End-to-End Learning of LTLf Formulae by Faithful LTLf Encoding

Abstract It is important to automatically discover the underlying tree-structured formulae from large amounts of data. In this paper, we examine learning linear temporal logic on finite traces (LTLf) formulae, which is a tree structure syntactically and characterizes temporal properties semantically. Its core challenge is to bridge the gap between the concise tree-structured syntax and the complex LTLf semantics. Besides, the learning quality is endangered by explosion of the search space and wrong search bias guided by imperfect data. We tackle these challenges by proposing an LTLf encoding method to parameterize a neural network so that the neural computation is able to simulate the inference of LTLf formulae. We first identify faithful LTLf encoding, a subclass of LTLf encoding, which has a one-to-one correspondence to LTLf formulae. Faithful encoding guarantees that the learned parameter assignment of the neural network can directly be interpreted to an LTLf formula. With such an encoding method, we then propose an end-to-end approach, TLTLf, to learn LTLf formulae through neural networks parameterized by our LTLf encoding method. Experimental results demonstrate that our approach achieves state-of-the-art performance with up to 7% improvement in accuracy, highlighting the benefits of introducing the faithful LTLf encoding.