A Sugeno Integral View of Binarized Neural Network Inference
For researchers in interpretable AI, this work provides a theoretical link between BNNs and fuzzy logic, enabling rule extraction from BNNs, though it is an incremental theoretical contribution.
The paper establishes a precise connection between binarized neural networks (BNNs) and Sugeno integrals, showing that BNN inference can be represented as a Sugeno integral, which provides an interpretable rule-based framework. This yields explicit set-function and rule-based representations for each neuron and the final score.
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.