A low-latency and energy-efficient tensor algebra accelerator design must optimize how data movement and operations are scheduled (i.e., mapped) in the accelerator architecture. A key mapping optimization is fusion, meaning holding data on-chip between computation steps in the workload, which has been shown to reduce energy and latency by reducing expensive off-chip data movement. However, the optimal fusion choice depends on the workload and workload shape, and a mapper, which searches for the optimal mapping, can improve energy and latency significantly. However, prior mappers cannot find optimal mappings with fusion (i.e., fused mappings) in a feasible runtime because the number of fused mappings to search increases exponentially with the number of computation steps in the workload. In this paper, we introduce the Fast and Fusiest Mapper (FFM), a mapper to quickly find optimal mappings in a comprehensive fused mapspace for tensor algebra workloads. FFM shrinks the search space by pruning subsets of mappings (i.e., partial mappings) that are shown to never be a part of optimal mappings, quickly eliminating all suboptimal mappings containing those partial mappings. Then FFM joins partial mappings to construct optimal fused mappings. Using FFM, we demonstrate an energy-delay-product (EDP) reduction by up to $1.8\times$ compared to TransFusion, a state-of-the-art accelerator with hand-optimized fusion. Moreover, we show that FFM finds mappings orders of magnitude faster ($>10,000\times$) than prior automated mappers TileFlow and SET, and given the same runtime, reduces EDP by $>2\times$.

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