Sparsified Preconditioned Conjugate Gradient Solver on GPUs
Bibliographic record
Abstract
Preconditioned iterative sparse linear solvers are memory-efficient for large scientific simulations, but the dependences between iterations introduced by preconditioners limit parallelization. This issue is exacerbated on GPUs, which feature many parallel cores. We propose a sparsified preconditioned conjugate gradient (SPCG) solver that increases parallelism by reducing dependences through sparsification, while preserving convergence behavior. We evaluate the proposed SPCG using both ILU(0) and ILU(K) preconditioners on a wide range of symmetric positive definite (SPD) matrices. The proposed SPCG improves the performance of the iterative phase of SPCG by a geometric mean speedup of 1.23 × and 1.65 × over the non-sparsified PCG using ILU(0) and ILU(K), respectively on an NVIDIA A100 GPU. SPCG also yields geometric mean end-to-end speedups of 1.68 × and 3.73 × over the non-sparsified versions with ILU(0) and ILU(K), respectively, on the same platform.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".