Active learning meets fractal decision boundaries: a cautionary tale from the Sitnikov three-body problem
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Bibliographic record
Abstract
Chaotic systems such as the gravitational N-body problem are ubiquitous in astronomy. Machine learning (ML) is increasingly deployed to predict the evolution of such systems, e.g. with the goal of speeding up simulations. Strategies such as active Learning (AL) are a natural choice to optimize ML training. Here we showcase an AL failure when predicting the stability of the Sitnikov three-body problem, the simplest case of N-body problem displaying chaotic behavior. We link this failure to the fractal nature of our classification problem's decision boundary. This is a potential pitfall in optimizing large sets of N-body simulations via AL in the context of star cluster physics, galactic dynamics, or cosmology.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.000 | 0.002 |
| 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