用模糊积分解析二值神经网络推理机制
A Sugeno Integral View of Binarized Neural Network Inference
- 将二值神经网络激活阈值转化为模糊积分形式
- 给出每层神经元决策的显式集函数表示
- 适合对模型可解释性与规则推理感兴趣的读者
本文建立了二值神经网络（BNNs）与模糊积分（Sugeno integral）之间的精确联系。在推理阶段，隐藏层神经元的激活阈值测试可表示为对二值输入的模糊积分，从而获得每个神经元决策的显式集函数表达及其对应的规则表示。同时，我们给出了最后一层输出分数的模糊积分表达式。该框架还可扩展以支持更丰富的输入交互关系，并可推广至非二值情形。
原文摘要 · Abstract (English)
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.
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