Tensor Data Scattering and the Impossibility of Slicing Theorem

Abstract:This paper proposes a standard way to represent sparse tensors. A broad theoretical framework for tensor data scattering methods used in various deep learning frameworks is established. This paper presents a theorem that is very important for performance analysis and accelerator optimization for implementing data scattering. The theorem shows how the impossibility of slicing happens in tensor data scattering. A sparsity measuring formula is provided, which can effectively indicate the storage efficiency of sparse tensor and the possibility of parallelly using it. A Python reference implementation is provided as ancillary material with this arXiv submission.

Machine Learning (cs.LG)

arXiv:2012.01982 [cs.LG]

(or arXiv:2012.01982v3 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2012.01982 Focus to learn more arXiv-issued DOI via DataCite

K. Arai (Ed.): IntelliSys 2021, LNNS 294, 280-290, 2022. Springer

https://doi.org/10.1007/978-3-030-82193-7_18 Focus to learn more DOI(s) linking to related resources

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