Path: utzoo!utgpu!news-server.csri.toronto.edu!bonnie.concordia.ca!thunder.mcrcim.mcgill.edu!snorkelwacker.mit.edu!mit-eddie!bbn.com!archive.bbn.com!aboulang From: aboulang@bbn.com (Albert Boulanger) Newsgroups: comp.theory.cell-automata Subject: Re: Missing the anthill for the ants? (was Re: RESEND Life Wars, Ants) Message-ID: Date: 18 Feb 91 19:57:18 GMT References: <9543@latcs1.oz.au> <1991Feb17.101444.17544@news.cs.indiana.edu> Sender: news@bbn.com Reply-To: aboulanger@bbn.com Organization: BBN, Cambridge MA Lines: 86 In-reply-to: marek@iuvax.cs.indiana.edu's message of 17 Feb 91 15:14:31 GMT In article <1991Feb17.101444.17544@news.cs.indiana.edu> marek@iuvax.cs.indiana.edu (Marek W Lugowski) writes: What I think is of interest is the path taken through the chaotic space. You may think of it as an informationally sensitive carrier wave, a la FM-modulation. There is enough richness specified in this path to encode a lot more than simple partition of the input space in a static recognition problem. For this you don't even need evolution to get started: I found out that for my tiles, which are no ants believe you me :), for different initial arrangements, under a particularly nasty set of rules that has the tiles leaping out of their little selves to wrap each species (color) around each other (you have to see the pictures...), I get stunningly different and beautifully chaotic paths to ...you guessed it, an attractor, one that, of course, I suspected anyway, since my rules don't change and I designed them for a square gworld and ran on a torus one. Now, if I could only learn how to modulate the path to effect an effective computation = controlled chaos... Any thoughts, disagreements? Yes, two thoughts: *****************************1************************************ Trajectories instead of basins for computation: Asymmetric recurrent (Hopfield) neural nets have interesting (and trainable) trajectories. "Temporal Associations in Asymmetric Neural Networks", H Sompolinsky and I. Kanter, Phys Rev Lettr, Vol 57, No 22, 2861-2864 "Statistical Mechanics of Neural Networks", H. Sompolinsky, Physics Today, Dec. 1988, 70-80 "Hebbian Learning Reconsidered: Representation of Static and Dynamic Objects in Associative Neural Nets", A. Hertz, B. Sulzer, R. Kuhn, and J.L. Hemmen, Biol. Cybern., Vol 60, 1989, 457-467 Freeman and others have been proposing an the use of periodic attractors for associative memory: "Associative Memory in a Simple Model of Oscillating Cortex" Bill Baird, NIPS 2 Proceedings, D. Touretsky Ed, Morgan Kaufman. Backprop has been modified to work with hidden-layer networks with feedback connections and have the ability to learn phase-space trajectories. Many people have worked on this one: "Learning State Space Trajectories in Recurrent Neural Networks, Barak Pearlmutter, CMU Computer Science Report CMU-CS-88-191, Dec. 31, 1988 "Generalization of Back-Propagation to Recurrent Neural Networks" Fernando Pineda, Phys Rev Lettr, Vol 59, No 19, 2229-2232 Optical feedback with 4-wave mixing using photorefractive materials have interesting associative cycling behavior. *******************************2********************************* Chaos and computation Actually there are times that one wishes to use the ergodic properties of chaos in computation. This is a way of doing search. There is an annealing-like algorithm that makes use of this: "Chaotic Optimization and the Construction of Fractals: Solution of an Inverse Problem" Giorgio Mantica & Alan Sloan Complex Systems 3(1989), 37-62 Finally, here is some recent work by Crutchfield and Young in analyzing the pattern generation properties (using grammars) of system on the verge of chaos: "Computation at the Onset of Chaos", James Crutchfield and Karl Young, appearing in "Complexity, Entropy, and the Physics of Information", W. Zurek, ed., Addison-Wesley, 1989/ Harnessing chaos, Albert Boulanger aboulanger@bbn.com