Sparse tensors represent data that is mostly zero or some other compressible fill pattern. Such datasets can be massive, so optimized tensor algebra libraries and compilers have been developed to exploit these patterns to improve performance. Existing systems, however, frequently lack support for parallelism, especially when outputs are sparse or multiple inputs are sparse. We propose WingSpan, a sparse tensor language enabling unrestricted parallel programming. WingSpan supports arbitrary composition of parallel loops and data structures, matching or exceeding the performance of hand-optimized parallel routines on critical kernels such as SpGEMM. We also introduce a dependence theory for the safety of parallel programs involving sparse tensors and structures beyond sparsity.

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