Abstract: Data movement between processor and memory hierarchy is a fundamental bottleneck that limits the performance of many applications on modern computer architectures. Tiling and loop permutation are key techniques for improving data locality. However, selecting effective tile-sizes and loop permutations is particularly challenging for tensor contractions due to the large number of loops. Even state-of-the-art compilers usually produce sub-optimal tile-sizes and loop permutations, as they rely on naïve cost models. In this paper, we provide an analytical model based approach to multi-level tile size optimization and permutation selection for tensor contractions. Our experimental results show that this approach achieves comparable or better performance than state-of-the-art frameworks and libraries for tensor contractions.
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