AbstractObtaining human-like performance in NLP is often argued to require compositional generalisation. Whether neural networks exhibit this ability is usually studied by training models on highly compositional synthetic data. However, compositionality in natural language is much more complex than the rigid, arithmetic-like version such data adheres to, and artificial compositionality tests thus do not allow us to determine how neural models deal with more realistic forms of compositionality. In this work, we re-instantiate three compositionality tests from the literature and reformulate them for neural machine translation (NMT).Our results highlight that: i) unfavourably, models trained on more data are more compositional; ii) models are sometimes less compositional than expected, but sometimes more, exemplifying that different levels of compositionality are required, and models are not always able to modulate between them correctly; iii) some of the non-compositional behaviours are mistakes, whereas others reflect the natural variation in data. Apart from an empirical study, our work is a call to action: we should rethink the evaluation of compositionality in neural networks and develop benchmarks using real data to evaluate compositionality on natural language, where composing meaning is not as straightforward as doing the math.