Approximation Capabilities of Neural Networks using Morphological Perceptrons and Generalizations
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Abstract (arXiv)
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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References · 8
- 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,399
- 2015Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Codingcited by 2,329
- 2016End to End Learning for Self-Driving Carscited by 1,009
- 2016Error bounds for approximations with deep ReLU networkscited by 574
- 2018Quantizing deep convolutional networks for efficient inference: A whitepapercited by 521
- 2016Convolutional Neural Networks using Logarithmic Data Representationcited by 99
- 2020Pre-defined Sparsity for Low-Complexity Convolutional Neural Networkscited by 15
- 2019Neural Network Training with Approximate Logarithmic Computationscited by 7
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