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Recent studies of the computational power of recurrent neural networks (RNNs)reveal a hierarchy of RNN architectures, given real-time and finite-precisionassumptions. Here we study auto-regressive Transformers with linearisedattention, a.k.a. linear Transformers (LTs) or Fast Weight Programmers (FWPs).LTs are special in the sense that they are equivalent to RNN-like sequenceprocessors with a fixed-size state, while they can also be expressed as thenow-popular self-attention networks. We show that many well-known results forthe standard Transformer directly transfer to LTs/FWPs. Our formal languagerecognition experiments demonstrate how recently proposed FWP extensions suchas recurrent FWPs and self-referential weight matrices successfully overcomecertain limitations of the LT, e.g., allowing for generalisation on the parityproblem. Our code is public.

Practical Computational Power of Linear Transformers and Their Recurrent and Self-Referential Extensions