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This paper proposes a standard way to represent sparse tensors. A broadtheoretical framework for tensor data scattering methods used in various deeplearning frameworks is established. This paper presents a theorem that is veryimportant for performance analysis and accelerator optimization forimplementing data scattering. The theorem shows how the impossibility ofslicing happens in tenser data scattering. A sparsity measuring formula isprovided, which can effectively indicate the storage efficiency of sparsetensor and the possibility of parallelly using it. The source code, includingCUDA code, is provided in a related open-source project.

Tensor Data Scattering and the Impossibility of Slicing Theorem