Proposed Computational Algorithms for Neural Operator Stability
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Bibliographic record
Abstract
This work explores preliminary computational approaches to neuraloperator conditioning analysis, where the complexity of exact analysisrequiring O(d2m + min{d,m}3) operations presents barriers to practicalstability assessment [3, 10]. We propose an exploratory frameworkincluding the Spectral Conditioning Monitor (SCM) and BlockwiseInversion Algorithm (BIA), employing stochastic approximationtechniques inspired by randomized matrix algorithms [4]. Preliminaryexperiments suggest potential complexity improvements from establishediterative methods, though theoretical advances remain unvalidatedon realistic problem scales and require extensive empirical investigation[6]. These ideas may motivate future research in algorithmicapproaches to neural operator stability analysis while highlighting substantialvalidation requirements for practical deployment.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.003 | 0.000 |
| Scholarly communication | 0.002 | 0.000 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
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