Are Transformers universal approximators of sequence-to-sequence functions?
This provides foundational theoretical insights into the capabilities of Transformers, which are widely used in NLP and other domains, addressing a gap in understanding their universal approximation properties.
The paper tackles the problem of understanding the expressive power of Transformer models, establishing that they are universal approximators of continuous permutation equivariant sequence-to-sequence functions with compact support, and extending this to arbitrary continuous functions using positional encodings.
Despite the widespread adoption of Transformer models for NLP tasks, the expressive power of these models is not well-understood. In this paper, we establish that Transformer models are universal approximators of continuous permutation equivariant sequence-to-sequence functions with compact support, which is quite surprising given the amount of shared parameters in these models. Furthermore, using positional encodings, we circumvent the restriction of permutation equivariance, and show that Transformer models can universally approximate arbitrary continuous sequence-to-sequence functions on a compact domain. Interestingly, our proof techniques clearly highlight the different roles of the self-attention and the feed-forward layers in Transformers. In particular, we prove that fixed width self-attention layers can compute contextual mappings of the input sequences, playing a key role in the universal approximation property of Transformers. Based on this insight from our analysis, we consider other simpler alternatives to self-attention layers and empirically evaluate them.