# Approximation Capabilities of Neural Networks using Morphological Perceptrons and Generalizations

arXiv: https://arxiv.org/abs/2207.07832 · HTML: https://mlsanity.com/paper/2207.07832/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 18 references that are in the map.
- First posted on arXiv 16 Jul 2022.

## Builds on (most cited first, 8 of 8)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)
- [Quantizing deep convolutional networks for efficient inference: A whitepaper](https://mlsanity.com/paper/1806.08342/) (2018)
- [Convolutional Neural Networks using Logarithmic Data Representation](https://mlsanity.com/paper/1603.01025/) (2016)
- [Pre-defined Sparsity for Low-Complexity Convolutional Neural Networks](https://mlsanity.com/paper/2001.10710/) (2020)
- [Neural Network Training with Approximate Logarithmic Computations](https://mlsanity.com/paper/1910.09876/) (2019)

## 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.