Zan‐Bo Zhang

Qi Zhang, Zhengan Yao, Zhenglu Jiang et al.

Sparse Matrix-Vector Multiplication (SpMV) is the cornerstone in many iterative workloads, including large-scale graph analytics and sparse iterative solvers. Accelerating SpMV on real-world graphs remains challenging due to highly irregular sparsity patterns. In this paper, we propose MERBIT, a GPU SpMV method designed for repeated SpMV on irregular, graph-like sparse matrices, with PageRank as a representative motivating workload. MERBIT combines two key ideas from existing GPU SpMV methods. At the global level, it uses merge-path partitioning to balance work over nonzeros and row boundaries. At the local level, it encodes each merge-path segment using a compact bit-field descriptor. MERBIT improves workload balance and promotes coalesced memory access for both matrix loading and output writes; moreover, three optimization strategies are incorporated to further enhance performance. Experiments on 50 large irregular datasets demonstrate that MERBIT outperforms competitive baselines, including cuSPARSE, Ginkgo, and academic approaches, achieving average speedups of 1.27 and 1.25 over cuSPARSE COO in single and double precision, respectively.

Aixiang, Chen, Jinting Zhang et al.

The fluctuation effect of gradient expectation and variance caused by parameter update between consecutive iterations is neglected or confusing by current mainstream gradient optimization algorithms.Using this fluctuation effect, combined with the stratified sampling strategy, this paper designs a novel \underline{M}emory \underline{S}tochastic s\underline{T}ratified Gradient Descend(\underline{MST}GD) algorithm with an exponential convergence rate. Specifically, MSTGD uses two strategies for variance reduction: the first strategy is to perform variance reduction according to the proportion p of used historical gradient, which is estimated from the mean and variance of sample gradients before and after iteration, and the other strategy is stratified sampling by category. The statistic \ $\bar{G}_{mst}$\ designed under these two strategies can be adaptively unbiased, and its variance decays at a geometric rate. This enables MSTGD based on $\bar{G}_{mst}$ to obtain an exponential convergence rate of the form $λ^{2(k-k_0)}$($λ\in (0,1)$,k is the number of iteration steps,$λ$ is a variable related to proportion p).Unlike most other algorithms that claim to achieve an exponential convergence rate, the convergence rate is independent of parameters such as dataset size N, batch size n, etc., and can be achieved at a constant step size.Theoretical and experimental results show the effectiveness of MSTGD