High-dimensional coded matrix multiplication
Bibliographic record
Abstract
Coded computation is a framework for providing redundancy in distributed computing systems to make them robust to slower nodes, or stragglers. In [1], the authors propose a coded computation scheme based on maximum distance separable (MDS) codes for computing the product ATB, and this scheme is suitable for the case where one of the matrices is small enough to fit into a single compute node. In this work, we study coded computation involving large matrix multiplication where both matrices are large, and propose a new coded computation scheme, which we call product-coded matrix multiplication. Our analysis reveals interesting insights into which schemes perform best in which regimes. When the number of backup nodes scales sub-linearly in the size of the product, the product-coded scheme achieves the best run-time performance. On the other hand, when the number of backup nodes scales linearly in the size of the product, the MDS-coded scheme achieves the fundamental limit on the run-time performance. Further, we propose a novel application of low-density-parity-check (LDPC) codes to achieve linear-time decoding complexity, thus allowing our proposed solutions to scale gracefully.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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) | 0.003 | 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".