A Sugeno Integral View of Binarized Neural Network Inference

TL;DR

This paper links binarized neural network inference to Sugeno integrals, providing a rule-based, explicit set-function representation of neuron decisions and extending the framework to richer interactions.

Contribution

It establishes a novel connection between BNNs and Sugeno integrals, enabling explicit rule-based interpretations of neural decisions.

Findings

Neuron activation thresholds can be expressed as Sugeno integrals.

Provides explicit set-function representations for BNN decisions.

Framework can be extended to more complex input interactions.

Abstract

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.