Tensor algebra compilation with workspaces

This paper shows how to extend sparse tensor algebra compilers to introduce temporary tensors called workspaces to avoid inefficient sparse data structures accesses. We develop an intermediate representation (IR) for tensor operations called concrete index notation that specifies when sub-computations occur and where they are stored. We then describe the workspace transformation in this IR, how to programmatically invoke it, and how the IR is compiled to sparse code. Finally, we show how the transformation can be used to optimize sparse tensor kernels, including sparse matrix multiplication, sparse tensor addition, and the matricized tensor times Khatri-Rao product (MTTKRP).