On the Relationship Between the Enforced Convergence Criterion and the Asymptotically Optimal Laguerre Pole
Bibliographic record
Abstract
When approximating dynamic systems with Laguerre basis functions (LBFs) it is important to tune the Laguerre pole such that the expansion can be both parsimonious and accurate. Expressing the sum of squared errors (SSE) as a function of the Laguerre pole leads to an objective function that has many local minima and therefore cannot be optimized directly. Two alternative methods have been proposed in the literature: an asymptotically optimal method, and the enforced convergence criterion (ECC). In this paper, a generalization of the ECC will be investigated such that in the limit minimizing this generalized ECC and computing the asymptotically optimal solution lead to the same Laguerre pole. Moreover, it will be proved that these generalized ECCs are quasiconvex functions which means they can be efficiently minimized using numerical optimization techniques. The concept of operator quasiconvexity is investigated and used to prove quasiconvexity of the ECC.
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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 | 0.005 | 0.028 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".