Computer Science > Machine Learning
arXiv:2305.18475 (cs)
[Submitted on 29 May 2023 (v1), last revised 2 Jan 2025 (this version, v4)]
Title:Approximation Rate of the Transformer Architecture for Sequence Modeling
View a PDF of the paper titled Approximation Rate of the Transformer Architecture for Sequence Modeling, by Haotian Jiang and 1 other authors
View PDFAbstract: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.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2305.18475 [cs.LG] |
| (orarXiv:2305.18475v4 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2305.18475 arXiv-issued DOI via DataCite |
Submission history
From: Haotian Jiang [view email][v1] Mon, 29 May 2023 10:56:36 UTC (2,075 KB)
[v2] Mon, 19 Feb 2024 03:38:19 UTC (4,529 KB)
[v3] Thu, 24 Oct 2024 08:13:01 UTC (4,515 KB)
[v4] Thu, 2 Jan 2025 05:02:48 UTC (4,515 KB)
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View a PDF of the paper titled Approximation Rate of the Transformer Architecture for Sequence Modeling, by Haotian Jiang and 1 other authors
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