Scheduling Sparse Tensor Contractions with Novel Intermediate Representations

Efficient code generation and performance optimization for sparse tensor algebra are critical in applications such as quantum computing, physical simulations, computational chemistry, and machine learning. While modern sparse tensor compilers automate code generation for tensor algebra, they often fall short of producing optimal code for sparse tensor contractions due to limitations in scheduling directives and intermediate representations (IRs) that enable advanced loop transformations. This dissertation introduces novel scheduling techniques and generalized loop restructuring transformations specifically leveraging kernel fission and fusion to significantly reduce time complexity and memory footprint. Additionally, we propose new IRs that eliminate the need for explicit tensor data layout changes, further optimizing memory efficiency. By materializing these enriched IRs, this work expands the searchable schedule space available to sparse compilers. Experimental evaluations demonstrate that these techniques yield substantial performance gains over state-of-the-art compilers across diverse real-world workloads. Finally, we present an auto-scheduler designed to navigate this expanded design space and automatically select optimal execution strategies for sparse tensor contractions.