Conquering the pre-computation in two-dimensional harmonic polynomial\n transforms
Bibliographic record
Abstract
We describe a skeletonization of the spherical harmonic connection problem\nthat reduces the storage and pre-computation to superoptimal complexities at\nthe cost of increasing the execution time by the modest multiplicative factor\nof $\\mathcal{O}(\\log n)$. One advantage of accelerating the spherical harmonic\nconnection problem over accelerating synthesis and analysis is that\nneighbouring layers (in steps of two) may be expanded in eachother's bases. The\nproposed skeletonization maximizes this interconnectivity by overlaying a\ndyadic partitioning on the connection problem. We derive the symmetric-definite\nbanded generalized eigenvalue problem required to accelerate spherical harmonic\ntransforms. We also include a full analysis of the weighted normalized Jacobi\nconnection problem with applications to fast harmonic polynomial transforms on\nthe disk, triangle, rectangle, deltoid, wedge, and any other geometry with a\nbivariate analogue of Jacobi polynomials.\n
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".