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TR94-012 | 12th December 1994 00:00
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#### Bounds for the Computational Power and Learning Complexity of Analog Neural Nets

TR94-012
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Publication: 12th December 1994 00:00

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**Abstract:**
It is shown that high order feedforward neural nets of constant depth with piecewise

polynomial activation functions and arbitrary real weights can be simulated for boolean

inputs and outputs by neural nets of a somewhat larger size and depth with heaviside

gates and weights from {-1,0,1\}. This provides the first known upper bound for the

computational power of the former type of neural nets. It is also shown that in the case

of first order nets with piecewise linear activation functions one can replace arbitrary

real weights by rational numbers with polynomially many bits, without changing the

boolean function that is computed by the neural net. In order to prove these results we

introduce two new methods for reducing nonlinear problems about weights in multi-layer

neural nets to linear problems for a transformed set of parameters. These transformed

parameters can be interpreted as weights in a somewhat larger neural net.

As another application of our new proof technique we show that neural nets with

piecewise polynomial activation functions and a constant number of analog inputs are

probably approximately learnable (in Valiant's model for PAC-learning).