Neural Networks: The Preferred Universal Function Approximator
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Neural networks can approximate any function, exhibiting the universal approximation theorem. This makes them very flexible and powerful.
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The Taylor Series represents a function as an infinite sum of terms calculated from the derivatives of the function. It approximates functions through polynomials.
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Fourier Series also approximate functions, specifically periodic functions, through sums of trigonometric functions.
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Neural networks became popular in the 1950s-60s despite the existence of other universal approximators like Taylor and Fourier Series.
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The text discusses why neural networks are preferred over Taylor and Fourier Series as function approximators.