The Art of Sparsity: Mastering High-Dimensional Tensor Storage

Sparse tensors are prevalent in many applications. While numerous approaches have emerged to optimize the organization of sparse tensors, with the goal of reducing storage requirements and enhancing access performance, a comprehensive examination of the associated tune and space complexities has been notably lacking. This study bridges this gap by conducting both theoretical and empirical investigations into various strategies for storing sparse tensors. Our major findings are as follows: (1) Linear address -based organization provides the best balance between storage size and access time; (2) Sparse high-dimensional tensor data can be transformed into lower-dimensional tensors, facilitating efficient storage and access; (3) In the absence of dimension transformation, tree-structured organizations offer compelling performance in low-dimensional tensors and exceptional performance in high-dimensional tensors.