Sumformer: Universal Approximation for Efficient Transformers
This work addresses a theoretical gap for researchers in NLP and machine learning, offering foundational insights into efficient Transformer architectures, though it is incremental in building upon existing methods.
The paper tackles the lack of theoretical understanding in efficient Transformers by introducing Sumformer, a novel architecture that achieves universal approximation for equivariant sequence-to-sequence functions, and uses it to provide the first universal approximation results for Linformer and Performer, while also proving that one attention layer suffices for Transformers.
Natural language processing (NLP) made an impressive jump with the introduction of Transformers. ChatGPT is one of the most famous examples, changing the perception of the possibilities of AI even outside the research community. However, besides the impressive performance, the quadratic time and space complexity of Transformers with respect to sequence length pose significant limitations for handling long sequences. While efficient Transformer architectures like Linformer and Performer with linear complexity have emerged as promising solutions, their theoretical understanding remains limited. In this paper, we introduce Sumformer, a novel and simple architecture capable of universally approximating equivariant sequence-to-sequence functions. We use Sumformer to give the first universal approximation results for Linformer and Performer. Moreover, we derive a new proof for Transformers, showing that just one attention layer is sufficient for universal approximation.