# A parameterized activation function for learning fuzzy logic operations in deep neural networks

arXiv: https://arxiv.org/abs/1708.08557 · HTML: https://mlsanity.com/paper/1708.08557/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Aug 2017.

## Built on by (most cited first, 3 of 3)

- [Logical Activation Functions: Logit-space equivalents of Probabilistic Boolean Operators](https://mlsanity.com/paper/2110.11940/) (2021)
- [ESC-Rules: Explainable, Semantically Constrained Rule Sets](https://mlsanity.com/paper/2208.12523/) (2022)
- [Uninorm-like parametric activation functions for human-understandable neural models](https://mlsanity.com/paper/2205.06547/) (2022)

## Abstract (arXiv)

We present a deep learning architecture for learning fuzzy logic expressions. Our model uses an innovative, parameterized, differentiable activation function that can learn a number of logical operations by gradient descent. This activation function allows a neural network to determine the relationships between its input variables and provides insight into the logical significance of learned network parameters. We provide a theoretical basis for this parameterization and demonstrate its effectiveness and utility by successfully applying our model to five classification problems from the UCI Machine Learning Repository.