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Automated code generation and performance optimizations for sparse tensoralgebra are cardinal since they have become essential in many real-worldapplications like quantum computing, physics, chemistry, and machine learning.General sparse tensor algebra compilers are not always versatile enough togenerate asymptotically optimal code for sparse tensor contractions. This papershows how to optimize and generate asymptotically better schedules for complextensor expressions using kernel fission and fusion. We present a generalizedloop transformation to achieve loop nesting for minimized memory footprint andreduced asymptotic complexity.  Furthermore, we present an auto-scheduler that uses a partially orderedset-based cost model that uses both time and auxiliary memory complexities inits pruning stages. In addition, we highlight the use of SMT solvers in sparseauto-schedulers to prune the Pareto frontier of schedules to the smallestnumber of possible schedules with user-defined constraints available at compiletime. Finally, we show that our auto-scheduler can select asymptotically betterschedules that use our compiler transformation to generate optimized code. Ourresults show that the auto-scheduler achieves orders of magnitude speedupcompared to the TACO-generated code for several real-world tensor algebracomputations on different real-world inputs.

SparseAuto: An Auto-Scheduler for Sparse Tensor Computations Using Recursive Loop Nest Restructuring