Approximation Rate of the Transformer Architecture for Sequence Modeling
- URL: http://arxiv.org/abs/2305.18475v2
- Date: Mon, 19 Feb 2024 03:38:19 GMT
- Title: Approximation Rate of the Transformer Architecture for Sequence Modeling
- Authors: Haotian Jiang, Qianxiao Li
- Abstract summary: 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.
- Score: 21.461856598336464
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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.
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