Sorting Algorithms on Manifolds
Bibliographic record
Abstract
Lipnowski and Page describe a quadratic-time algorithm to build a grid of approximately evenly-spaced points on certain locally-symmetric manifolds M .A modification to this algorithm using a k-d tree on some map M → R k seems likely to run faster in many cases, in particular requiring fewer distance computations.Empirical results from building a fine grid on SL 2 (Z)\H suggest that it indeed performs better and might even offer better probabilistic asymptotic time complexity in interesting examples.also thank the inefficiency and compartmentalization of the McGill bureaucracy for making it possible for me to write the previous sentence without putting my degree at risk.More seriously, thank you to Profs.Mike Lipnowski and Henri Darmon for the supervision and support throughout my degree; to Elia Afanasiev, for instantly answering all my texts for help with the Rust type system; and to Marcel Goh, who worked with me on an undergraduate summer research project about these algorithms, even if it was his fault we wrote all the code in OCaml
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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) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.005 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.021 | 0.004 |
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".