In the two years since it’s been introduced, the Transformer architecture, which uses multi-headed self-attention in lieu of recurrent models to consolidate information about input and output sequences, has more or less taken the world of language processing and understanding by storm. It has become the default choice for language for problems like translation and questioning answering, and was the foundation of OpenAI’s massive language-model-trained GPT. In this context, I really appreciate this paper’s work to try to build our collective intuitions about the structure, specifically by trying to understand how the multiple heads that make up the aforementioned multi-head attention divide up importance and specialize function. 

As a quick orientation, attention works by projecting each value in the sequence into query, key, and value vectors. Then, each element in the sequence creates its next-layer value by calculating a function of query and key (typically dot product) and putting that in a softmax against the query results with every other element. This weighting distribution is then used as the weights of a weighted average, combining the values together. By default this is a single operation, with a single set of projection matrices, but in the Transformer approach, they use multi-headed attention, which simply means that they learn independent parameters for multiple independent attention “filters”, each of which can then notionally specialize to pull in and prioritize a certain kind of information. 
https://i.imgur.com/yuC91Ja.png

The high level theses of this paper are: 
- Among attention heads, there’s a core of the most crucial and important ones, and then a long tail of heads that can be pruned (or, have their weight in the concatenation of all attention heads brought to nearly zero) and have a small effect on performance 
- It’s possible and useful to divide up the heads according to the kinds of other tokens that it is most consistently pulling information from. The authors identify three: positional, syntactic, and rare.  Positional heads consistently (>90% of the time) put their maximum attention weight on the same position relative to the query word. Syntactic heads are those that recurringly in the same grammatical relation to the query, the subject to its verb, or the adjective to its noun, for example. Rare words is not a frequently used head pattern, but it is a very valuable head within the first layer, and will consistently put its highest weight on the lowest-frequency word in a given sentence. 

An interesting side note here is that the authors tried at multiple stages in pruning to retrain a network using only the connections between unpruned heads, and restarting from scratch. However, in a effect reminiscent of the Lottery Ticket Thesis, retraining from scratch cannot get quite the same performance.