STLnet: Signal Temporal Logic Enforced Multivariate Recurrent Neural Networks

Recurrent Neural Networks (RNNs) have made great achievements for sequential prediction tasks. In practice, the target sequence often follows certain model properties or patterns (e.g., reasonable ranges, consecutive changes, resource constraint, temporal correlations between multiple variables, existence, unusual cases, etc.). However, RNNs cannot guarantee their learned distributions satisfy these properties. It is even more challenging for the prediction of large-scale and complex Cyber-Physical Systems. Failure to produce outcomes that meet these properties will result in inaccurate and even meaningless results. In this paper, we develop a new temporal logic-based learning framework, STLnet, which guides the RNN learning process with auxiliary knowledge of model properties, and produces a more robust model for improved future predictions. Our framework can be applied to general sequential deep learning models, and trained in an endto-end manner with back-propagation. We evaluate the performance of STLnet using large-scale real-world city data. The experimental results show STLnet not only improves the accuracy of predictions, but importantly also guarantees the satisfaction of model properties and increases the robustness of RNNs.