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Standard artificial neural networks (ANNs) use sum-product ormultiply-accumulate node operations with a memoryless nonlinear activation.These neural networks are known to have universal function approximationcapabilities. Previously proposed morphological perceptrons use max-sum, inplace of sum-product, node processing and have promising properties for circuitimplementations. In this paper we show that these max-sum ANNs do not haveuniversal approximation capabilities. Furthermore, we consider proposedsigned-max-sum and max-star-sum generalizations of morphological ANNs and showthat these variants also do not have universal approximation capabilities. Wecontrast these variations to log-number system (LNS) implementations which alsoavoid multiplications, but do exhibit universal approximation capabilities.

Approximation Capabilities of Neural Networks using Morphological Perceptrons and Generalizations