The MOMMS Family of Matrix Multiplication Algorithms

Abstract

As the ratio between the rate of computation and rate with which data can be retrieved from various layers of memory continues to deteriorate, a question arises: Will the current best algorithms for computing matrix-matrix multiplication on future CPUs continue to be (near) optimal?is paper provides compelling analytical and empirical evidence that the answer is "no". e analytical results guide us to a new family of algorithms of which the current state-of-the-art "Goto's algorithm" is but one member. e empirical results, on architectures that were custom built to reduce the amount of bandwidth to main memory, show that under different circumstances, different and particular members of the family become more superior.us, this family will likely start playing a prominent role going forward.

A BLIS-like matrix multiplication for machine learning in the RISC-V ISA-based GAP8 processor

“…The family of BLIS-like algorithms for gemm comprises 6 variants which are obtained by re-ordering the loops of the algorithm in Fig. 1 (though BLIS only implements one: the baseline algorithm) [18][19][20]. We next briefly discuss the main features of these alternative realizations:…”