Graph Models and their Efficient Implementation for Sparse Jacobian Matrix Determination.
Bibliographic record
Abstract
Large-scale combinatorial scientific computing problems arising in sparse or otherwise structured matrix computation are often expressed using an appropriate graph model, and sometimes the same problem can be given in more than one graph model with similar asymptotic computational complexity. The relative merits of different graph models for the same problem can then be expressed in terms of factors such as generality of the model or ease of computer implementation. We review contemporary graph formulations for large-scale sparse Jacobian matrix determination problem (JMDP) and suggest the pattern graph as a unifying framework for methods that exploit sparsity by matrix compression: row compression, column compression, or a combination of the two. We argue that with the pattern graph, which is structurally close to the underlying matrix, exploitable sparsity and structures in the matrix are unlikely to be lost in ''translation'' from a matrix problem to a graph problem. From an algorithmic view point the structural correspondence between the matrix and its graph, as we demonstrate in this paper, leads to a better exposition of the compression heuristics and their efficient computer realization. Array-based data structures are suggested as the basic building-blocks for the efficient implementation of relevant graph algorithms. Results from the numerical testing of a subset of implemented algorithms on a suite of test instances drawn from the standard test matrix collection are presented.
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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 | 0.001 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 0.003 |
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".