∞-former: Infinite Memory Transformer

Transformers are unable to model long-term memories effectively, since the amount of computation they need to perform grows with the context length. While variations of efficient transformers have been proposed, they all have a finite memory capacity and are forced to drop old information. In this paper, we propose the ∞-former, which extends the vanilla transformer with an unbounded longterm memory. By making use of a continuousspace attention mechanism to attend over the long-term memory, the ∞-former's attention complexity becomes independent of the context length, trading off memory length with precision. In order to control where precision is more important, ∞-former maintains "sticky memories," being able to model arbitrarily long contexts while keeping the computation budget fixed. Experiments on a synthetic sorting task, language modeling, and document grounded dialogue generation demonstrate the ∞-former's ability to retain information from long sequences. 1