem so that Mathematica evaluation engine worked out the minimum amount of reevaluation it had to do to update the output. I wondered whether displaying an appropriate output could be used to trick Mathematica's Dynamic into doing this reevaluation for me. I realise that this is probably not what the designers of Dynamic had in mind, but wouldn't it be nice if it was a side-effect of their design? If the reevaluations that Dynamic asks the Kernel to do are computationally intensive then the overhead for FrontEnd-Kernel communications is negligible in comparison. So, if I insist on not simply reevaluating everything then I am going to have to trace through the dependencies myself in order to determine what needs to be reevaluated. I am surprised that there isn't already a shrink-wrapped Mathematica solution (a cunning Mathematica idom, maybe) to this type of partial reevaluation problem. OO "OmniaOpera" <OmniaOpera at _deletethistext_googlemail.com> wrote in message news:hqmok8$4ch$1 at smc.vnet.net... >I want to implement a multilayer feedforward network in such a way that > changing value(s) in the input layer automatically causes reevaluation of > only those parts of the network that are involved in the display of a > result, and it seems to me that Dynamic does what I want. > > A simple 3-layer example would be: > > f1[x_] = x^2; > f2[x_] := f1[x] + 1; > f3a[x_] := f2[x] + 1; > f3b[x_] := f2[x] - 1; > > Dynamic[{f3a[2], f3b[2]}] > > Any subsequent change to the f1[x_] = definition in the input layer > automatically causes the above Dynamic to reevaluate. > > That's fine, except that this causes f2[x] to be evaluated twice, once for > f3a[x] and once for f3b[x], which would be inefficient when generalised to > very large layered networks in which the f functions are costly to > evaluate. > Unfortunately, the f2[x]:=f2[x]=... trick for memorising previously > evaluated results doesn't help us here because it prevents the Dynamic > from > being sensitive to changes in the f1[x_] = definition in the input layer. > > There are messy ways of programming around this problem (e.g. using the > memorisation trick but modified so you forget memorised results that are > "out of date"), but is there any solution that finesses the problem by > cleverly using Mathematica's evaluation engine? > > OO > >

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