On the rate of convergence of a classifier based on a Transformer encoder

• URL: http://arxiv.org/abs/2111.14574v1
• Date: Mon, 29 Nov 2021 14:58:29 GMT
• Title: On the rate of convergence of a classifier based on a Transformer encoder
• Authors: Iryna Gurevych, Michael Kohler, G\"ozde G\"ul Sahin
• Abstract summary: The rate of convergence of the misclassification probability of the classifier towards the optimal misclassification probability is analyzed. It is shown that this classifier is able to circumvent the curse of dimensionality provided the aposteriori probability satisfies a suitable hierarchical composition model.
• Score: 55.41148606254641
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Pattern recognition based on a high-dimensional predictor is considered. A classifier is defined which is based on a Transformer encoder. The rate of convergence of the misclassification probability of the classifier towards the optimal misclassification probability is analyzed. It is shown that this classifier is able to circumvent the curse of dimensionality provided the aposteriori probability satisfies a suitable hierarchical composition model. Furthermore, the difference between Transformer classifiers analyzed theoretically in this paper and Transformer classifiers used nowadays in practice are illustrated by considering classification problems in natural language processing.

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