Knowing Your Nonlinearities: Shapley Interactions Reveal the Underlying Structure of Data

Measuring nonlinear feature interaction is an established approach to understanding complex patterns of attribution in many models. In this paper, we use Shapley Taylor interaction indices (STII) to analyze the impact of underlying data structure on model representations in a variety of modalities, tasks, and architectures. Considering linguistic structure in masked and auto-regressive language models (MLMs and ALMs), we find that STII increases within idiomatic expressions and that MLMs scale STII with syntactic distance, relying more on syntax in their nonlinear structure than ALMs do. Our speech model findings reflect the phonetic principal that the openness of the oral cavity determines how much a phoneme varies based on its context. Finally, we study image classifiers and illustrate that feature interactions intuitively reflect object boundaries. Our wide range of results illustrates the benefits of interdisciplinary work and domain expertise in interpretability research.