加权信号时序逻辑的神经网络
Neural Network for Weighted Signal Temporal Logic
摘要：
在本文中，我们提出了一个神经符号框架称为加权信号时序逻辑神经网络（wSTL-NN），结合了神经网络和时序逻辑的特点。加权信号时态逻辑（wSTL）公式是由使用逻辑和时态运算符组合的子公式递归组成的。定义了wSTL的定量语义，使得具有较高权重的子公式的定量满意度对整个wSTL公式的定量满意度具有更大的影响。在wSTL-NN中，每个神经元对应于wSTL子公式，其输出对应于公式的定量满足。我们使用wSTL-NN来表示wSTL公式作为特征来分类时间序列数据。STL特征比经典方法中使用的特征更易于解释。wSTL-NN是端到端可微的，这允许使用反向传播来学习wSTL公式。为了减少权重的数量，我们引入了两种技术来稀疏化wSTL-NN。我们将我们的框架应用于占用检测时间序列数据集，以学习预测办公室占用状态的分类器。
英文摘要：
In this paper, we propose a neuro-symbolic framework called weighted Signal Temporal Logic Neural Network (wSTL-NN) that combines the characteristics of neural networks and temporal logics. Weighted Signal Temporal Logic (wSTL) formulas are recursively composed of subformulas that are combined using logical and temporal operators. The quantitative semantics of wSTL is defined such that the quantitative satisfaction of subformulas with higher weights has more influence on the quantitative satisfaction of the overall wSTL formula. In the wSTL-NN, each neuron corresponds to a wSTL subformula, and its output corresponds to the quantitative satisfaction of the formula. We use wSTL-NN to represent wSTL formulas as features to classify time series data. STL features are more explainable than those used in classical methods. The wSTL-NN is end-to-end differentiable, which allows learning of wSTL formulas to be done using back-propagation. To reduce the number of weights, we introduce two techniques to sparsify the wSTL-NN.We apply our framework to an occupancy detection time-series dataset to learn a classifier that predicts the occupancy status of an office room.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
