  Understanding how a learned black box works is of crucial interest for the
future of Machine Learning. In this paper, we pioneer the question of the
global interpretability of learned black box models that assign numerical
values to symbolic sequential data. To tackle that task, we propose a spectral
algorithm for the extraction of weighted automata (WA) from such black boxes.
This algorithm does not require the access to a dataset or to the inner
representation of the black box: the inferred model can be obtained solely by
querying the black box, feeding it with inputs and analyzing its outputs.
Experiments using Recurrent Neural Networks (RNN) trained on a wide collection
of 48 synthetic datasets and 2 real datasets show that the obtained
approximation is of great quality.
