Multiplication of Sparse Matrices and their Transpose Using Compressed Sparse Diagonals
Bibliographic record
Abstract
Matrix-matrix multiplication is one of the most important kernel in linear algebra operations with a multitude of applications in scientific and engineering computing. Sparse matrix computation on modern High-performance Computing (HPC) architecture presents challenges such as load balancing, data locality optimization, and computational scalability. Data structures to store sparse matrices are designed to minimize overhead information as well as to optimize the operations count and memory access. In this study, we present a new data structure, “compressed sparse diagonal” (CSD), to efficiently store and compute with general sparse matrices. The CSD builds upon the previously developed diagonal storage - an orientation-independent uniform scheme to compute with “structured” matrices [1]. Compared with the widely used compressed sparse row/column (CSR/CSC), the CSD scheme avoids explicit transposition operation when multiplying a matrix with its transpose. The results from preliminary numerical experiments with the aforementioned types of matrices demonstrate the CSD scheme's effectiveness in matrix-transposed matrix multiplication.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 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) | 0.004 | 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".