O(n) Connections are Expressive Enough: Universal Approximability of Sparse Transformers

Recently, Transformer networks have redefined the state of the art in many NLP tasks. However, these models suffer from quadratic computational cost in the input sequence length n to compute pairwise attention in each layer. This has prompted recent research into sparse Transformers that sparsify the connections in the attention layers. While empirically promising for long sequences, fundamental questions remain unanswered: Can sparse Transformers approximate any arbitrary sequence-to-sequence function, similar to their dense counterparts? How does the sparsity pattern and the sparsity level affect their performance?