zed@mdbs.uucp (Bill Smith) (10/28/90)
In article <70159@lll-winken.LLNL.GOV> loren@tristan.llnl.gov (Loren Petrich) writes: >In article <3740@media-lab.MEDIA.MIT.EDU> minsky@media-lab.media.mit.edu (Marvin Minsky) writes: >> [that I should read _Perceptrons_...] > > I guess some algorithm like back-propagation looks simple -- >after one discovers it. But it does seem easy to generalize the >two-state output of the original perceptrons to a continuous-valued >output, from which the back-prop algorithm readily follows from >minimizing the quantity <|actual - calculated|>. I wonder if anyone >had ever considered continuous-output perceptrons in the early days of >the field. Literally, this is a EE problem in the field of Signals and Systems. You have a differential equation (possibly multivariate) that describes the system. Any EE will tell you that you want the system to be linear because it simplifies life incredibly. In the simplest case, it is well understood and a child of 2 can understand the basic principles. It can be made more and more complicated by adding arithmetic, simultaneous exquations, linear algebra, differential equations, complex mathematics, time delays, non-linear effects, ad infinitum until the problem you started out to solve with has been sufficiently impressed with your knowledge (or the MIP rating of your computer if that fails :-) that is capitulates into the universal equation: x=1 (or x=0 as the case may be.) If x=0 you had a trivial problem that you should try to find out why it was so hard for you to see from the start that it was trivial. If x=1, you know know something you didn't know before. Extrapolate backwards through your steps until you find out the answers to the original question. In life there are *no* trivial problems, therefore, the answer to all problems is x=1. Now, you have to find out what is different between the problem you have and x=1 so that you can extrapolate backwards. This is pure philosophy. I am glad you have asked your questions because now *I* understand myself better than I did before. This is the benefit of answering other peoples problems: you solve 2 problems at the same time, their problem and one of your own. However, if you find out that they did not want the answer to the problem they asked but instead the answer to some other problem you will have 4 problems on your hand: 2 real and 2 imaginary. The real problems are their original problem and the problem that you created for yourself with your solution. The imaginary problems are the one that they asked and the one that you created by solving a problem in yourself that did not exist to begin with. Theses are the fundamental theorems of boolean arithemetic and complex analysis: 1 + 1 = 0 (boolean) i + 1 + -1 + -i = 0 (complex) The whole of boolean arithmetic is that life's problems are real. The whole of complex analysis is that imaginary problems are complex. >$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ >Loren Petrich, the Master Blaster: loren@sunlight.llnl.gov > >Since this nodename is not widely known, you may have to try: > >loren%sunlight.llnl.gov@star.stanford.edu Thank you Loren. You have made me happy. Bill Smith pur-ee!mdbs!zed