Büchi automata using graph neural networks

Recently [arXiv:2206.09619], an approach for analyzing Büchi automata using graph neural networks (GNN) was proposed. The experimental analysis revealed that this GNN-based approach can predict basic properties on independent test automata quite well. Further, it seems to be able to generalize from training data in a meaningful way, as the predictions were successful on instances much larger than those provided in the training data. Thus far, the analysis has been limited to the emptiness problem and simple properties like "does the automaton accept a word containing at least one/infinitely many $b$ ?". My immediate question was what the limits of learning-based approaches are and whether one can identify certain properties which cannot be learned GNNs.