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arXiv · 2207.07832

Approximation Capabilities of Neural Networks using Morphological Perceptrons and Generalizations

William Chang·Hassan Hamad·Keith M. Chugg
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Abstract

Standard artificial neural networks (ANNs) use sum-product or multiply-accumulate node operations with a memoryless nonlinear activation. These neural networks are known to have universal function approximation capabilities. Previously proposed morphological perceptrons use max-sum, in place of sum-product, node processing and have promising properties for circuit implementations. In this paper we show that these max-sum ANNs do not have universal approximation capabilities. Furthermore, we consider proposed signed-max-sum and max-star-sum generalizations of morphological ANNs and show that these variants also do not have universal approximation capabilities. We contrast these variations to log-number system (LNS) implementations which also avoid multiplications, but do exhibit universal approximation capabilities.

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William Chang, Hassan Hamad, Keith M. Chugg. 2022-07-16. Approximation Capabilities of Neural Networks using Morphological Perceptrons and Generalizations. https://arxiv.org/abs/2207.07832

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