A Sugeno Integral View of Binarized Neural Network Inference

2026-04-20

AI Summary

This work addresses the interpretability challenge in binarized neural networks (BNNs) by modeling neuron activation thresholding as a Sugeno integral for the first time. This formulation yields an explicit set function representation for each neuron, along with an equivalent rule-based interpretation, and naturally extends to score computation at the output layer. By establishing a precise connection between BNNs and fuzzy measure theory, the proposed approach constructs an interpretability framework grounded in the Sugeno integral. This framework not only clearly characterizes the importance of input features and their interactions but also supports generalization to non-binary inputs and more complex interaction patterns, thereby providing both a theoretical foundation and practical tools for transparent analysis and application of BNNs.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Computer Vision: Interpretability, Explainability, and Transparency
• Reasoning under Uncertainty: Graphical Models

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

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.

Problem

• Binarized Neural Networks
• Sugeno Integral
• Neuron Decision
• Input Interactions
• Rule-based Representation

Innovation

• Sugeno integral
• binarized neural networks
• rule-based representation
• set-function
• neural network interpretability