Toward Scalable Tucker Decomposition: Skew-Aware Multi-Level Partitioning with GPU-Storage Co-Processing

Given billion- scale sparse tensors with highly skewed distributions, how can Tucker decomposition be performed both scalably and robustly?Tucker decomposition is a principled method for capturing latent structures and cross- mode interactions across diverse domains. However, its applicability to billion- scale tensors is fundamentally constrained by two major challenges: (1) the intermediate data explosion, and (2) severe data skew, which lead to memory exhaustion. Existing CPU-, GPU-, and distributed- based approaches alleviate runtime only in limited scenarios but fail to scale under skewed, billion- scale tensors. To overcome these limitations, we present the GSP- Tucker framework, a scalable and robust Tucker decomposition system. GSP- Tucker integrates four key components: (1) skew- aware multi- level partitioning that adaptively splits dense tensor regions into balanced sub- tensors, (2) GPU acceleration for high- throughput factor updates, (3) a multi- level asynchronous I/O pipeline that overlaps storage- to- GPU data transfers with GPU kernels to maximize bandwidth utilization, and (4) a tiling streaming technique that reduces main memory requirements. This unified design of partitioning, data representation, computation, and I/O eliminates intermediate data explosion and mitigates skew- induced failures. Extensive experiments with real datasets, including billion- scale sparse tensors, demonstrate that GSP- Tucker is (1) scalable, efficiently processing tensors with billions of nonzeros; (2) robust, handling highly skewed distributions that prior methods cannot process; and (3) efficient, fully utilizing GPUs and high- bandwidth storage.