Masha Sosonkina

Eugene Vecharynski, Yousef Saad, Masha Sosonkina

Prior to the parallel solution of a large linear system, it is required to perform a partitioning of its equations/unknowns. Standard partitioning algorithms are designed using the considerations of the efficiency of the parallel matrix-vector multiplication, and typically disregard the information on the coefficients of the matrix. This information, however, may have a significant impact on the quality of the preconditioning procedure used within the chosen iterative scheme. In the present paper, we suggest a spectral partitioning algorithm, which takes into account the information on the matrix coefficients and constructs partitions with respect to the objective of enhancing the quality of the nonoverlapping additive Schwarz (block Jacobi) preconditioning for symmetric positive definite linear systems. For a set of test problems with large variations in magnitudes of matrix coefficients, our numerical experiments demonstrate a noticeable improvement in the convergence of the resulting solution scheme when using the new partitioning approach.

Evan Coleman, Masha Sosonkina

Asynchronous iterative methods tolerate straggling processors by allowing workers to proceed with stale data, but at a cost: the iterates become inconsistent, potentially degrading convergence. We investigate whether convergence accelerators such as Anderson acceleration compensate for this degradation. We experimentally study three fixed-point iterations: the Jacobi method for sparse linear systems, value iteration for the Bellman equation, and the Hartree--Fock self-consistent field (SCF) iteration. The experiments are conducted using a high-performance execution framework Ray, which abstracts the complexity of distributed systems and enables code parallelization and fault injection with minimal changes. We establish two main results. First, straggler tolerance is universal: asynchronous execution provides wall-clock speedups of $2.9\times$ (Jacobi), $7.7\times$ (VI), and $16.9\times$ (SCF) over synchronous execution with a 100\,ms-delayed worker, independent of whether acceleration is used. Second, Anderson acceleration's effectiveness under asynchrony depends on where staleness enters the computation. We identify two staleness mechanisms: iterate-level corruption, where stale worker returns directly overwrite portions of the accelerated iterate (as in block Jacobi), and evaluation-level perturbation, where staleness acts as a bounded perturbation to the fixed-point map evaluation (as in VI and SCF). Anderson acceleration fails categorically under the first mechanism but retains its benefits under the second, consistent with the perturbation analysis of Toth et al.\ (2017). This distinction, rather than the contraction norm or smoothness of the map, is the primary determinant of whether acceleration survives asynchronous execution.

Jiawei Chen, Lusi Li, Daniel Takabi et al.

Heterogeneous Graph Neural Networks (HGNNs) excel in modeling complex, multi-typed relationships across diverse domains, yet their vulnerability to backdoor attacks remains unexplored. To address this gap, we conduct the first investigation into the susceptibility of HGNNs to existing graph backdoor attacks, revealing three critical issues: (1) high attack budget required for effective backdoor injection, (2) inefficient and unreliable backdoor activation, and (3) inaccurate attack effectiveness evaluation. To tackle these issues, we propose the Heterogeneous Graph Backdoor Attack (HGBA), the first backdoor attack specifically designed for HGNNs, introducing a novel relation-based trigger mechanism that establishes specific connections between a strategically selected trigger node and poisoned nodes via the backdoor metapath. HGBA achieves efficient and stealthy backdoor injection with minimal structural modifications and supports easy backdoor activation through two flexible strategies: Self-Node Attack and Indiscriminate Attack. Additionally, we improve the ASR measurement protocol, enabling a more accurate assessment of attack effectiveness. Extensive experiments demonstrate that HGBA far surpasses multiple state-of-the-art graph backdoor attacks in black-box settings, efficiently attacking HGNNs with low attack budgets. Ablation studies show that the strength of HBGA benefits from our trigger node selection method and backdoor metapath selection strategy. In addition, HGBA shows superior robustness against node feature perturbations and multiple types of existing graph backdoor defense mechanisms. Finally, extension experiments demonstrate that the relation-based trigger mechanism can effectively extend to tasks in homogeneous graph scenarios, thereby posing severe threats to broader security-critical domains.

Bruno Carpentieri, Jia Liao, Masha Sosonkina et al.

The paper describes an improved parallel MPI-based implementation of VBARMS, a variable block variant of the pARMS preconditioner proposed by Li,~Saad and Sosonkina [NLAA, 2003] for solving general nonsymmetric linear systems. The parallel VBARMS solver can detect automatically exact or approximate dense structures in the linear system, and exploits this information to achieve improved reliability and increased throughput during the factorization. A novel graph compression algorithm is discussed that finds these approximate dense blocks structures and requires only one simple to use parameter. A complete study of the numerical and parallel performance of parallel VBARMS is presented for the analysis of large turbulent Navier-Stokes equations on a suite of three-dimensional test cases.