At the bottom you'll find the reference you asked for.
Just think about this: A neural network performs analog mathematical operations (sums, multiplications and so on.
A Turing machine is DIGITAL. It can simulate analog computations at a finite level of presition. But something is lost. Remember that some numbers have infinite decimals (1/3=0.333333...).
But those are only comments to begin to understand. Check the reference!
Now I'm really sorry, because my reply was incorrect, this is the 2.0 version: --- I'm sorry, but that is incorrect. Artificial Neural Networks are Turing Machines. In the first place, they are ANALOG. I has been recently prooved that Artificial Neural Networks have more computational power than Turing Machines Computational power is the ability to solve classes of problems. There are problems that can be solved with ANNs and at the same time cannot be solved by TMachines. So, Church's thesis was proven to be incorrect!. [s]
I'm sorry, but that is incorrect. Artificial Neural Networks are not Von Neumann Model-based computing devices. In the first place, they are ANALOG. I has been recently prooved that Artificial Neural Networks have more computational power than Turing Machines (who in turn have the same computational power as Von Neumann Computers). Computational power is the ability to solve classes of problems. There are problems that can be solved with ANNs and at the same time cannot be solved by TMachines. So, Church's thesis was proven to be incorrect!. [s]
Slashdot Mirror
At the bottom you'll find the reference you asked for.
Just think about this: A neural network performs analog mathematical operations (sums, multiplications and so on.
A Turing machine is DIGITAL. It can simulate analog computations at a finite level of presition. But something is lost. Remember that some numbers have infinite decimals (1/3=0.333333...).
But those are only comments to begin to understand. Check the reference!
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@TechReport{DasGupta99, author = "Bhaskar DasGupta and Georg Schnitger", title = "On the Computational Power of Analog Neural Networks", institution = "DIMACS", number = "99-49", month = oct # " 8", year = "1999", url = "f tp://dimacs.rutgers.edu/pub/dimacs/TechnicalReporOr...
When the NN can make a quicker guess than an exponentially complex (expensive, time consuming) algorithm.
This is cool in situations where a good guess is all you need and you don't need axact answers
Now I'm really sorry, because my reply was incorrect, this is the 2.0 version: --- I'm sorry, but that is incorrect. Artificial Neural Networks are Turing Machines. In the first place, they are ANALOG. I has been recently prooved that Artificial Neural Networks have more computational power than Turing Machines Computational power is the ability to solve classes of problems. There are problems that can be solved with ANNs and at the same time cannot be solved by TMachines. So, Church's thesis was proven to be incorrect!. [s]
I'm sorry, but that is incorrect. Artificial Neural Networks are not Von Neumann Model-based computing devices. In the first place, they are ANALOG. I has been recently prooved that Artificial Neural Networks have more computational power than Turing Machines (who in turn have the same computational power as Von Neumann Computers). Computational power is the ability to solve classes of problems. There are problems that can be solved with ANNs and at the same time cannot be solved by TMachines. So, Church's thesis was proven to be incorrect!. [s]