An Iterative Minimization Formulation for Saddle Point Search
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Bibliographic record
Abstract
This paper proposes and analyzes an iterative minimization formulation for searching index-1 saddle points of an energy function. We give a general and rigorous description of eigenvector-following methodology in this iterative scheme by considering an auxiliary optimization problem at each iteration in which the new objective function is locally defined near the current guess. We prove that this scheme has a quadratic local convergence rate in terms of number of iterations, in comparison to the linear rate of the gentlest ascent dynamics [W. E and X. Zhou, Nonlinearity, 24 (2011), pp. 1831--1842] and many other existing methods. We also propose the generalization of the new methodology for saddle points of higher index and for constrained energy functions on the manifold. Preliminary numerical results on the nature of this iterative minimization formulation are presented.
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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