How to Dissect a Muppet: The Structure of Transformer Embedding Spaces

Pretrained embeddings based on the Transformer architecture have taken the NLP community by storm. We show that they can mathematically be reframed as a sum of vector factors and showcase how to use this reframing to study the impact of each component. We provide evidence that multi-head attentions and feed-forwards are not equally useful in all downstream applications, as well as a quantitative overview of the effects of finetuning on the overall embedding space. This approach allows us to draw connections to a wide range of previous studies, from vector space anisotropy to attention weights.