This paper is an attempt to bridge the gap between deep learning and grammatical inference. Indeed, it provides an algorithm to extract a (stochastic) formal language from any recurrent neural network trained for language modelling. In detail, the algorithm uses the already trained network as an oracle—and thus does not require the access to the inner representation of the black-box—and applies a spectral approach to infer a weighted automaton. As weighted automata compute linear functions, they are computationally more efficient than neural networks and thus the nature of the approach is the one of knowledge distillation. We detail experiments on 62 data sets (both synthetic and from real-world applications) that allow an in-depth study of the abilities of the proposed algorithm. The results show the WA we extract are good approximations of the RNN, validating the approach. Moreover, we show how the process provides interesting insights toward the behavior of RNN learned on data, enlarging the scope of this work to the one of explainability of deep learning models.

本文旨在弥合深度学习与语法推理之间的鸿沟。实际上，它提供了一种算法，可从任何经过语言建模训练的递归神经网络中提取（随机）形式语言。详细地说，该算法将已经训练好的网络用作预言机，因此不需要访问黑匣子的内部表示，并应用频谱方法来推断加权自动机。加权自动机计算线性函数时，它们在计算上比神经网络更有效，因此，该方法的本质是知识提取之一。我们详细介绍了62个数据集（包括合成数据和来自实际应用程序）的实验，这些数据集可以对所提出算法的功能进行深入研究。结果表明，我们提取的WA是RNN的良好近似值，验证了该方法。此外，我们展示了该过程如何为从数据中学到的RNN行为提供有趣的见解，将这项工作的范围扩大到深度学习模型的可解释性之一。