Interpretable neural networks based on continuous-valued logic and multicriteria decision operators
This work addresses interpretability in machine learning, which is crucial for safety-critical applications, but it appears incremental as it builds on existing logical frameworks and focuses on architecture design without broad validation.
The authors tackled the problem of neural networks being black boxes by combining them with continuous nilpotent logic and multicriteria decision operators to improve interpretability and safety, resulting in a designed architecture that drastically reduces the number of parameters to be learned.
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.