The Census-Stub Graph Invariant Descriptor
Why this work is in the frame
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Bibliographic record
Abstract
An 'invariant descriptor' captures meaningful structural features of networks, useful where traditional visualizations, like node-link views, face challenges like the 'hairball phenomenon' (inscrutable overlap of points and lines). Designing invariant descriptors involves balancing abstraction and information retention, as richer data summaries demand more storage and computational resources. Building on prior work, chiefly the BMatrix-a matrix descriptor visualized as the invariant 'network portrait' heatmap-we introduce BFS-Census, a new algorithm computing our Census data structures: Census-Node, Census-Edge, and Census-Stub. Our experiments show Census-Stub, which focuses on 'stubs' (half-edges), has orders of magnitude greater discerning power (ability to tell non-isomorphic graphs apart) than any other descriptor in this study, without a difficult trade-off: the substantial increase in resolution doesn't come at a commensurate cost in storage space or computation power. We also present new visualizations-our Hop-Census polylines and Census-Census trajectories-and evaluate them using real-world graphs, including a sensitivity analysis that shows graph topology change maps to visual Census change. Availability: Our Supplemental materials are available at osf.io/nmzra.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it