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Interpretability methods aim to understand the algorithm implemented by atrained model (e.g., a Transofmer) by examining various aspects of the model,such as the weight matrices or the attention patterns. In this work, through acombination of theoretical results and carefully controlled experiments onsynthetic data, we take a critical view of methods that exclusively focus onindividual parts of the model, rather than consider the network as a whole. Weconsider a simple synthetic setup of learning a (bounded) Dyck language.Theoretically, we show that the set of models that (exactly or approximately)solve this task satisfy a structural characterization derived from ideas informal languages (the pumping lemma). We use this characterization to show thatthe set of optima is qualitatively rich; in particular, the attention patternof a single layer can be ``nearly randomized'', while preserving thefunctionality of the network. We also show via extensive experiments that theseconstructions are not merely a theoretical artifact: even after severelyconstraining the architecture of the model, vastly different solutions can bereached via standard training. Thus, interpretability claims based oninspecting individual heads or weight matrices in the Transformer can bemisleading.

Transformers are uninterpretable with myopic methods: a case study with bounded Dyck grammars