# A Sugeno Integral View of Binarized Neural Network Inference

arXiv: https://arxiv.org/abs/2604.17967 · HTML: https://mlsanity.com/paper/2604.17967/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 33 references that are in the map.
- First posted on arXiv 20 Apr 2026.

## Builds on (most cited first, 12 of 12)

- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [Binary Neural Networks: A Survey](https://mlsanity.com/paper/2004.03333/) (2020)
- [Neural-Symbolic Computing: An Effective Methodology for Principled Integration of Machine Learning and Reasoning](https://mlsanity.com/paper/1905.06088/) (2019)
- [Verifying Properties of Binarized Deep Neural Networks](https://mlsanity.com/paper/1709.06662/) (2017)
- [From Statistical Relational to Neurosymbolic Artificial Intelligence: a Survey](https://mlsanity.com/paper/2108.11451/) (2021)
- [A comprehensive review of Binary Neural Network](https://mlsanity.com/paper/2110.06804/) (2021)
- [On Tractable Representations of Binary Neural Networks](https://mlsanity.com/paper/2004.02082/) (2020)
- [Logistic Regression, Neural Networks and Dempster-Shafer Theory: a New Perspective](https://mlsanity.com/paper/1807.01846/) (2018)
- [Defining neurosymbolic AI](https://mlsanity.com/paper/2507.11127/) (2025)
- [Machine Learning with the Sugeno Integral: The Case of Binary Classification](https://mlsanity.com/paper/2007.03046/) (2020)
- [On learning capacities of Sugeno integrals with systems of fuzzy relational equations](https://mlsanity.com/paper/2408.07768/) (2024)
- [Pi-NeSy: A Possibilistic Neuro-Symbolic Approach](https://mlsanity.com/paper/2504.07055/) (2025)

## Abstract (arXiv)

In this article, we establish a precise connection between binarized neural networks (BNNs) and Sugeno integrals. The advantage of the Sugeno integral is that it provides a framework for representing the importance of inputs and their interactions, while being equivalent to a set of if-then rules. For a hidden BNN neuron at inference time, we show that the activation threshold test can be written as a Sugeno integral on binary inputs. This yields an explicit set-function representation of each neuron decision, and an associated rule-based representation. We also provide a Sugeno-integral expression for the last-layer score. Finally, we discuss how the same framework can be adapted to support richer input interactions and how it can be extended beyond the binary case induced by binarized neural networks.