<i>SVDdiagnostic</i>, a program to diagnose numerical conditioning of Rietveld refinements
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Bibliographic record
Abstract
Singular value decomposition (SVD) of the matrix of normal equations is used here both passively to assess numerical stability, and actively to troubleshoot problem refinements, singular or not. Such systems can then either be cured by rank reduction or solved with arbitrary-precision arithmetic carrying a number of digits known to be sufficient. SVD analysis provides objective information about such required rank reduction or number of digits. Pre-conditioning of the normal matrix is seen to decrease its condition number by many orders of magnitude in actual cases, illustrating its great practical usefulness. The methods and tools developed here have general applicability to diagnose problems with least squares, in particular ill-conditioned Rietveld refinements. Crystal-chemical and standard refinements described in the work by Mercier et al. [ J. Appl. Cryst. (2006), 39 , 369–375] are shown to have similar numerical stability. The program SVDdiagnostic is freely available at http://www.tothcanada.com.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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