Bipartite grammar-based representations of large sparse binary matrices: Framework and transforms
Bibliographic record
Abstract
In this paper, we introduce a new concept called context-free bipartite grammar (CFBG) and present a framework wherein large sparse binary matrices can be compactly represented by CFBGs. Similar to the traditional concept of context-free grammar (CFG), a CFBG consists of a set of production rules. Unlike CFGs, however, the right member of each production rule in a CFBG is a labeled bipartite graph with each edge labeled either as a variable or terminal symbol. Given a CFBG, start with its initial variable and repeatedly expand each variable labeled edge by first deleting that edge and then inserting in some manner all edges contained in the right member of that variable. The CFBG is admissible if the edge expansion process leads to a unique bipartite graph containing only terminal symbol labeled edges, in which case the CFBG is said to represent the matrix equal to the biadjacency matrix of the unique graph. Two bipartite grammar transforms, a sequential D-neighborhood pairing transform and an iterative pairing transform (IPT), are further presented to convert any binary matrix into a CFBG representing it. Experiments show that compared with popular sparse matrix storage methods such as compressed row storage and quadtree, CFBGs obtained by IPT can reduce the storage of sparse matrices significantly (by a factor of as much as 68).
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| 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".