  Tensor algebra is a crucial component for data-intensive workloads such as
machine learning and scientific computing. As the complexity of data grows,
scientists often encounter a dilemma between the highly specialized dense
tensor algebra and efficient structure-aware algorithms provided by sparse
tensor algebra. In this paper, we introduce DASTAC, a framework to propagate
the tensors's captured high-level structure down to low-level code generation
by incorporating techniques such as automatic data layout compression,
polyhedral analysis, and affine code generation. Our methodology reduces memory
footprint by automatically detecting the best data layout, heavily benefits
from polyhedral optimizations, leverages further optimizations, and enables
parallelization through MLIR. Through extensive experimentation, we show that
DASTAC achieves 1 to 2 orders of magnitude speedup over TACO, a
state-of-the-art sparse tensor compiler, and StructTensor, a state-of-the-art
structured tensor algebra compiler, with a significantly lower memory
footprint.
