Comparative Theory for Graph Polynomials (Dagstuhl Seminar 19401)
Bibliographic record
Abstract
This report documents the programme and outcomes of Dagstuhl Seminar 19401 ``Comparative Theory for Graph Polynomials''. The study of graph polynomials has become increasingly active, with new applications and new graph polynomials being discovered each year. The genera of graph polynomials are diverse, and their interconnections are rich. Experts in the field are finding that proof techniques and results established in one area can be successfully extended to others. From this a general theory is emerging that encapsulates the deeper interconnections between families of graph polynomials and the various techniques, computational approaches, and methodologies applied to them. The overarching aim of this Seminar was to exploit commonalities among polynomial invariants of graphs, matroids, and related combinatorial structures. Model-theoretic, computational and other methods were used in order to initiate a comparative theory that collects the current state of knowledge into a more cohesive and powerful framework.
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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 | 0.003 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.013 | 0.002 |
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".