Adaptive Algebraic Reuse of Reordering in Cholesky Factorizations with Dynamic Sparsity Patterns
Bibliographic record
Abstract
We introduce Parth, a fill-reducing ordering method for sparse Cholesky solvers with dynamic sparsity patterns (e.g., in physics simulations with contact or geometry processing with local remeshing). Parth facilitates the selective reuse of fill-reducing orderings when sparsity patterns exhibit temporal coherence, avoiding full symbolic analysis by localizing the effect of dynamic sparsity changes on the ordering vector. We evaluated Parth on over 175,000 linear systems collected from both physics simulations and geometry processing applications, and show that for some of the most challenging physics simulations, it achieves up to 14x reordering runtime speedup, resulting in a 2x speedup in Cholesky solve time—even on top of well-optimized solvers such as Apple Accelerate and Intel MKL.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".