Sep. 4, 1998 A revolutionary new computing technique that uses a network of chaotic elements to "evolve" its answers could provide an alternative to the digital computing systems widely used today. Described for the first time in the September 7 issue of Physical Review Letters this "dynamics-based computation" may be well suited for optical computing using ultra-fast chaotic lasers and computing with silicon/neural tissue hybrid circuitry.
The system has so far demonstrated an ability to handle a wide range of common operations, including addition and multiplication, as well as Boolean logic and more sophisticated operations such as finding the least common multiplier in a sequence of integers. Because it depends on interaction among its coupled elements, the system is naturally parallel.
"We have shown that this can be done, but we've only seen the tip of the iceberg," said Dr. William L. Ditto, professor of physics at the Georgia Institute of Technology. "This is a glimpse of how we can make common dynamic systems work for us in a way that's more like how we think the brain does computation. It's an entirely new computing paradigm."
For many years, scientists have observed the rich variety of behavioral patterns created by chaotic systems, including those found in living organisms. Ditto and collaborator Sudeshna Sinha of the Institute of Mathematical Sciences in Madras, India, reasoned that these natural chaotic systems should have been eliminated through evolution unless they served a purpose.
Ditto and Sinha devised an experiment to see if a simple network of chaotic computer elements could be made to handle computations. They joined the chaotic elements into a lattice using an adaptive connecting mechanism that would open whenever an element exceeded a certain critical value. The mechanism was designed so that the researchers could set a wide range of critical values to vary the connection between elements.
The researchers then encoded values into the chaotic lattice using a variety of different techniques. In some cases, they chose patterns in the chaotic elements to represent numbers. In other cases, the numbers were represented by the amplitude of waves emitted by the chaotic elements or the frequency of "spiking" behavior.
After encoding the numbers, they stimulated the elements to begin interacting.
Elements containing values above the critical level triggered the connecting mechanism, allowing the excess value to "avalanche" into neighboring elements. That transfer then created additional avalanches in other connected elements. With additional stimulation, the domino effect continued until the imbalance was conducted out of the system -- as the answer to the mathematical problem.
"We have the elements interconnected so that they respond to their neighbors like the avalanching that occurs when you pile grains of sand onto a sandpile," Ditto explained. "You allow the elements to avalanche and the system to evolve chaotically, then do the avalanching again until the system settles down to the right answer. It takes a couple of iterations for it to settle down."
In a simple example, values of three and four would be encoded into a system set with a critical value of one. The values would create an imbalance that would avalanche through the chaotic elements until it was conducted out of the system -- as the value of seven.
Chaotic elements are useful to this system because they can assume an infinite number of behaviors that can be used to represent different values or different systems such as logic gates. Because of this flexibility, altering the initial encoding and changing the connections between the chaotic elements allow a single generic system to perform a variety of computations using its inherent self organization. In conventional computing, systems are more specialized to perform certain operations.
"We are not really setting up rules in the same sense that digital computers are programmed," Ditto explained. "The system develops its own rules that we are simply manipulating. It is using pattern formation and self-organized criticality to organize toward an answer. We don't micromanage the computing, but let the dynamics do the hard work of finding a pattern that performs the desired operation."
Just as the numbers can be encoded in a variety of ways, the answer also comes out in a variety of ways: a rate of change, an amplitude, or a specific chaotic behavior.
"There are a surprisingly large number of ways that the system can perform the computations and give you the answer," he added. "By slightly changing the connectivity and the parameters of the chaotic system, we can have it multiply several different ways through the system's self organization."
Because this new system differs dramatically from existing digital computers, it is likely to have different strengths and weaknesses. "It might be better than digital computing for those activities that digital computing doesn't do very well -- such as pattern recognition or detecting the difference between two pieces of music," Ditto said.
He compared dynamics-based computation to DNA computing and quantum computing, both of which are new computing paradigms still in their early stages of development.
Ditto believes the new system would work particularly well in optical systems. He has done theoretical work applying dynamics-based computing to an ammonia laser system and hopes to see the system implemented experimentally.
"Potentially, we could stimulate a very fast system of coupled lasers to perform a highly complicated operation like very fast arithmetic operations, pattern detection and Fourier transforms" he said. "We have something that very naturally performs an operation in an optical system. This would provide an alternative to existing efforts, which try to make optical systems do operations more like transistors."
Beyond the systems they have tried, Ditto believes virtually any coupled dynamic system could be used to perform computation. "We hope that you can take any dynamical system, stimulate it in the correct way, and then get it to perform an operation for you," he said. "This would provide an alternative to engineering a system from the ground up."
Ditto acknowledges a number of engineering issues that may hamper development of a practical system based on this new computing paradigm. But he notes that in their early days, digital computers had to overcome a daunting set of obstacles to overtake earlier techniques.
Support for the work has come from the U.S. Office of Naval Research, and from Control Dynamics, Inc., a company partially owned by Ditto.
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