On Generalisation Error Bounds for Transformers

Abstract:In this paper, we establish a collection of covering number bounds for linear function classes under various norm constraints on the inputs and matrices. We then combine these results with existing covering number bounds to derive improved estimates and, based on these estimates, develop generalization error bounds for single-layer Transformers. The resulting generalization bounds improve upon several existing results in the literature and, in particular, are independent of the input sequence length. Moreover, our generalization error bound decays at the rate $O(1/\sqrt{n})$, where $n$ denotes the sample size, thereby improving upon existing bounds that scale as $O((\log n)/\sqrt{n})$. Furthermore, our covering number analysis explicitly incorporates rank constraints on the underlying matrix classes, allowing us to characterize how low-rank structures affect the metric entropy and, consequently, the resulting generalization bounds for Transformer architectures.

Machine Learning (stat.ML); Machine Learning (cs.LG); Functional Analysis (math.FA)

arXiv:2410.11500 [stat.ML]

(or arXiv:2410.11500v2 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2410.11500 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.