3-D Projected <i>L</i> 1 inversion of gravity data using truncated unbiased predictive risk estimator for regularization parameter estimation
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Bibliographic record
Abstract
Summary Sparse inversion of gravity data based on L1-norm regularization is discussed. An iteratively reweighted least squares algorithm is used to solve the problem. At each iteration the solution of a linear system of equations and the determination of a suitable regularization parameter are considered. The LSQR iteration is used to project the system of equations onto a smaller subspace that inherits the ill-conditioning of the full space problem. We show that the gravity kernel is only mildly to moderately ill-conditioned. Thus, while the dominant spectrum of the projected problem accurately approximates the dominant spectrum of the full space problem, the entire spectrum of the projected problem inherits the ill-conditioning of the full problem. Consequently, determining the regularization parameter based on the entire spectrum of the projected problem necessarily over compensates for the non-dominant portion of the spectrum and leads to inaccurate approximations for the full-space solution. In contrast, finding the regularization parameter using a truncated singular space of the projected operator is efficient and effective. Simulations for synthetic examples with noise demonstrate the approach using the method of unbiased predictive risk estimation for the truncated projected spectrum. The method is used on gravity data from the Mobrun ore body, northeast of Noranda, Quebec, Canada. The 3-D reconstructed model is in agreement with known drill-hole information.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 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