“On the Turing Completeness of Modern Neural Network Architectures”, Jorge Pérez, Javier Marinković, Pablo Barceló2019-01-10 (RNN, self-attention, computability)⁠:

Alternatives to recurrent neural networks, in particular, architectures based on attention or convolutions, have been gaining momentum for processing input sequences. In spite of their relevance, the computational properties of these alternatives have not yet been fully explored.

We study the computational power of two of the most paradigmatic architectures exemplifying these mechanisms: the Transformer (Vaswani et al 2017) and the Neural GPU (Kaiser & Sutskever2016).

We show both models to be Turing complete exclusively based on their capacity to compute and access internal dense representations of the data. In particular, neither the Transformer nor the Neural GPU requires access to an external memory to become Turing complete.

Our study also reveals some minimal sets of elements needed to obtain these completeness results. [published 2021 as “Attention is Turing Complete”]