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. 2021 Sep 27;11:19127. doi: 10.1038/s41598-021-98693-3

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© The Author(s) 2021

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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MTBAN model structure. We implemented BAN with mutationTCN as both the teacher and the student network. In the first step, only the teacher network is trained, with the loss function being the label loss (red arrow), which refers to the cross entropy loss between the input sequence and the softmax output distribution of the teacher network. In the second step, only the student network is trained, with the loss being the sum of the label loss (red arrow) and the teacher loss (blue arrow). Here, the label loss refers to the cross entropy loss between the input sequence and the softmax output of the student network. The teacher loss refers to the cross entropy loss between the softmax output of the student network and the “softened” output distribution of the teacher network.