Abstract:
Recently Barron (1993) has given rates for hidden layer feedforward networks with sigmoid activation functions approximating a class of functions satisfying a certain smo...Show MoreMetadata
Abstract:
Recently Barron (1993) has given rates for hidden layer feedforward networks with sigmoid activation functions approximating a class of functions satisfying a certain smoothness condition. These rates do not depend on the dimension of the input space. We extend Barron's results to feedforward networks with possibly nonsigmoid activation functions approximating mappings and their derivatives simultaneously. Our conditions are similar but not identical to Barron's, but we obtain the same rates of approximation, showing that the approximation error decreases at rates as fast as n−1/2, where n is the number of hidden units. The dimension of the input space appears only in the constants of our bounds.
Published in: Neural Computation ( Volume: 6, Issue: 6, November 1994)
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- Index Terms
- Activation Function ,
- Dimensional Space ,
- Hidden Layer ,
- Functional Class ,
- Feed-forward Network ,
- Function Approximation ,
- Sigmoid Activation Function ,
- Smooth Conditions ,
- Neural Network ,
- Artificial Neural Network ,
- Probability Density Function ,
- Integrable ,
- Space Of Functions ,
- Hilbert Space ,
- Fourier Series ,
- Heaviside Function ,
- Convex Combination ,
- Degree Of Approximation ,
- Lebesgue Measure ,
- Property Space ,
- Fubini’s Theorem ,
- Absolutely Continuous ,
- Series Approximation ,
- Sobolev Space ,
- Weak Sense ,
- Combination Of Family ,
- Degree Of Results ,
- Square Root
Keywords assist with retrieval of results and provide a means to discovering other relevant content. Learn more.
- Index Terms
- Activation Function ,
- Dimensional Space ,
- Hidden Layer ,
- Functional Class ,
- Feed-forward Network ,
- Function Approximation ,
- Sigmoid Activation Function ,
- Smooth Conditions ,
- Neural Network ,
- Artificial Neural Network ,
- Probability Density Function ,
- Integrable ,
- Space Of Functions ,
- Hilbert Space ,
- Fourier Series ,
- Heaviside Function ,
- Convex Combination ,
- Degree Of Approximation ,
- Lebesgue Measure ,
- Property Space ,
- Fubini’s Theorem ,
- Absolutely Continuous ,
- Series Approximation ,
- Sobolev Space ,
- Weak Sense ,
- Combination Of Family ,
- Degree Of Results ,
- Square Root
