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Departmental Technical Reports (CS)

Why Neural Networks Are Computationally Efficient Approximators: An Explanation

Jaime Nava, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

7-2011

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Technical Report: UTEP-CS-11-40

Abstract

Many real-life dependencies can be reasonably accurately described by linear functions. If we want a more accurate description, we need to take non-linear terms into account. To take nonlinear terms into account, we can either explicitly add quadratic terms to the regression equation, or, alternatively, we can use a neural network with a non-linear activation function. At first glance, regression algorithms would work faster, but in practice, often, a neural network approximation turns out to be a more computationally efficient one. In this paper, we provide a reasonable explanation for this empirical fact.

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