Tensor algebra is essential for data-intensive workloads in various computational domains. Computational scientists face a trade-off between the specialization degree provided by dense tensor algebra and the algorithmic efficiency that leverages the structure provided by sparse tensors. This paper presents StructTensor, a framework that symbolically computes structure at compilation time. This is enabled by Structured Tensor Unified Representation (STUR), an intermediate language that can capture tensor computations as well as their sparsity and redundancy structures. Through a mathematical view of lossless tensor computations, we show that our symbolic structure computation and the related optimizations are sound. Finally, for different tensor computation workloads and structures, we experimentally show how capturing the symbolic structure can result in outperforming state-of-the-art frameworks for both dense and sparse tensor algebra.

@article{paperbot1842,
  title = {Compiling Structured Tensor Algebra},
  author = {Mahdi Ghorbani and Mathieu Huot and Shideh Hashemian and Amir Shaikhha},
  journal = {Proceedings of the ACM on Programming Languages},
  volume = {7},
  number = {OOPSLA2},
  year = {2023},
  doi = {10.1145/3622804}
}