Approximation Rate of the Transformer Architecture for Sequence Modeling
This work provides foundational theoretical insights into Transformers, addressing a gap in understanding for researchers in machine learning and sequence modeling.
The authors tackled the limited theoretical understanding of the Transformer architecture by investigating its approximation rate for sequence modeling, establishing an explicit Jackson-type estimate that reveals structural properties and suitability for specific sequential relationships.
The Transformer architecture is widely applied in sequence modeling applications, yet the theoretical understanding of its working principles remains limited. In this work, we investigate the approximation rate for single-layer Transformers with one head. We consider a class of non-linear relationships and identify a novel notion of complexity measures to establish an explicit Jackson-type approximation rate estimate for the Transformer. This rate reveals the structural properties of the Transformer and suggests the types of sequential relationships it is best suited for approximating. In particular, the results on approximation rates enable us to concretely analyze the differences between the Transformer and classical sequence modeling methods, such as recurrent neural networks.