# Interpretable neural networks based on continuous-valued logic and multicriteria decision operators

arXiv: https://arxiv.org/abs/1910.02486 · HTML: https://mlsanity.com/paper/1910.02486/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Oct 2019.

## Built on by (most cited first, 4 of 4)

- [Regulating eXplainable Artificial Intelligence (XAI) May Harm Consumers](https://mlsanity.com/paper/2209.03499/) (2022)
- [Causal effect of racial bias in data and machine learning algorithms on user persuasiveness & discriminatory decision making: An Empirical Study](https://mlsanity.com/paper/2202.00471/) (2022)
- [A Logical Neural Network Structure With More Direct Mapping From Logical Relations](https://mlsanity.com/paper/2106.11463/) (2021)
- [Uninorm-like parametric activation functions for human-understandable neural models](https://mlsanity.com/paper/2205.06547/) (2022)

## Abstract (arXiv)

Combining neural networks with continuous logic and multicriteria decision making tools can reduce the black box nature of neural models. In this study, we show that nilpotent logical systems offer an appropriate mathematical framework for a hybridization of continuous nilpotent logic and neural models, helping to improve the interpretability and safety of machine learning. In our concept, perceptrons model soft inequalities; namely membership functions and continuous logical operators. We design the network architecture before training, using continuous logical operators and multicriteria decision tools with given weights working in the hidden layers. Designing the structure appropriately leads to a drastic reduction in the number of parameters to be learned. The theoretical basis offers a straightforward choice of activation functions (the cutting function or its differentiable approximation, the squashing function), and also suggests an explanation to the great success of the rectified linear unit (ReLU). In this study, we focus on the architecture of a hybrid model and introduce the building blocks for future application in deep neural networks. The concept is illustrated with some toy examples taken from an extended version of the tensorflow playground.