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Sumformer: Universal Approximation for Efficient Transformers

MCML Authors

Gitta Kutyniok

Prof. Dr.

Principal Investigator

Mathematical Foundations of Artificial Intelligence

Abstract

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.

inproceedings

ICML 2023

2nd Annual Workshop on Topology, Algebra, and Geometry in Machine Learning at the 40th International Conference on Machine Learning. Honolulu, Hawaii, Jul 23-29, 2023.