ScalFrag: Efficient Tiled-MTTKRP with Adaptive Launching on GPUs

Tensor decomposition, a pivotal technique in mining underlying patterns from voluminous and high-dimensional sparse datasets, plays a crucial role in unraveling latent structures within complex data. Among the various methods employed for tensor decomposition, Canonical Polyadic Decomposition (CPD) stands out as a prominent choice, widely embraced across numerous scientific disciplines and practical applications due to its effectiveness in capturing multi-linear relationships. However, the computational efficacy of CPD is significantly hampered by the Matricized Tensor Times Khatri-Rao Product (MTTKRP) operation, which constitutes its primary bottleneck. While of-floading the MTTKRP computation onto Graphics Processing Units (GPUs) has emerged as a prevalent strategy to leverage their parallel processing capabilities for enhancing performance, the inherent sparsity and irregular data access patterns intrinsic to these operations introduce new complexities. Addressing this challenge, we introduce an innovative method-ology ScalFrag designed to accelerate sparse MTTKRP computations on GPU platforms. A key insight underlying our approach is the recognition that the optimal kernel launch configuration-a critical factor influencing GPU performance-varies consider-ably depending on the unique characteristics of the input tensor. We devise a dynamic kernel launch configuration selection mech-anism to tackle this variability. This novel strategy autonomously identifies and applies the most advantageous launch setup tai-lored to each input tensor, optimizing computational efficiency. Additionally, we present a stream-based algorithm for sparse MTTKRP, further overlapping data access time. By leveraging streaming architectures, our algorithm significantly improves data access efficiency, mitigating the bottlenecks associated with the irregularities of sparse tensor patterns. The experimental results show that ScalFrag performs better than the SOTA library ParTI, and is able to find more suitable kernel launch parameter configurations in a short time.