## An Efficient Mixed-Mode Representation of Sparse Tensors

**Authors:** Israt Nisa (Ohio State University), Jiajia Li (Pacific Northwest National Laboratory (PNNL)), Aravind Sukumaran-Rajam (Ohio State University), Prashant Rawat (Ohio State University), Sriram Krishnamoorthy (Pacific Northwest National Laboratory (PNNL)), P. (Saday) Sadayappan (University of Utah)

**Abstract:** The Compressed Sparse Fiber (CSF) representation for sparse tensors is a generalization of the Compressed Sparse Row (CSR) format for sparse matrices. For a tensor with d modes, typical tensor methods such as CANDECOMP/PARAFAC decomposition (CPD) require a sequence of d tensor computations, where efficient memory access with respect to different modes is required for each of them. The straightforward solution is to use d distinct representations of the tensor, with each one being efficient for one of the d computations. However, a d-fold space overhead is often unacceptable in practice, especially with memory-constrained GPUs.

In this paper, we present a mixed-mode tensor representation that partitions the tensor's nonzero elements into disjoint sections, each of which is compressed to create fibers along a different mode. Experimental results demonstrate that better performance can be achieved while utilizing only a small fraction of the space required to keep d distinct CSF representations.

**Presentation:** file

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