基于连续值逻辑和多准则决策算子的可解释神经网络
Interpretable neural networks based on continuous-valued logic and multicriteria decision operators
摘要：
将神经网络与连续逻辑和多准则决策工具相结合可以减少神经模型的黑箱性质。在这项研究中，我们表明，幂零逻辑系统提供了一个适当的数学框架，连续幂零逻辑和神经模型的杂交，有助于提高机器学习的可解释性和安全性。在我们的概念中，感知器模型软不等式，即隶属函数和连续逻辑运算符。我们在训练之前设计了网络架构，使用连续逻辑运算符和多准则决策工具，并在隐藏层中使用给定的权重。适当地设计结构会导致要学习的参数数量急剧减少。理论基础提供了一个简单的选择激活函数（切割函数或其可微近似，挤压函数），并提出了一个解释的巨大成功的整流线性单元（ReLU）。在这项研究中，我们专注于混合模型的架构，并介绍了未来在深度神经网络中应用的构建模块。这个概念是从一个扩展版本的tensorflow游乐场的一些玩具的例子来说明。
英文摘要：
Combining neural networks with continuous logic and multicriteria decision making tools can reduce the black box nature of neural models. In this study, we show that nilpotent logical systems offer an appropriate mathematical framework for a hybridization of continuous nilpotent logic and neural models, helping to improve the interpretability and safety of machine learning. In our concept, perceptrons model soft inequalities; namely membership functions and continuous logical operators. We design the network architecture before training, using continuous logical operators and multicriteria decision tools with given weights working in the hidden layers. Designing the structure appropriately leads to a drastic reduction in the number of parameters to be learned. The theoretical basis offers a straightforward choice of activation functions (the cutting function or its differentiable approximation, the squashing function), and also suggests an explanation to the great success of the rectified linear unit (ReLU). In this study, we focus on the architecture of a hybrid model and introduce the building blocks for future application in deep neural networks. The concept is illustrated with some toy examples taken from an extended version of the tensorflow playground.
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